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2. 42 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 VII Storage Ring Object Parameters of the global variable of class xRing and results of calculation of the Ring main parameters are collected in the Main Menu item Ring that includes submenu items Lattice Structure and Parameters 1 Parameters of Ring Window Ring Parameters contains the TabSheets Ion kind Lattice Mean params RF system Reference point 1 1 Setting of ion kind parameters The corresponding visual form Fig 1 has 6 TabSheets containing input and output parameters of the storage ring Ring Parameters Ioj x Ring Parameters lol x Ton kind Lattice Mean params RF system Reference point Barrier bucket lon kind Taice Mean params RF system Reference paint Barrier bucket Reference Energy C Gamma Circumference 222 11 m 1 794416 0 83032 Gamma transition 15 74 gt C Imagenary 40 Mev u v Horizontal Vertical 183 2 Gee Tunes aa 22 Beta Kinetic Momentum l Chromaticity 45 65 Atomic mass 132 A Acceptance 0 0002 FE 5 ial m rad Charge number 50 Z Life time Decay JIE sec Longitudinal Acceptance 0 02 Fig 1 Ring Parameters visual form TabSheet lon kind amp Lttice This example corresponds to the totally stripped gold ions at kinetic energy 100 GeV u To set the beam energy one can use any of t
3. Fig 6 ECOOL Electron beam TabSheet Uniform Cylinder amp Gaussian Cylinder 2 2 Gaussian cylinder If DC electron beam with elliptic cross section and Gaussian distribution in the transverse plane is chosen user must use TabSheet Gaussian cylinder Fig 6 to set parameters Horizontal rms dimension Vertical rms dimension and Linear electron density Beam current will be automatically calculated 2 3 Hollow beam If hollow beam is chosen user must use TabSheet Hollow beam Fig 7 to set parameters Hole radius Density in the hole Beam radius Density in circle Beam current will be automatically calculated To take into account space charge effect inside electron beam user must Check Beam current ECOOL Electron beam IOl xj Hole radius cer Density in the hole em 3 91000000 Beam radius em 2 Density in circle fera 3 3 387 Beam current A 0 2387854333 W Space Charge Fig 7 ECOOL Electron beam TabSheets Hollow beam and Parabolic 68 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 2 4 Parabolic beam If parabolic beam is chosen user must use TabSheet Parabolic beam Fig 8 to set parameters Radius Current V_tr gradient Current density will be automatically calculated ECOOL Electron beam lO xi Radius cm fo 263 Current 4 0 1 VO tr gradient 1 3 fo Central density 1 m 3 2 016853659613 Fig 8 ECOOL Electron beam TabSheets Pa
4. If the option Coulomb logarithm is chosen the integral is ru by expression expl D u v z In 1 z dez z aT where the value of 2Lc is introduced in the edit window Coulomb logarithm It was shown that in the last case the 2D integral over 44 v variables can be reduced to 1D integral and the Martini model coincides with the model described in the article J D Bjorken S K Mtingwa Intrabeam scattering Particle Accelerators Vol 13 p 115 1983 3 Other models of IBS The Bjorken Mtingwa model is based on plasma physics approach The growth rates are calculated as combinations of collision integral for three degrees of freedom This model is realized as evaluation of 1D integral at infinite upper limit To calculate the growth rates one needs to introduce Coulomb logarithm value it should be estimated from the beam density before the calculation in Betacool usual value is about 20 upper limit of the integral and number of the integration steps by rectangular method Fig 4 The two last values have to be chosen manually by a few subsequent calculations of the rates The Bjorken Mtingwa model is accurate within the Coulomb logarithm accuracy Effects Intrabeam Scattering _ Oj x Martini Je wei Gas relaxation Byjorken IBS model Martini ol eee Upper limit E Coulomb Log 40 number of steps f 000 Fig 4 The visual form for choice of the IBS model Bjorken TabSheet 56 BETACOOL User manua
5. Particle Humber Footprint of invarinats Fig 9 Control of the evolution plots Step 8 The starting of RMS Dynamics simulation To start simulation one needs to choose Menultem TaskIRMS Dynamics Fig 10 Task RMS Dynamics Y Oj xj Integration step Initial 0 0001 sec Maximum 0 04 EE sec Step fitting Step multilpier fe Max growth 50 2 Find fbetacool exe Fig 10 RMS dynamics parameters It s necessary to choose Initial and Maximum step in seconds on this Form Integral step determinates the initial step of simulation in time Maximum step sets limit for the upper step growing Changing of the step 1s defined by Step multiplier and Max growth where Step multiplier is the value of step increment Max growth is the max difference between previous and next values of calculated beam r m s parameters Push Button Open to begin simulation 25 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 IV Model Beam Algorithm Introduction Model Beam MB algorithm was developed on the base of SIMCOOL code which was developed by Novosibirsk group This algorithm uses a few thousands of test particles with arbitrary distribution The action from IBS on the each test particle 1s calculated from the current distribution of test particles This algorithm can reach a good accuracy when the distribution of test particle is closed to Gaussian Some modification of
6. T Life time Decay Scattering on Rest Gas Acceptance F Internal Target Separatriz length Generate model particles on losses with distribution Real Fig 11 Form Effect Particle losses Step 8 Output results Results of the beam dynamics simulation are output in the following main Forms Beam Distribution Beam Evolution Beam Real space Form Beam Distribution Fig 12 includes the following TabSheets for results Coordinate dependence of particle number in percent on momentum deviation and coordinate normalized on corresponding rms parameter and particle number Profile real particle distribution for every coordinate analogue of previous plot averaged on betatron or synchrotron oscillations Invariant particle number in percent which occupies corresponding emittance invariants and Evolution 3D plot for saving of Coordinate or Invariants evolutions in time TabSheet Control Fig 14 provides settings for plot on all TabSheets listed above As on every plot window user can choose which plots he wants to be redrawn on line More detailed description is given in Beam Manual Beam Distribution Sele Beam Distribution Seles KZ cu Evolution Coordinate Profile Coord x Sigma 8 Coord y Divisions 400 lt E ma normalized or Protile_x C current initial 3 T E a E m Coord p e C Profile y m Evolution Profile_p Slices 40 if invar
7. 2 square barriers stationary bucket and moving bucket Position and duration of BB are defined in the unit of circumference in the range 0 5 lt s lt 0 5 amplitude of buckets are given in volts Ring Barrier Bucket aj x Bucket model Momentum Beam profile Voltage 0 2bariers Analytic Barrier height do p 0 0005186026585 Amplitude kM RAMS amplitude dpp 0 0007307712931 RF duration fo Bucket length m 220743425 Gap duration 0 2 Synchrotron period sec 2766056943 Stationary Bucket File Find chandra bar Moving Bucket File Find feharidra0 mov IBS normalise Longitudinal profile divisions fao on longitudinal divisions e Normalize Potential Integral on barrier distribution Fig 4 Parameters of BB 2 barriers Options 2 barriers is used for the simple model of two barriers which has as analytical as numerical approximation Analytic solution was done for the region between barriers only If the particle momentum spread becomes larger than the barrier height than the particle does not move in the longitudinal direction The numerical solution simulates the longitudinal particle dynamics around whole ring If the initial distribution of particles is chosen not from file than the parameters of 2 barriers model are used for the initial longitudinal distribution of particles which will be fitted in the accordance with barriers parameters particle can not have the momentum spread larger tha
8. Longitudinal 65 Horizontal acceptance m rad fi W bean Longitudinal Invariant Verticalaccenlance miad E Fig 7 Beam Parameters Emittance amp Injection One has to define beam emittance representation Go to Beam Parameters Emittance and choose Emittance definition Fig 7 Here 4 types of emittance definition are proposed Root Mean Square usual rms emittance when 1 sigma of Gaussian distributed particles is presumed Courant Snyder when emittance is calculated as Courant Snyder invariant Full Width on Half Maximum emittance corresponded to particles inside full width on half maximum of distribution Enclosed Percents emittance occupied by the indicated percent of beam particles Use for IBS kick means the using the choosing emittance definition for the intrabeam scattering kick otherwise the Root Mean Square definition is used for the intrabeam scattering kick If one chooses Emittance definition as Enclosed Percents it is necessary to add value of Enclosed Percents for Transverse and Longitudinal phase space Fig 7 Mean Longitudinal Invariant parameter has to be switched on in the case when the momentum spread has some deviation from the reference energy If multi injection process is used for simulations user can use TabSheet Beam Parameters Injection Fig 7 Here necessary to switch ON the process Checkbox Inject ions with interval and to define injection repetition period Inject ions with i
9. There are several TabSheets for controlling visualization process Control Transverse Longitudinal 1 D force Force along angle 4 1 Control of friction force drawing TabSheet ECOOL Draw forces Control Fig 19 lets user to determine parameters of the mesh and boundaries for the range where friction force will be calculated and drawn The model of the friction force to be drawn and calculated has to be chosen on the form ECOOL Friction force Model Fig 8 Edit windows here are used for setting the boundaries of transverse and longitudinal ion velocities minimum and maximum values and division number in every range User has to set the following parameters In the program code they are following variables boundaries for transverse velocity range transverse velocity minimum value and maximum value boundaries for longitudinal velocity range long velocity minimum value and maximum value number of divisions in the velocity range Divisions boundaries for velocity range to draw a plot of 1 D force Fig 21 Velocity minimum value and maximum value and number of Divisions for 1 D force plot angle of ion velocity inclination Angle boundaries for velocity range Velocity number of divisions for the plot Force angle Divisions ECOOL Draw forces AE W Draw 3 0 o E Divisions 20 Minimum Maimum El Viransverse zj 100000 5 Srt W longitudinal o zj 100000 Velocity m s 0
10. 7 an example of the task specification when the Electron cooling Internal Target and Intrabeam Scattering effects are active is presented For more details about each effect one has to look their description IBS manual Restgas manual Target manual et all 2101 x step multiplier Fates Evolution Horizont Vertical Long 3D rate fi Electron Cooling fo Rest Gas Horizontal 46 94 704579 lzec fi Internal Target VeiEal 1145238287 l sec fo _z_ Particle Losses Longitudinal 6082 762412 sec fi Intrabeam Scattering mm Particle number o 1 sec Calculate Find betacool exe Draw Evolution of Fates Additional Heating Stochastic Cooling EEE Fig 7 Effect switching list Step 7 Output results Evolution of the beam parameters such as emittances momentum spread and particle numbers during simulation can be observed on TabSheets Emittance Momentum and Number of Menultem BeamlEvolution Fig 8 Instructions for working with the 2D plot are presented in the file Bolide doc Beam Evolution i loj x Fig 8 Beam parameters evolution Set up a list of observed parameters is presented on TabSheets Control Fig 9 24 BETACOOL User manual Ill RMS Dynamics Algorithm 101x Horizontal emittance J Vertical emittance 30 Phase Diagram Gamma Criterium Last update 30 Sep 2007 e Momentum spread Temperature Equilibriurn
11. A A RN 62 Moder Or ESAS o a 62 2 UC MS HOSS C ae A A cons Deanne ewes 62 DG Bie od Fee A ter E et inert eee mettre Nester arr at tence nr Mere A A eat dT eer eer ee ener 64 A 14 1116 0 emegtere wenn eae eae rea me er mente etre ance or ee aR TE ere anne or eee ee a eee 64 be Electon coole ensena si iia 64 LE COIE parameters eii dial dels 65 A o A O 65 LIS Latice PARAM LETS a a 66 A CCRT OME DS am aseri 66 Le pace charse or clec DEA AAA AAA 67 Zeke Wei Ol DEMO de or lobo 67 Zk Ue ages IGN RRE REO Tn tne net encase crus mpd eee vans tages tetas aces 68 22 AS AAA II II 68 ZO NM OW OC ALIN aia taeectacmsmer E daa tusendamen tensa users eaters tietocsusenGaeion tose iacacsecceanectoess 68 2 Para OMG DCAM seeetane tence tare sraha a ce ea oh house EE 69 Zed ROMP LUC E NO 69 Sd Labrary OF the friction TOPCES cesinsusessinndenadssvesmaciandcadacadaee danedeeadssiusededandsataceadtestunnderadeasudeadiandeetaens 69 SL Models OFICON TOU CC Ao ude 69 iD NONSING SNC AZ TIC UL OM OE 70 Die Masnetized model Of AMCHOM TORCE arta 70 Seas Fal KMOMCAUK mod ac enue 71 NI A A O A 71 Dy O ECON ai od Ibor else io tion 12 4 Using of Friction forces drawing TOOL aiii A E 72 AA Control OF friction force drawing A A AA 12 4 2 Transverse and longitudinal components of friction OTCES oooocnccccncnononncnnnnnnnnnononananonnos 73 Bee 1 PilOts Ol Mn CUOMO TO 73 BETACOOL User manual Introduction Last update 08 Nov 2008 Dx Tabulatea ICHON VOCE nin 1
12. As AS where Ax Ax Ay Ay As A dp p vector of current shifts Ax Ax ini ini AY ini gt AY mis S nio ACAP I PY ini and Ax of initial and final shifts l distance between points of shift A current position of ion ano AX in AY fins AV in AS fins MCAD P on vectors If Solenoid error option is not enabled then Leggo and h Lecoo 2 Lecoo electron cooler length If Solenoid errors option is enabled then is the length of magnetic field unhomogeneity which calculated from input data file err with field errors h is equal to difference between ion longitudinal coordinate and position of the correspondence field unhomogeneity This file has 3 columns which correspond to the longitudinal coordinate horizontal and vertical shifts along the longitudinal axis Note that the Solenoid errors option will work properly if Euler or Runge Kutta cooler model is chosen on the TabSheet Cooler 66 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 If parameter Final is not enabled then final vector of shifts is equal to initial vector The painting procedure is used when the parameter Painting period in enabled Ax Ax Ay Ay As A dp p Ax Ax Ay Ay As A dp p x R 2 2 where R is the remainder of integer division Nstep Pstep Nstep Step number of beam simulation Pstep parameter of Painting period If Final parameters is enabled for painting p
13. Horizontal Bandwidth GHz p Ape f tf Initial position jonr H poz jonr H a Finalposiion f0 25 foo A fos Sf More parameters Time fpick kick sec fsez tft Bh Bhp p 8 Slip factor pickkick fos p p p Slip factor kickpick fos fi fo tf No O p W Optimal Gain 01807549424 A AAA gt Fig 1 Parameters of gated stochastic cooling 79 BETACOOL User manual XII Gated Stochastic cooling Last update 08 Nov 2008 For optimal gain and assuming that T equal to the revolution time T ev 77 equal to the ring sleep factor Mring neglect term 1 M a One can use simple approximation of cooling rates 2 Ap 1 wW 1 2W Tring rev P Te 3 Ttr I N M kp N To use this approximation switch off option More parameters Fig 1 Position of each active cooling section is indicated by the black horizontal line with square points on the Barrier Bucket Form Fg 2 ao E wal A E Fig 2 Barrier Bucket voltage distribution For simulation of gated cooling rates for each model particle the average distribution of the momentum spread Fig 3 blue line and average density of particles Fig 3b red line 1s used Ring Barrier Duc Ioj x THT T A A e Ae Fg1 3 a Longitudinal distribution of model particles and barrier bucket in momentum space b longitudinal beam profile along longitudinal coordinate
14. Interface Launch file bolide exe As a result the MainForm window is opened Fig 1 F Pi in GSI_betacool 1 2 E5R BLD oj x File Beam ECOOL Ring Task Effects SH E ES Fig 1 MainForm Step 2 Open file Open file of input parameters bld format a Choose FilelOpen or on the MainForm Fig 1 and choose file Fig 2 Se Look ir O GSI_betacool_v1 2 e Er CELSIUS BLO HESR _Dag bld RESR bid 3 cosy bld E himac bld rhic bld 2 EDMD bld leir bld 3 SLSR Mg BLD 2 ELENA BLD 2 napm bld 2 5LSR p BLD ESR ELD EB NESR bid E TARN2 BLD hesr bld IB RECYCLER BLD JUSR bld File name JESR BLD Files of type BOLIDE s File bld v Cancel Zi Fig 2 File open window Step 3 Setting of the ring parameters One needs to choose Menultem RinglParameters Fig 3 It s necessary to set Reference Energy on TabSheet lon kind Fig 3 Energy can be set in four ways Lorenz factor y Gamma Particle velocity in the units of the speed of light Beta Kinetic energy Kinetic Particle momentum in GeV c Momentum 21 BETACOOL User manual III RMS Dynamics Algorithm Last update 30 Sep 2007 ioi xi Reference Energy C Gamma 400 Mew y fossi42 Gew C Beta Kinetic E Momentum Atomic mass fi A Charge number fi Z Life time Decay MEE sec Fig 3 Ring parameters Also it s necessary to set up Atomic mass Charge n
15. MAD format Lattice Structure File Input MAD file Dutput MAD filename Find ESR tts asnos raft IEA YU AT Modify Lattice Structure Mo Changes i Y Y i Reduce filename Find JESR RED TAT YI NE Extended step cm 1 E Auto skip of points I j fl Calculate Lattice Make output MAD file KNAAR E e tm Fig 6 Ring lattice structure In the TabSheet Lattice Filename ComboBox Lattice Structure File the option Output MAD file has to be chosen For IBS calculations using Martini or Jei Wei models one needs to find appropriate lattice structure file Button Find of the TBrowse component opens the file manager window Button Open opens the file using internal text editor The chosen file name is indicated in the edit window of the TBrowse component and saved in the input BETACOOL file This name is used for initialization of the ring structure after start of the program Validity of the file can be checked using TBrowse component Calculate Lattice Button Open of this TBrowse component starts BETACOOL with the parameter lattice At this parameter BETACOOL reads MAD output file transforms lattice parameters into internal format and saves them into the files BetaX cur BetaY cur DispX cur AlfaX cur AlfaY cur DispX_ cur During this procedure the program checks validity of the data in all positions of lattice structure file in accordance with the description tacking from the TabSheet Output MAD format For more detailed i
16. MAD input file with optics element consequence there is an algorithm that provides a calculation of transformation matrix for whole ring then the second step 1s calculation of lattice parameters in the point So and after tracking of lattice parameters takes place If one has a lattice at the chosen point and matrix after it is possible to calculate lattices after matrix and so on and so force For this procedure user has to choose Input MAD format ComboBox Item and to click Calculate Optics Structure After some time period calculated lattices will be visualized onto corresponded plots Reverse procedure is also provided co called reverse tracking when one chooses the Output MAD format ComboBox Item the consequence of transformation matrices for optical elements of the structure will be restored from the consequence of lattices 2 2 Parameters of lattice structure If CheckBox Auto skip of points Fig 9 is switched on then the following procedure takes place when the number of points in any curve here the curves with lattice parameters is to be exceeded then because of the limited size of the curve with every next point inserted to the curve array one looses first point from the array So if CheckBox is ON every second point in this array will be deleted and all left points will be suppressed then at least a half of the curve array will be released for the expected calculated data This procedure can be eternal alway
17. TabSheet Pellet Horizontal shift Flux width Horizontal size Vertical size Vertical velosity and Interval between pellets Description of parameters is on Fig 6 Effects Internal Target O x Horizontal da Horizontal shift rm 0 3 Flux width mm F Horizontal size mm aos Vertical size mm 0 03 Vertical velocity rs BU Interval between pellets mm 0 3 j la 065300247875 Effective density cm 2 Horizontal shift Fig 4 Pellet target scheme and parameters 60 BETACOOL User manual IX Internal Target Last update 30 Sep 2007 6 Particle losses Effects Internal Target Losses TabSheet Losses Fig 5 gives a possibility to take into account particle losses on target interaction There are 3 kind of losses are foreseen Electron capture recombination Single scattering Nuclear reactions Cross section for probability of every event can be defined as a value in barn If one wants to set Cross section for probability it is necessary to set CheckBox Interaction events ON and to set value in EditWindow Cross section Effects Particle Losses Ioj x Eres Active Effects Additional Losses I Single scattering Electron Capture in ECOOL Life time Decay E Vue cen eetan M Scattering on Rest Gas Acceptance Interaction events Separatris length Cross section barn 10 04 Luminosity I cm cm s 444833431 7E 3
18. Task Growth Rates step multiplier hp 3 i i_ BS Zz mi Oa Electron Cooling Rest Gas Internal Target Particle Losses Intrabeam Scattering Additional Heating Stochastic Cooling Task Growth Rates step multiplier m Oe a m E Es Electron Cooling Rest Gas Internal Target Particle Losses Intrabeam Scattering Additional Heating Stochastic Cooling Task Growth Rates step multiplier Z eS NN IS mm E mS Electron Cooling Rest Gas Internal Target Particle Losses Intrabeam Scattering Additonal Heating Stochastic Cooling Rates Evolution Horizont vertical Long 30 rate 001 Horizontal Emittance pi mm mrad a 1E 6 l Ei 1E 7 1E 5 0 001 Momentum Spread 1E9 1E9 1E5 1EF 1E6 1E5 10000 1000 100 10 1 Rates Evolution Horizont Wertical Long 30 rate 001 Vertical Emittance pi mm mrad 0 1E 6 l 1E 7 1E 5 0 001 Momentum Spread 1 Horizontal Emittance pi mm mrad 0 001 1E 6 Momentum Spread 18 1E9 1E9 1E6 1E7 Last update 30 Sep 2007 BETACOOL User manual Il Growth Rates Algorithm Last update 30 Sep 2007 4 Example of analysis of phase space diagrams of growth rates The example of r m s evolution during cooling process for HESR is presented on Fig 8 After cooling process all parameters achieved constant value and does not change for a long time Particle loss rates are in a fe
19. are measured in m sec Another two TabSheets are 1 D Force Fig 15 which is intended to draw 2 D plot of the friction force component eV m over velocity in pre determined range and Force along angle Fig 15 here user can plot friction force component eV m when the ion velocity directed along specified angle ECOOL Draw forces AE ECOOL Draw forces Sele E D oo rz SI a Le 20000 40000 60000 0000 0 525 Velocity ms Angle rad Fig 15 Example of 2 D friction force line over velocity calculation ECOOL Draw forces 1D Force amp Force along angle 5 Tabulated friction force Window ECOOL Tabulated is a special toolkit for testing and interpolation of tables with pre calculated transverse and longitudinal friction force values which are created by another code for example tables generated by program created in Erlangen Univ 73 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 5 1 Input files TabSheet Control Fig 16 here 3 TBrowse components two for choosing files containing tables with transverse and longitudinal friction force values File with transverse velocity table File with longitudinal velocity table These files have to have special extensions for transverse component tvt for longitudinal component lvt And one TBrowse component Generate table with velocities Here user must launch betacool exe to generate tables with friction force values in accordance wi
20. cooler position must be defined on TabSheet Lattice Fig 4 Beta Horizontal Vertical Alpha Horizontal Vertical Dispersion Horizontal Vertical Dispersion derivative Horizontal Vertical 01x lx Cooler lon Beam Cattice Shifts Space Charge Cooler lori Beam Lattice shifts Space Charge l Enable Initial 4 Final Horizontal Mewes II A Horizontal m o o Beta m 16 l 6 88 l Vertical m 5 686 o Abha Jo E jo eal Longitudinal m fo o Dispersion m fo fo Momentum spread 0 0002 o Dispersion po Painting period integration steps 10 derivative Leal Solencidenors m Find SOLENOID E Painting md painting pat pen Paint 3 Find O Fig 4 ECOOL Cooler menu item TabSheet Lattice amp Shifts 1 4 Electron beam shifts In BETACOOL code was realized different procedures for the changing of the electron beam position in transverse and longitudinal plans the distance between electron and ion bunches solenoid errors and so on Parameters for these procedures were placed on different windows and sometime duplicate each other Now all these possibilities are placed on the same TabSheet Shifts on ECOOL Cooler Form Fig 4 The definition for the electron beam shifts in the laboratory rest frame is written as following Ax Ax p Ax 11 Ax Ax Ax h Ay gt Ay a NY a lr 2 1 Ay Ay Ay h A dp p Aldp p
21. input file and their default values For instance if after program termination the Betacool war contains the following warnings START 2006 4 11 24 TT 8 14 D sao GSI 2006 betacool GSI v2 betacool exe EDMD bld Input parameter 87 1 was initialised with default value 0 Input parameter 87 2 was initialised with default value 0 001 Input parameter 87 3 was initialised with default value 0 Input parameter 87 4 was initialised with default value 2 Input parameter 87 5 was initialised with default value 0 Input parameter 87 6 was initialised with default value 0 Input parameter 87 7 was initialised with default value 0 001 Input parameter 87 8 was initialised with default value 2 END 2006 11 24 17 8 14 it means that in the file EDMD bld the parameters 87 1 8 are absent and for calculations their values indicated in the last position of warning will be used 1 3 Input files General input parameters are collected in bld file The format of this file is developed in a way to make easy collect and edit 1t in any simple editor All the parameters are provided with comments and structure of parameters list is connected to the program algorithm BETACOOL User manual Interface Last update 30 Sep 2007 The example of one of the parameter groups 1s presented below row 1 Beam Parameters Emittance 1 6 Horizontal emittance pi mm mrad 1 6 Vertical emittance
22. ioj x 10 xi Transverse welocit Velocity range rms steps in range let point fi OOOO 2nd point feoooon drd point 3000000 Longitudinal velocit Velocity range mz steps in range 1st point fi 00000 2nd point 400000 Transverse velocit Velocity range ms steps In range Tat point fi 0000 nd pont 800000 ard point 3000000 Longitudinal velocit Velocity range mrs steps in range 1st point fi 00000 2nd point 400000 i i il Fig 17 TabSheets Transverse force Longitudinal force First range is from 0 to 1 point value with splitting steps in range second range is from 1 point to 2 point with splitting steps in range corresponding to 2 point third range is from 2 point to 3 point with splitting steps in range corresponding to 3 point TabSheet Longitudinal Force Fig 15 is used for definition of the parameters of the table for longitudinal component of the friction force All the parameters are analogue to TabSheet Transverse Force General note The algorithm of using this ECOOL Tabulated is the following If user wants to create a table by himself using any of existing friction force models in BETACOOL it is necessary to 1 choose a model in Ecool Friction forcel Model any but Tabulated 2 set up the mesh Ecool Tabulated Transverse amp Longitudinal Fig 17 3 Push button Open at TBrowse Generate table with ve
23. z 100000 ra We Draw line Angle 5 Divisions 50 rm z r ke Draw circle Velocity m s 1000000 Divisione 50 al Draw friction force Find betacoolese Open Fig 13 ECOOL Draw forces TabSheet Control 12 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 4 2 Transverse and longitudinal components of friction forces Component TBrowse Draw friction force is used for visualization of the friction force dependence on ion velocity Button Open of the TBrowse starts BETACOOL program with parameter fr At this parameter BETACOOL calculates and saves two 3D plots FFtr sur and FFlong sur The 3D plots are loaded and visualized into corresponding tab sheets Transverse and Longitudinal of the ECOOL Friction force Form see example of the friction force 3D plot in the Fig 14 ECOOL Draw forces Ea fx ECOOL Draw forces AE Control Transverse Longitudinal 1 0 force Force along angle Control Transverse Longitudinal 1 0 force Force along angle 0 1220 0 1220 0976 O 0732 0 048 O 0244 T pi E E 2 E E fiction force em 0002420 0480 07320 09765116 00 01 920 03900 05860 OF E42 50000 F 50000 longitudinal velocity ms longitudinal velocity m s Fig 14 Example of the friction force shape calculation ECOOL Draw forces Transverse amp Longitudinal 4 3 2 D plots of friction forces The friction force is performed in eV m units the velocity components
24. 0 de Other losses eal Fig 2 Visual form for input parameters for power consumption calculation Table 2 Input parameters for the cooling rate calculation Notation in the report momentum distribution Losses in combiner prom B Power of additional losses Poss IB Characteristic impedance i Ohm To control a validity of input data the program outputs the parameters listed in the Table 3 These parameters can be calculated without beam dynamics simulation for this one needs to calculate sum of the rates of active effects Table 3 Output parameters Notation in the report Thermal noise power Schottky power INS 7 A Total power a a ZU Equilibrium emittance ee ema O Cooling rate tems NO 1 2 Longitudinal degree of freedom For longitudinal plane Fig 3 the program uses standard set of input parameters for the cooling chain description that are listed in the Table 4 T1 BETACOOL User manual XII Gated Stochastic cooling Last update 08 Nov 2008 Effects Stochastic cooling lOl xj Horizontal Vertical Longitudinal Common parameters M Lise z Electronic gain Lower frequency E GHz Boos 216227 8 Upper frequency fe GHz logarithm frio dE Electrode length E cm Optimum linear gain 534848 7801 Pickup number of loop pairz 128 Approx length 2 344 m kicker number of loop pairs E Approx length 0 736 m Thermal noise power 02945425752 YA Schottky power 0 228
25. 0 Generate model particles on losses with distribution Rea Fig 5 Particle losses in target Note One has to choose Menultem Effects Particle Losses Fig 5 on the MainForm and switch ON Internal Target to choose Menultem TasklGrowth Rates Fig 6 and to switch ON Particle Losses if it necessary to consider particle losses effect in target Information about Generate model particles on losses with distribution is given in Particle Losses manual ax step multiplier Rates Evolution Horizont Vertical Long 30 rate fi Electron Cooling P Rest Gas le T Horizontal 0 073237 r 4605 1 sec Internal T arge Farticle Losse Intrabeam Scattering i Additional Heating jo eal Stochastic Cooling Yertical U 03521144113 1 sec 0 1 769013853 1 zec Longitudinal Particle number fo 1er Calculate Find betacool exe Draw Evolution of Rates Fig 6 Growth Rates calculation Finally one has to choose Menultem TasklGrowth Rates Fig 6 and switch ON Internal Target 61 BETACOOL User manual X Rest Gas Last update 30 Sep 2007 X Rest Gas 1 Model of Rest Gas Growth rates due to the scattering on the residual gas are calculated with the same mechanism to the internal target effect for example gas jet target In program assumed that residual gas is the gas cell target which is distributed along whole circumference of the ring L
26. 00064702724944 Induction acceleration w 0 3 Fig 4 Form Ring Parameters TabSheet RF system The Separatrix size parameter is used for the particle loss simulation and it can be arbitrary positive number Separatrix length and Synchrotron tune are output parameters The check box Induction acceleration has to be not checked Using the TabSheet Lattice Fig 5a set up Circumferensce Gamma transition Tunes Chromaticity Acceptance and Longitudinal Acceptance These characteristics of ring are necessary for numerical calculations At Fig 5a an example of ESR ring lattice is shown Ring Parameters E E lon kind Lattice Mean params RF system Reference point Ring Parameters lon kind Lattice Mean params RF system Reference paint Lattice functions at point User ki Mean Ring User Lattice functions Frad Chokes Horizontal Imagerary Horizontal Vertical Beta m m zj Tunes 2 2952 2 265 2AT r mj Chromaticity 2 5511 j 2 3415 aj Acceptance 0 00025 0 00015 m rad Alpha Dispersion rn Dispersion derivative Longitudinal Acceptance 0 003 a Fig 5 Ring parameters Using the TabSheet Reference point Fig 5b set up Lattice functions at point and User Lattice functions This Reference point means the point characterized with lattice where turn over the ring will start for model beam simulation matching the particle array with the ring optic stru
27. 007 1 4 Calculated characteristics The TabSheet Characteristics includes beam parameters calculated when main parameters of the beam and ring are determined This TabSheet Fig 2 includes the following input and output variables Mean beam radius a Longitudinal form NN Used for longitudinal form factor calculation a 2 0 0 G 1 a b 1s the mean radius of the vacuum chamber Longitudinal Ohm space charge longitudinal coupling impedance Zz sc ZG Lise O E Zo 377 Ohm 2By factor Gr Transverse Ohm m Space charge transverse coupling impedance Z 5 ZR 1 1 Z se 57 z 272 R is the ring mean radius vy la Peak current A Current of the coasting beam or peak current for the bunched beam ZeN E io Bris the bunching factor B f i 2 Visualization of beam parameters 2 1 Evolution of emittances The Window Beam Evolution Fig 3 is used for visualization of the beam parameter time dependencies TabSheet Emittance Fig 3 contains 2D plot for output two curves Ex2t cur Ey2t cur time dependencies of horizontal and vertical emittances TabSheet Momentum Fig 3 contains 2D plot for output curve Dp2t cur time dependence of momentum spread and 2D plot dpmo2t cur deviation of momentum spread TabSheet Number contains plot for output Num2t cur particle number time dependence TabSheet Bunch contains plot for output Bunch2t cur for time dependence of bunch length Beam l Evolution Beam
28. 1 7 1 8 de dt or longitudinal momentum spread 1 7 1 Ap dAp dt I W gt Ti N EIA pr gp 0 l d i coherent incoherent effect cooling effect heating where N is the number of particles in the ring W fmax fmin 18 the cooling system bandwidth g is the gain parameter U is the noise to signal ratio Mpg is the mixing factors from pick up to kicker and My from kicker to pick up Mixing facto is 1 M pk kp 2 2W 11 pk kp T pk kp where pk kp Slip factor from pick up to kicker and from kicker to pick up Tpk kp time flight from pick up to kicker and from kicker to pick up Ap p momentum spread The gated stochastic cooling has four identical Sections Fig l with the same input parameters Type horizontal vertical or longitudinal Bandwidth GHz Initial position and Final position of the cooling section in the unit of circumference the same as position of Barrier Buckets Check enabled option More parameters for simulation with Formula 1 Time pick kick flight time from pick up to kicker flight time from kicker to pick up is calculated via revolution time Slip factor slip factors between pick up and kickers Noise supposed to be equal 0 User can define le I M i Gain manually or use Optimal gain which will be calculated with formula g M kp U lolx Parameters W Section 1 Section 3 Section 4 Type Longitudinal Horizontal Longitudinal
29. 3 SU MEPS UNC ML GRA An A en Nh cinta at cae ect eaten EN cinta ca se ci cane cia ttee 74 D7 AUER A TI 74 5 5 Transverse and longitudinal veloc inside EEE EEA 74 ALL SUOCMASIIC COOMIN a5 soetarash ten lasaentiabar he aaneieiach aie laaneeianias eee igutesaiese atch naeeianiee dat iaueaeeiaaatep aaa 76 l Standard Stochastic Cooling ir A A AA 76 tl Transyerse de fees OF rec aia 76 1 2 Eonsitodinal Ge eres OF EM AE AAA AAA T eE UOC MASE CeO OO MIN oes E T O EAE TOES 79 BETACOOL User manual Interface Last update 30 Sep 2007 I Interface Introduction The interface part of the software consists of executable file Bolide exe files containing information about BETACOOL exterior and input files for post processing of the calculated data bolideNN dfm each file corresponds to Form and describes parameters of visual components bolide top position of Forms bolide grf setting of 2D graphs bolide srf setting of 3D graphs The physical part of the software consists of the executable file Betacool exe compiled for Windows or UNIX operation system and a few input and output files betacool war output file which saves of console messages bid input files with simulation parameters ela input files with distribution of electrons err input files with distribution of solenoid errors inj input files with initial ion distribution lat input files with lattice structure of storage ring Ivt in
30. 571 6053 wal Total power 6 353501 276 al 0 01319704914 5 Optimum cooling rate 0 024417745 4 3 1 Cooling rate Equilibrium momentum spread 729444925566 Fig 3 2 Visual form for input and output parameters for longitudinal cooling chain Table 4 Input parameters for the cooling chain description Lower frequency Upper frequency Electronic Gain Ga Dimensionless or in dB G dB 20logG iin Loop length Pickup and kicker parameters Number of loop pairs Ee For the pickup and kicker the program calculates approximate length of the electrodes in accordance with the same estimation as for transverse planes N k 7 ep lem electrode For the cooling rate and consumption power calculation the program uses the input parameters which are the same as for both transverse planes which are listed in the Table 2 Output parameters for longitudinal degree of freedom are listed in the Table 5 Table 5 Output parameters Equilibrium momentum spread Ap P eq 78 BETACOOL User manual XII Gated Stochastic cooling Last update 08 Nov 2008 2 Gated Stochastic cooling The stochastic cooling can be interpreted as the composition of the coherent single particle effect when each particle is cooled by means of signal generated itself and the incoherent noise signal generated by all its neighbour particles The basic formula shows the relation between these two processes and determines the cooling rate of transverse emittance
31. Cooling Horizontal 0 1187722908 1 sec o Rest Gas Yertical 0 156637 7213 1 sec detal Internal Target Longitudinal 0 0356439061 4 sec Particle Losses Particle number o 1 sec Calculate Find betacoolexe e Draw Evolution of Fates Intrabeam Scattering Additional Heating Stochastic Cooling alal ulm Fig 1 Form Task Growth Rates Here user must choose active effect by changing number in front of the effect name to arbitrary non zero value All the Effect classes have the same parent class xEffect which has a Boolean variable use When the corresponding Counter is non zero this variable of the effect is true A value of the step multiplier has effect for the Model Beam algorithm only All the variables Effect are put in the array using self counter system The program calculates sum of the rates in cycle calculating the rates of the effects at use true Parameters of each effect involved into calculation must be set in appropriate Forms In addition user must prepare beam and ring parameters For the ion beam one should use the Form Beam Parameters Fig 2 TabSheet Emittance Beam Parameters lOl xj lon beam state Coasting Horizontal emittance m pi mm mrad Vertical emittance 5 B pi mm mrad Momentum spread po gt Humber of particles 1E9 Z Model particle number fi 000 Emmitance definition Root beam Square use for IBS kick Enclosed Pe
32. Coun gt sold 2 beta Point style Size me Fe Il Y betay i z Dx Fabs 4 visible autoload Beter O Beter O Curve File Hame Color Reset fsaz2 Size Save Load IZ Redraw Fig 15 Values of horizontal beta function initialized from the file 53 BETACOOL User manual VIII Intrabeam Scattering Last update 30 Sep 2007 VIII Intrabeam Scattering After launching the Bolide exe file and checking a validity of an input file one needs to set the storage ring and beam parameters using corresponding menu items of the main interface window Fig 1 D sa0 betacool RHICmb BLD oj x File Beam Effects ECOOL Ring Task 2458 39 ln 0 e Fig 1 Main interface window Thereafter the model for IBS rate calculation has to be chosen using menu item Effects submenu item Intrabeam Scattering If the model requires a lattice structure of the ring it has to be imported from external file using menu item Ring submenu item Lattice Structure If user wants to switch IBS effect as active into simulation 1t 1s necessary to switch step multiplier corresponding to the Intrabeam Scattering on the Form Task Growth Rates to non zero value for details please look for Numerical algorithm manuals At the first step one needs to choose menu item Ring submenu item Parameters How to set the Ring parameters please look RING manual Parameters of six dimensional phase volume of the beam required for IBS rate calculati
33. Dy p hz fa Dp T Sa a a en ak o i AAA Fig 14 Ring Lattice Structure Form TabSheet Output MAD format If the column number in the output MAD file does not coincide with one of the standards the option User has to be chosen In this case initial and final column in the output file corresponding to each lattice function have to be input manually in the table of edit windows User definition of Column Position The column corresponding to the cursor position is indicated in the BOLIDE text editor in the left bottom corner Names of the lattice functions in the User definition of Column Position table coincide with the names of corresponding lattice function in output MAD file 32 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 To be sure the lattice parameters are initialized correctly one needs to push right button of the mouse at the plot of lattice function in the Ring Lattice Structure Form In the plot control window one of the curves containing lattice parameters has to be chosen in Curves TabSheet Fig 15 left window In the TabSheet Values right window in the Fig 15 one can see the values of chosen lattice function The first column in the tab sheet contains the distance from the ring initial point in meters the second column corresponding lattice function Anis Grids Other Curves Values Trendline Axis Grids Other Curves Malues Trendline Line style Width 3
34. Fig 8 has any number of columns first column is time in seconds each other pairs define position of barrier in circumference units and amplitude in volts During simulation process the linear fitting of barrier positions and barrier amplitudes are realized between lines When reference time is reached the final line then the parameters of barriers don t change more chandradmoy AE suf osea An Oo 0 4167 2000 0 2619 0 0 3452 2000 0 4167 2000 0 2619 0 0 3452 2000 0 4167 2000 0 0923 0 0 1756 2000 0 4167 2000 0 0923 0 0 1756 2000 Row LES Cal 2111 Modified we Fig 8 a File for definition of moving bucket 2 Lattice Structure To specify ring lattice structure which is necessary first of all for IBS effect simulation user must use Window Lattice Structure Fig 9 which contains TabSheets Lattice Filename Output MAD format and three TabSheets connected to lattices of optic channel and its transformation matrix two of 2D plots beta functions and alfa functions and Matrix 2 1 Input files with lattice structure Using TabSheet Lattice Filename Fig 9 one must select and save to the input file the names of files containing information about ring optics structure This TabSheet contains ComboBox Lattice structure File with three possible items Output MAD format Input MAD format No file and three of TBrowse components This ComboBox is used when user has a file with some lattice structure obtained from MAD
35. J Evoluta O xj 1 5 1 5 Reference time sec Reference time sec Fig 3 Window of the Beam Evolution Emittance amp Momentum 40 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2007 TabSheet 3D Diagram Fig 4 contains plot for output gamma2 cur criterion I n gamma3 cur equilibrium between transverse and longitudinal ion temperature footprint cur unsorted invariants of particles the dependence evolution of the horizontal emittance on the momentum spread txy2t cur The TabSheet Control Fig 4 allows user managing of the plots visualization It contains list of all the plots of the current window which presented by Checkboxes User must check plots which are needed to be redrawn on line and or check off unnecessary plots Such a scheme allows to manage CPU resource in order to fasten calculation time An evolution of transverse emittances and momentum spread can be plotted with different definitions Fig 4 the transverse emittance one sigma un normalized and normalized with certain percent value of the particle number the momentum spread relative and absolute values These definitions correspond to parameters on Beam Parameters window Fig 1 2101 Emittance Momentum Number Bunch Luminosity Beam beam 3D Diagram E mittance f 1 sigma me normalized Momentum prea f relative i absolute Gamma2 Equilibrium FootPrint Evolution Gamm
36. Last update 08 Nov 2008 Introduction BETACOOL User manual AT ax WF BETACOOL User Manual based on BOLIDE interface since 1995 I Meshkov A Sidorin A Smirnov G Trubnikov R Pivin Joint Institute for Nuclear Research Joliot Curie 6 Dubna 141980 Russian Federation http lepta jinr ru betacool Dubna 2007 BETACOOL User manual Introduction Last update 08 Nov 2008 Introduction The user manual describes how to work with BETACOOL software developed for calculation of ion beam parameters in a storage ring taking into account peculiarity of electron stochastic and laser cooling intrabeam scattering processes beam interaction with residual gas beam interaction with internal target interaction with colliding beam in a collider mode of the ring operation The version of the program includes three basic algorithms RMS Dynamics simulates evolution in time of second order momentum of the ion distribution function r m s emittances under a common action of a few heating or cooling effects which are described in terms of characteristic times of the beam r m s parameter variation Model Beam simulates evolution of the distribution function shape The beam is presented as an array of modelling particles Evolution of the particle momentum components is described in terms of Langevin equation Each heating or cooling effect is characterized by friction and diffusion components The friction leads to regu
37. Rates Rates to check in Particle number window the growth rates due to particle losses lox step multiplier Rates Evolution Horizont Vertical Lang 3D rate z Horizontal 0 03433063111 1 sec _ Res Gas Yertical U 0251 153225 l sec I Internal Target Longitudinal 0 03083995483 1 sec 1 Particle Losses Particle number 0 1678193559 17sec Intrabeam Scattering Calculate Find betacool exe 0 Sj Additional Heating e Draw Evolution of Rates 0 Stochastic Cooling Fig 5 TasklGrowth Rates 36 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2007 VI Ion Beam Object 1 Beam parameters Parameters of the global variable of class xBeam and results of calculation of the beam parameter evolution in time are collected in the Main Menu tem Beam which includes following submenu items Parameters Distribution Evolution Real space The Window Parameters Fig 1 includes 5 tab sheets Emittance Model Beam Multi Injection Bunch Characteristics 1 1 Emittances and particle number The TabSheet Emittance is used to define main beam parameters When Model Beam Algorithm is used user must choose Emittance Definition Here 4 types of emittance presentation are proposed Root Mean Square usual rms emittance when 1 sigma of Gaussian distributed particles is presumed Courant Snyder when emittance is calculated as Courant Snyder invariant Full Width on Half Maximum emit
38. TACOOL User manual Il Growth Rates Algorithm Last update 30 Sep 2007 II Growth Rates Algorithm Introduction This procedure is intended for calculation of characteristic times of the beam r m s parameter variation growth rates in accordance with few heating or cooling active effects Characteristic times Thor T ver T lon are functions of all three emittances and particle number The horizontal and vertical rates are determined in the program as l1 lde T ed where e is the corresponding emittance The longitudinal rate is determined as 1 1 do a ao T o dt where o is rms relative momentum spread Rates have positive sign for a heating process and negative for cooling one The negative sign of the lifetime ty corresponds to the particle loss and the sign of the lifetime can be positive in the presence of particle injection when particle number increases In the program code this procedure is described in void xDynamics Rates files xdynamic cpp xdynamic h 1 Starting the calculations setting of parameters 1 1 Command prompt mode The simplest way to start a Growth Rates calculation GR is to put the Betacool exe file file of input parameters bld format other required files from archived Betacool kit download from website http lepta jinr ru betacool and SAVE bat file into the same folder To start the GR one needs to type in the command line the following command lt path gt betacool ex
39. Vertical Long 3D rate Electron Cooling E Fest Gas Horizontal 48 94704579 l sec h 3 Internal Target Vertical 1145230297 Fl ieee fo Particle Losses Intrabeam Scattering O ERDERA Mee z Additional Heating Particle number fo l sec a ll Stochastic Cooling Calculate Find betacool exe Draw Evolution of Fates Fig 9 Effect switching list Next step is setting the calculation parameters At the Form Task Model Beam Model Beam Fig 10 one has to set up Integration step There are two possibilities to do this User can set either Time step in seconds or the step in number of turns Turn number Stop time indicates the 31 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 reference time when the simulation will finish automatically zero value means infinity calculation In the case of Common betatron tune all model particles have the same value of the random phase advance on each integration step otherwise each particle gets the different phase advance For the synchrotron tune user can choose random value Random synchrotron tune or synchrotron tune will be calculated from ring parameters Task Model Beam 2 x Task Model Beam O xj ntegration step f Time sec 0 0025 Turn number 5351413 gt Bi Gaussian IBS model Core T ai Bi Gaus TA z Core definition sigma fe z lnvarinats in core 1 3 2 W Corect core number definit
40. a e Equilibrium Horizontal Emittance pi mm mrad Fig 4 Window of the Beam Evolution 3D Diagram Control 2 2 Phase space of model particles The Window Beam Real Space Fig 5 is used for visualization of the particle distribution in different planes during simulation procedure TabSheet Control here is a manager of plots user can choose which plot is active for on line redrawing and what a coordinate plane will be represented on it for example Y X transverse real space of particles X X horizontal phase space Y S longitudinal real space etc Beam Phase Space 0 x Beam Phase Space O x Beam Phase Space Oj x Space 1 e Draw MEHE 5 50 Ix 5 50 Y aF Fig 5 Windows of the Beam Phase Space menu item 2 3 Distribution of profiles and invariants The Window Beam Distribution Fig 6 7 is used for visualization of the real particle distribution for model beam TabSheet Coordinate is the dependence of particle number in percent on momentum deviation dist_sp cur and coordinate dist_sx cur and 41 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2007 dist_sy cur normalized on corresponding rms parameter and particle number 100 AP P o N TabSheet Profile is real particle distribution for every coordinate analogue of previous plot averaged on betatron or synchrotron oscillations dist_ix cur dist_iy cur
41. a 3D Binney Number of steps Step Friction force model EA inte ale cs Electron beam qualit Transverse Longitudinal CO Emittance 3 6344608218 6 9 023406938E 5 f Temperature ev Jo 03 0 0001 C Rms velocity m s 72638 92953 4193 810552 Longitudinal fat fo 003 i Transverse fat peer Azimuthal fn z FF rho min via rel tho min Plus e rms Fig 10 ECOOL Friction force TabSheet Model amp Non magnetized 3 2 Non magnetized fiction force The TabSheet ECOOL Friction force Non Magnetized Fig 10 is used to determine and define parameters for Non magnetized friction force model calculation Here user can change the following parameters on the corresponding Panel RadioButton Asimptotic or Numerical choice of the calculation method for this model either using asymptotic assumption asymptotic formulae obtained with Coulomb analogy are used formalism derived either by Derbenev or by Meshkov or integrating over longitudinal and transverse ion velocities this is Numerical choice If Numerical calculation is chosen here user can select method for numerical integration with RadioGroup Numerical either 3D or using Binney formalism If integration will be performed over all three velocities two transverse and one azimuthal then user have to define Number of steps for each integral The following CheckBoxes if switched on are intended for definition of integration paramete
42. ame will be ESR BLD Auto Saving interval defines the time interval after what the Betacool code saves all output files on disk Number of skip points indicates how many points of 2D graphs will be saved 0 means all point are saved 1 each second points are saved 2 each third etc Size of curves length of 2D graphs If output points reach the limit of curve size then the output points will be saved on the beginning of curve If Auto skip point is switched on then parameters Number of skip point will be automatically incremented when output points reach the limit of curve size Appendix List of graphs alfax cur horizontal alpha function Ring Lattice Structure alfa functions alfay cur vertical aplpha function Ring Lattice Structure alfa functions betax cur horizontal beta function Ring Lattice Structure beta functions betay cur vertical beta function Ring Lattice Structure beta functions bunch2t cur bunch length on time Beam Evolution Bunch charge cur space charge parabola of electron beam ECOOL Cooler Space charge dispx cur horizontal dispersion Ring Lattice Structure beta functions dispx_ cur derivative of horizontal dispersion Ring Lattice Structure alfa functions dist_dp cur sorted longitudinal invariants Beam Distribution Invariant dist_ex cur sorted horizontal invariants Beam Distribution Invariant dist_ey cur sorted vertical invariants Beam Distribution Invariant dist_1p cur longi
43. angular method The interval of integration over each of variables is divided by a few equal steps and number of divisions over each of the variables is introduced in the corresponding edit window The integral over z has the infinite upper limit exp D u v z In I 2 laz 0 and in the program the upper limit is chosen corresponding to exponent power equal to 20 Necessary number of steps over each variable depends on beam and ring parameters and required accuracy of the growth rate calculation The numbers of steps has to be chosen manually by a few subsequent calculations of the growth rates The numbers have to be increased until the growth rates reach saturation with required accuracy Algorithm for automatic choice of the step number is under development 55 BETACOOL User manual VIII Intrabeam Scattering Last update 30 Sep 2007 To speed up the calculation the integral over z variable can be calculated using simplified expressions If the option Analytical is chosen in combo box Integral over z the integral is calculated using analytical expression in accordance with the book by Abramowitz amp Stegun Effects Intrabeam Scattering Ioj x Martini Jie wei las a Bjorken IBS model o Integral over z Integral divsion Martini Coulomb gaiti ga T 20 e Average transverse Analtical oo DE jo Humerical AI Fig 3 The visual form for choice of the IBS model TabSheet Martini ComboBox Integral over z
44. ate calculation are realized in Betacool now The choice between them is provided using ComboBox IBS models Fig 2 2 Martini model General theory of IBS process in a storage ring based on binary collision approach is described in the article M Martini Intrabeam scattering in the ACOOL AA machines CERN PS 84 9 AA Geneva May 1984 this model is called Martini model in our program in another sources it can be refer as Extended Piwinsk1 model This model is valid independently of the mode of a ring operation and does not require additional assumption about optic structure of the ring and Coulomb logarithm value It is more accurate model and if the calculation speed is not important for a solving task it is preferable to use this model From the side of mathematics the growth rate calculation is reduced to evaluation in each optic element a 3D integrals over u vand z of the following form 21 le f fsin ue u v exp D u v 2 im 1 z lavdud E 0 0 o 8 a 2 T y 2 2 2 bin cos v sin asinv dcosv b cos Dp v Pe ul 2 El g u v 1 3sin cos v g u v 1 3sin usin v 6d sin usin vcosv a 23 u V 1 3c0s u here the coefficients k a b c d depend on the beam phase volume and lattice parameters of the optic element If in the combo box Integral over z in the TabSheet Martini Fig 3 the option Numerical is chosen then all three integrals are calculated using rect
45. attice functions are used from each optics element It means that summary rates due to the heating on the residual gas are integrated over the lattice structure In BETACOOL program two objects need the real lattice structure Intrabeam Scattering and Rest Gas Accordingly to the residual gas pressure the effective density of the gas is calculated then energy loss on scattering with Bethe Bloch formulae r m s angles of ions after scattering on atoms of the residual gas and emittance and momentum deviation are calculated consequently After in accordance with the percentage of components the characteristic growth rates are obtained More detailed information is given in physical description of BETACOOL program Window of the Effects Rest Gas Fig 1 includes a kit of parameters characterized vacuum composition in the ring Effects Rest Gas Vacuum composition Pressure defines vacuum pressure in Torr under room temperature Four component vacuum is presumed for now in the program Below the above mentioned parameters the table of the vacuum components is situated For every component provided the following kit of parameters percentage of the component in a whole composition Atomic number of the component A and Charge number correspondingly Z iol x1 Pressure 1E 10 a Torr 10 Fig 1 Form of Rest gas object 2 Particle losses Effects Rest Gas Particle losses TabSheet Particle Losses Fig 2 gives a possibil
46. be set in the tab sheet Lattice Fig 1 If the transition energy is imaginary the corresponding check box has to be checked Variable lable Comment Formula m Gamma transition used for off momentum factor calculation Tunes Horizontal and vertical tune values Chromatisity used for tune spread calculation Acceptance Tr M rad used for calculations of life time due to single scattering on big angles Longitudinal used for calculations of life time due to particle off the acceptance separatrix length Chromaticities are used for stability estimation and for the rate calculation the values can be arbitrary The acceptance values are used for the particle loss simulation For the rate calculation the acceptances can be set as arbitrary nonzero positive numbers Imagenary J si used to determine complex value of y factor 1 3 Mean parameters The TabSheet Mean params Fig 2 contains only output parameters which will be calculated after start of Betacool calculations Variable caption Mean radius Horiz beta function Vertical beta function DEBO o O Dispersion D BO Revolution period Trey CIBc Off momentum factor Ring Parameters Ioj xj Ring Parameters q lol xj lon kind Lattice Mean parame RF system Reference point Barrier bucket lon kind Lattice Mean params HE system Reference point Barrier bucket Mean ring parameters bean radius 35 3499044 m Harmonic number 20 Horizo
47. cnnnnnonononnccnnnnnnnnnnonaninenoss 12 Appendix ASCO Straps cos 12 Growth Rates Ale Ori tint asada 14 E 14 1 Starting the calculations setting Of parameters seernes n E 14 Ll Ae Ommana POMP Mode add tl iio 14 12 WANGOWS IEA a ad and 14 2 Specification of the task Calculation of sum of the rates ccoooooonnnnnnnnnononononncnnnnnnnnononaniononoss 15 I JUD les cs o ni led ceda ni cien 18 4 Example of analysis of phase space diagrams Of growth rate cccccccccooononccnnnnnnnnononanonannnnnnnos 19 HE TR IVES Nas a S 21 MEAN dd es as 21 gt e A TC 21 Step Ope ml on 21 Step gt elin OF the TINS Parameters ua 21 Step 4 ettine Ot lattice sto CLES diia 22 step gt Selling Of the bean paramet ei Sirenia id 23 Step 0 Seine the aCcUve EHEC ia ad 24 SEP 7 QUEUE Pe SUS serias 24 Step 8 The starting of RMS Dynamics Simulation ccooooooonnnnnnnnnnnnnnnonnnnnnnnnnnononanonnnnnnnnnnnnnnnos 25 We Modei Beirm Also Msi cano 26 rodu IO y PA A E 26 Step ck Tune ht aee a ninco ted weenie aula wean aus whedon iedmee eae 27 Step OpenT Oe E sees aad sana beara lana 21 Stp Sz Se tine Or The Tne Paramotor ici E oct co laias 2I Step 4 Set ne of TINS laica 29 Sepa Sene Dean Parane EiS r 29 Step 6 Setting the active effects and starting the calculations ooccccccccnnnnnononnnnnnnnnnnnnnoo 31 Step 7 Lakin into account particle OS a 32 SEPS OUMU A a A 33 Y Parac le Losas 35 ML AON Bean OD eat ido 37 B oer clin alg pa
48. cture Depending on the user choice ComboBox Lattice functions at point it can be either mean ring lattice mean ring here program automatically takes averaged calculated lattice see TabSheet Mean params or first optics here program counts that reference point is first optic element from the MAD lattice structure or user defined here user must indicate lattices for the reference point see Edit windows on the current TabSheet below 28 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Step 4 Setting of ring lattice If IBS effect is included into calculation depending on the IBS model one has to set ring lattice structure All other effects either use lattice in their location defined in the effect parameters or use lattice in the Reference point IBS Piwinski model needs only mean ring lattice so it is not necessary to set this Form Other models need real or reduced lattice structure of the ring The ring lattice structure can be imported from input or output MAD file Betacool translator does not support all the possibilities of MAD input file syntax and sometime it is necessary to modify the input file manually Therefore for IBS rate calculation it is easier to use output MAD file To provide a choice of the lattice file name and its specification the Menultem RinglLattice Structure and corresponding visual form Fig 6 are used Ring Lattice Structure Lattice Filename Output
49. d user must push Open at Task Model Beam Model Beam to start simulation Fig 12 Step 7 Taking into account particle losses If one plans to use Particle Losses effect go to Effects Particle Losses Fig 11 and choose Generate model particles on losses with distribution It allows to recover lost particle in the model beam BETACOOL operates with two number of particles beams the first number major it contains real number of particles The second one is model beam it usually contains a few thousands particles and is used for dynamics simulation in accordance with active effects When particle is lost due to some factors we have to decrease number of particles in the major beam but the number of particles in the model beam has to stay unchanged The ComboBox Generate model particles on losses with distribution allows to make a choice how lost particles will be recovered in the model beam in accordance with defined distribution from the list Gaussian particles will be regenerated by Gauss Real particle will be regenerated according to existing distribution or None model particles don t re generated and its value decrease If Off is chosen then the model particles don t loss but anyway the number of major particle decrease for example decay process 32 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Effects Particle Losses IOl xj Active Effects Additional Losses
50. dist_ip cur TabSheet Invarinat is plot of all three sorted invariants dist_ex cur dist_ey cur dist_dp cur actually it shows particle number in percent which occupies corresponding emittance abscissa axis 3 J m m Lo FE B E E a Fig 6 Windows of the Beam Distribution menu item TabSheet Evolution Fig 7 3D plot for evolution of Coordinates or Invariants in time evolution sur Tabsheet Control settings for plot on all TabSheets listed above As on every plot window user can choose which plots he wants to be redrawn on line GroupBox Coordinate Profile correspond to first two TabSheets and defines Sigma is range in number of sigmas Division split number normalized on emittance choice of rms parameter for sigma to be normalized on GroupBox Evolution defines settings for 3D plot Slices number of steps in time scale Step sec value of step in time Bi Gaussian show interpolation for profiles sum averaging on time lelx ojx Draw Hi Evolution Coordinate Profile E Coord_x Sigma Li Coord y Divisions 200 a m Coord p T normalised on D ml i co Ed Profile_x C curent initial m E he Profile_p Li Profile_p Era z Slices 100 a W Invariant x z 2 on Step sec fo wo mranani y Mean between slices M Invariant p TF Bi Gaussian aum Po Fig 7 Windows of the Beam Distribution menu item
51. e Betacool is launched with 3d parameter iniz step multiplier Fates Evolution Horizont El Long 30 rate Electron Cooling Emittances pi mm mrad Best Gas Horizontal foom 0 1 Vertical foom 0 1 fo intemal Target Divisions E 4 Logarithmic fo Particle Losses os Momentum Sprea Intrabeam Scattering i E E Momentum fr 5 0 01 eS Stee Divisions 12 M Logarithmic fo es hase Cooling ul Calculate 3D rate Find betacool exe Fig 6 Window of the Task Growth Rates 3D rate 17 BETACOOL User manual 3 Output files As a result of GR Betacool modifies the input file bld format and creates a few files cur which Il Growth Rates Algorithm contain time dependencies of the beam parameters Simultaneously results of GR are visualized to TabSheets of the current Form 2 D plot of the function of Absolute Growth Rates over the time is on the Evolition TabSheet Fig 1 5 and 3 D plots of the growth rates vs transverse and or longitudinal emittances are on the TabSheets Horizont Vertical Long Fig 7 lt parameter gt rates 3d Fig 7 Window of the Horizontal Vertical and Longitudinal 3D Growth Rates Procedure Sum of the rates of active effects Output into input file 3D maps of sum of the rates in the range of the beam emittances specified in and momentum spread specified in Output rateeh sur rateev sur ratedp sur
52. e energy loss value in the simulation If one uses Calculate from material and wants to see value of Density atom cm 2 one should push Button on TasklGrowth Rates Sometime one needs to push Button on the Main Form to redraw parameters 59 BETACOOL User manual IX Internal Target Last update 30 Sep 2007 3 Lattice functions Effects Internal Target Lattice TabSheet Lattice Fig 3 defines the lattice functions in the target position Here the following parameters has to be set Horizontal and vertical values for beta alpha dispersion dispersion derivative Horizontal Vertical Beta m fi 5 74 154 E Alpha 0 Sj Dispersion m fo Type Scattering mode f gas cell f Gaussian pellet Real fiber lolo Dispersion fo derivative Ratio of lonization vs Excitation jo j Fig 3 Lattices amp Type 4 Target type Effects Internal Target Type TabSheet Type is used for choosing the following parameters Type of the target gas sell pellet or fiber gas cell is the uniform gas cylinder pellet is the flux of the macroparticles Fig 3 Scattering Model defines distribution it the target Gaussian according Gauss law Real uniform distribution Ratio of Ionization vs Excitation defines parity between ionization and excitation energy losses 5 Pellet target Effects Internal Target Pellet If type of the target will be pellet or fiber one has to set parameters on the
53. e lt inputfilename gt rates The parameter lt inputfilename gt is obligatory 1 2 Windows interface The interface part of the software consists of executable file Bolide exe dfm files containing information about BETACOOL exterior and input files for post processing of the calculated data The simplest way to start a work with GR is the following to put the Interface files Betacool exe file file of input parameters bld format and other required input files from archived Betacool kit download from website http lepta jinr ru betacool to the same folder to start Bolide exe file load the input file check its validity to import absent parameters from correct input file see below 14 BETACOOL User manual Il Growth Rates Algorithm Last update 30 Sep 2007 to start GR program using TBrowse component Calculate on the Form Task Growth Rates during the calculation the Interface program automatically reads the results from output files and represents them in numerical or graphical format to the corresponding windows The detailed description of the interface is presented in Bolide doc 2 Specification of the task Calculation of sum of the rates To provide a choice of effects acting on the ion beam distribution function one needs to specify the task using menu item Task submenu item Growth Rates Fig 1 210 step multiplier Fates Evolution Horizont Vertical Long 3D rate Electron
54. e dynamics Fig 5 ECOOL Parameters menu item TabSheet Space Charge 2 Electron beam models General parameters of the cooling section must be set using Form ECOOL Electron beam This Form contains the following TabSheets Uniform cylinder Hollow beam Gaussian cylinder Parabolic From File 67 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 2 1 Uniform cylinder On the TabSheet Uniform Cylinder Fig 6 user must choose model of the electron beam using ComboBox Electron beam model there are the following models implemented DC cylindrical electron beam with uniform electron density DC electron beam with elliptic cross section and Gaussian distribution in the transverse plane Hollow electron beam with determined densities in the center and edges and define parameters for the corresponding beam model If Uniform cylinder chosen the current form contains EditWindows for its setting electron Beam radius electron Beam current V_tr gradient derivative of the transverse temperature over radius Neutralization factor it has to be positive and lt 1 ECOOL Electron beam O xj Ame dimensions cm Horizontal fo A Vertical 10 15 E Electron beam mode f Cylinder Gauss cylinder Hollow beam Parabolic Linear electron density cm Uniform cylinde Beam radius em Beam curent A Neutralization 72 Y tr gradient 1 3 1E9 Beam current 4 0 744649244
55. e input file and continue the simulations BETACOOL User manual Interface Last update 30 Sep 2007 1 2 BETACOOL procedures Parameter Procedure rates Sum of the rates of active effects Output into input file 3d 3D maps of sum of the rates in the range of the beam emittances specified in and momentum spread specified in output rateeh sur rateev sur ratedp sur friction 3D maps of the friction force in the range of plot of the friction force components as function of the ion velocity at a fixed angle between the velocity and electron beam axis output ftr cur flong cur plot of the friction force components as function of angle between the velocity and electron beam axis at a fixed 10n velocity output fatr cur falong cur g Generates tables of the friction force in the range of ion velocity output fftr sur fflong sur space Potential distribution inside electron beam output inecool cur charge cur vdrift cur lattice Calculation of lattice functions along the ring collision Choice of parameters for luminosity calculation in the frame of Model Beam algorithm injection Visualization of the initial ion distribution when the injected beam parameters are dynamics RMS dynamics algorithm model Model beam algorithm tracking Tracking procedure Note program analyses only the first letter in the parameter name If lt parameter gt field is empty the program reads input file and generates list of parameters skipped in the
56. es The friction force components acting on the ion inside the electron beam can be calculated using different analytic formulae and in principle using results of numerical calculations Choice between different presentation of the friction force is provided by ComboBox Friction Force Model of the TabSheet Model of the ECOOL Friction force menu tem window Fig 10 For the 69 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 moment the following formulae realized in the program Budker formula Non magnetized Derbenev Skrinsky Meshkov Parkhomchuk Erlangen Tabulated 3D for electron Array When user chooses a model for friction force calculation some necessary parameters can be determined in corresponded EditWindows of TabSheets on the current Form If Tabulated model is chosen then user must indicate file with tabulated values of friction force component pre calculated by another program see ECOOL Tabulated At the TabSheet Model electron beam characteristics quality can be selected to be represented as one of the following corresponding parameters transverse and longitudinal emittance temperature or rms velocity User must set the appropriate values in selected pair of parameters ECOOL Friction force 2 Ol x Model Non magnetized Magnetized Parkhomchuk Erlangen Electron array ECOOL Friction force _ O x Nurmencal Asymptotic te Numerical se Derbenew a Meshkay El Smath rho mas Numeric
57. eters Example of the cur file format 0 0 000364 9600 109 18 00003703453546 36 9s 0003063022994 54 0 0003430464386 12 0 000S SO LAGTS 90 O ODO3SOS4 7 31154 99 0000290051200 108 00002 71960398 0 0 Ly OOJO 25 6 1 ee TOLL The first column of the files with beam parameter time dependencies contains the current time in sec second column values of corresponding variable The columns are divided by tabulator symbol Strings are finished by the end of line symbol List of graphs is described in Appendix The files sur contain functions of two variables Example of sur file 9 BETACOOL User manual Interface Last update 30 Sep 2007 0 0000333333 0 000666666 0 001 0 0 000333333 2 90404e l2 2 98364e 12 Ze 204 18 12 2 9804e 12 000666666 2 16460e 12 2 16452e 12 2 16426e 12 2 1638e 12 001 1 01881e 12 1 01879e 12 1 01873e 12 1 01864e 12 OOOO First element in the first string of the file is empty Other elements in the first string contain the value of first variable The elements of the first column contain the values of second variable Corresponding value of the function are placed at the cross of the string and column Numbers in the string are divided by tabulator symbol Strings are finished by the end of line symbol For post processing of the output BETACOOL files one can use any graphical editor 2 Working with windows interface The interface part of the software consists of executable file Bol
58. f integration steps can be a few hundreds for each variable if 1 accuracy 1S necessary To calculate the rates one needs to use menu item Task submenu item Growth Rates and push the button Open at the TabSheet Rates of the corresponding visual form See in details below To estimate the Coulomb logarithm value required for other models one needs to chose Integral over z Coulomb logarithm and adjust the log value to have the rates close to numerically calculated The value in edit window Coulomb logarithm in Martini tab sheet has to be divided by 2 and thereafter it can be used as a Coulomb logarithm in Jie Wei or Bjorken Mtingwa models In presence of the vertical dispersion in the ring one needs to use Bjorken Mtingwa model This model is realized in Betacool in accordance with its modification proposed in the article M Venturini Study of intrabeam scattering in low energy electron rings Proceedings of the 2001 PAC Chicago pp 2961 2963 and the growth rates are calculated tacking into account the vertical dispersion and its derivative To use this model one needs initially to estimate Coulomb logarithm value using Martini model If the ring is operated above transition energy to speed up the calculations one can use Jie Wei or Gas relaxation model Piwinski model can be used when the ring is operated above the transition energy and this model does not require ring optic structure This model can be used for preliminary e
59. force calculation developed by group from Erlangen University This model has algorithm which combine calculation of the friction force for both magnetized and non magnetized fast collisions On the TabSheet there are 3 CheckBoxes presented Fast Tight Stretched When any combination of them is switched ON different options of calculation are taken into account in algorithm If to take into account during calculations fast collisions user has to check Fast CheckBox During magnetized interaction there are 2 models of the electron Larmour spiral to be presented as a Tight helices and Stretched helices Also there are 3 EditWindows for definition of the number of integration steps over velocities during numerical calculation of the friction force value over longitudinal velocity over transverse velocity over azimuth are presented 71 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 3 6 Electron array TabSheet ECOOL Friction force Electron array Fig 12 EditWindows for integration step numbers are presented which are parameters of the 3D friction force calculation for the case when electron beam is presented as an Array of particles Here are number of integration steps over velocities can be defined over longitudinal velocity over horizontal velocity and over vertical velocity 4 Using of Friction forces drawing tool Form ECOOL Draw Forces Fig 13 is a toolkit for checking 3D shape of friction force
60. g warning START 2006 7 11 24 13 4 22 2 39 D sao GSI 2006 betacool_GSI_v2 betacool exe NE bld rates Cannot open file NE bld and stops the calculations All the messages and warnings generated by the program during calculations are saved in the current folder to the file Betacool war Depending on lt parameter gt value Betacool can execute corresponding procedure and stop the work or provide simulations in infinite cycle In the last case to stop the work of the program one needs to create in the same folder the file bolide stp The program will delete this file and stop the work To pause the calculations for instance to edit input file one needs to create in the same folder the file bolide pau To continue the calculations one needs to delete this file To change parameters during calculations one needs to make necessary editions in the input file and create the file bolide run The program will re read the input file delete the bolide run file and continue the calculations when working with interface these files are generated by the interface tools During simulations the program creates output files and saves them in the current folder To save a total set of input and output files for further post processing one needs to execute SAVE bat file In the current folder the subfolder with the name lt inputfilename gt will be created and all input and output files will be copied into this subfolder Whereupon one can renam
61. he following possibilities chosen with RadioButton Reference Energy Lorenz factor y Gamma Particle velocity in the units of the speed of light Beta Kinetic energy Kinetic Particle momentum in GeV c Momentum The chosen option corresponds to input parameter all other numbers will be recalculated after launching the Betacool program The kinetic energy can be set as a total value or divided by number of nucleons The units of the kinetic energy are to be chosen using combo box aligned with the corresponding edit window The Atomic mass is set as a number of nucleons in the nuclei and usually it is integer number The rest energy of the particle is calculated in the program as A 938 MeV In principle the atomic mass can be arbitrary positive number and the IBS growth rates can be calculated for different particles muons electrons etc The parameter Charge number corresponds to the charge state of the ion and can vary from 1 to the atomic number The Charge number is set as an absolute value for instance as for protons as for antiprotons Z 1 43 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 The input parameter Life Time Decay is used for the particle loss simulations only For the rate calculation it can be arbitrary 1 2 Lattice parameters of Ring The storage ring circumference Lorenz factor corresponding to the ring transition energy horizontal and vertical tunes have to
62. he ion number Like any other Effect IBS Additional Heating etc the electron cooling model returns heating and loss rates what is a part of 64 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 the Effect library Separate menu item ECOOL is intended for electron cooling due to complicated structure of this Effect To calculate the cooling rates user needs to determine models of the cooler general parameters of the cooling section ion beam models of the electron beam formulae for the friction force calculation from corresponding library parameters of the tables of pre calculated friction forces plot tools for checking Ecool parameters validity To make the procedure clear these four steps are divided into four submenu Items and can be done independently using corresponding windows Additional useful tool is developed for studying of cooling friction force behaviour It is pointed in the submenu tem Draw Forces 1 1 Cooler parameters On the TabSheet Cooler of the ECOOL Cooler Window Fig 3 using ComBox element Cooler model user must choose calculation model for the ion coordinates after crossing the cooling section Thin lens model only angle variation or numerical integration of the ion motion equation The numerical integration can be performed by two methods Euler Euler method or 4 th order Runge Kutta RK method For the numerical integration one needs to determine the number of integrat
63. he longitudinal profile Fig6b green line is calculated in accordance with parameter Longitudinal profile divisions Fig 4 red line is the average particle density in each barrier black line integration of particle along longitudinal coordinate Intrabeam scattering heating rates are calculated via longitudinal density of particle which can be chosen in parameter IBS normalized Fig 4 on longitudinal divisions means that IBS is calculated in accordance with particle density with longitudinal divisions on barrier divisions in the accordance with particle density in barrier region Ring Barrier Bucket Fig 6 a Particle and barrier distribution in the longitudinal phase space and b particle density along longitudinal coordinate Moving barrier bucket The moving barrier can be used for manipulation with particles in the longitudinal phase space Note that integration step for this task should be much smaller than synchrotron tune and option Random synchrotron Fig 7 should be switched off Task 7 Model Beam _ O xj Betatron tune C Regular for whole beam Random for whole beam C Random for each particle Coupling resonance rate Hz 5 Random synchrotron Find betacool exe Fig 7 Options for betatron and synchrotron tunes 47 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 Moving Bucket File
64. heet Characteristics Fig 8 includes beam parameters calculated when main parameters of the beam and ring are determined For more detailed information about setting Beam parameters please see Beam Manual Step 6 Setting the active effects and starting the calculations To switch ON active effects into simulation the Menultem TasklGrowth Rates is used Left part of the corresponding visual form contains the list of the effects that can be used in simulations An effect is switched ON in simulations when the corresponding step multiplier parameter has integer non zero value If this value is integer positive it defines how many times the effect will be In the Fig 9 an example of the task specification when the Electron cooling Internal Target and Intrabeam Scattering effects are active is presented For more details about each effect one has to look their description IBS Manual Rest Gas Manual Target Manual et al Any integer value of step multiplier means that this effect 1s active Positive value more then unit means that this effect skip a few integration steps in accordance with step multiplier and applies the kick one time per a few integration steps Negative value means that this effect applies a few kicks per one integration step This possibility can be very useful if the different effects have a different calculation time or different values of kicks io xi step multiplier Fates Evolution Horizont
65. iant x a A Step sec 2 j E w lavariant E overa e Mean between slices jf Invariant p iw Show Bi Gaussian Fig 12 Form Beam Distribution Form Beam Real Space Fig 13 includes 4 TabSheets used for visualization of the particle distribution in different planes during simulation procedure and a special TabSheet Control which is a manager of plots user can choose which plot is active for on line redrawing and what a coordinate plane will be represented on it for example X Y transverse real space of particles X X horizontal phase space X dP P longitudinal real space S So dP P longitudinal phase space More detailed description is given in Beam Manual 33 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Beam Real Space Siz E Beam Real Space Siz E Space D Space W Draw Draw MEHE y axis MEHE E Space 2 Space 3 W Draw Draw MEHE y axis MEHE E E En 5 50 PP Fig 13 Form Beam Real Space Form Beam Evolution Fig 14 is intended for visualization of beam parameters evolution during simulations and includes the following TabSheets for time dependencies of horizontal and vertical emittances Emittance momentum spread Momentum particle number Number horizontal emittance on the momentum spread 3D Diagram bunch length Bunch TabSheet Control allows user to manage the visualization It contains list of all the plots of the cur
66. ide exe dfm files containing information about BETACOOL exterior and input files for post processing of the calculated data The simplest way to start a work with BETACOOL program is the following to save the Interface files Betacool exe file file of input parameters bld format and other required input files from archived Betacool kit download from website http lepta jinr ru betacool to the same folder to start Bolide exe file load the input file check its validity to import absent parameters from correct input file if necessary to start BETACOOL program using one of the TBrowse components in the visual Windows of the Interface and click Open button BETACOOL program is working as Win application and stops the calculations after their completion or can be stopped using corresponding Interface tool during the calculation the Interface program automatically reads the results from output files and represents them in numerical or graphical format to the corresponding windows The detailed description of the interface is presented in Bolide doc 2 1 Load input file check its validity import of absent parameters After start the Bolide exe file the main window of the interface is opened Fig 2 if the desktop was saved the windows active in previous run are opened also Main window manages the interface operation and has global menu and buttons which duplicate actions from the Files menu The bar title indicate
67. ion Core from FH bi Stop time sec fie to 4 Common betatron tune W Random synchrotron tune Find betacoal EXE Fig 10 Form Task Model Beam After that one should choose IBS kick model at the Form Task Model Beam Bi Gaussian Fig 10 ComboBox 1BS model gives user a choice of model for kick applying on particles Gaussian momentum deviation is distributed on particles in accordance with Gaussian law Bi Gaussian particle beam distribution is assumed as sum of two Gauss distributions one for core another for tails momentum deviation is distributed on particles in accordance with two independent Gausses and area where they are overlapped FWHM momentum deviation is distributed on particles assuming Gaussian distribution with determined FWHM The detailed description of these models one can find in IBS Physics Guide Core definition describes how many particles in the rms sigma units are defined as core particles Invariants in core is describes how many invariants horizontal vertical and longitudinal are used for the definition of the particles in core User can set the Correct core number in the accordance with Invariants in core otherwise the particle number in the core the will be used from Bi Gaussian or FWHM interpolation Core from FWHM means that the core sigma always is defined from FWHM method anyway the tail sigma is defined from choosing IBS model When all parameters are define
68. ion steps along the cooling section MEE aix Cooler lon Beam Lattice Shifts Space Charge Cooler Fon Beam Lattice Shifts Space Charge z lon beam mode Cooler length m 11 8 l l E f Single particle f Monte Carlo Magnetic field kG 11 Section number ME fi Number of integration step Particle number Bunch number f Transverse E fi 000 Distance between bunches m 0 2 Longitudinal f aa bunch beam Cooler model Thin lens Integration steps fao FF Fringe Field Fig 3 Window of the ECOOL Cooler menu item TabSheet Cooler amp Ion beam User must specify the following cooler parameters on this TabSheet cooler length magnetic field magnitude section number number of section of cooler this parameter is used only when Model Beam algorithm If to switch ON RadioButton Fringe Fields then effect of fringe fields of cooling solenoid will be taken into account for calculations 1 2 Ion beam model The cooling rates can be calculated for r m s particle using Single particle model using settings on the TabSheet lon beam of the ECOOL Model Window Fig 3 Rates are calculated by averaging over phases of betatron and synchrotron oscillations Numbers of integration steps over the phases are input in corresponding EditWindows Transverse and Longitudinal 65 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 1 3 Lattice parameters The lattice parameters at the
69. ity to take into account particle losses on target interaction the same definition as for internal target Electron capture Single scattering Nuclear reactions Parameter Mean vacuum chamber radius is used for the calculation of the beam stability average beam radius should be smaller than mean vacuum chamber Do not forget check options Scattering on Rest Gas on the Form Effects Particle losses 62 BETACOOL User manual X Rest Gas Last update 30 Sep 2007 Effects Rest Gas Effects Particle Losses jaj m F 1 Ej m E 1 Fig 2 Particle losses parameters for Rest Gas 63 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 XI Electron cooler Introduction After launching the Bolide exe file and checking a validity of an input file one needs to set the storage ring and beam parameters using corresponding menu items of the main interface window Fig 1 D sao betacool RHICmb BLO z oj x File Beam Effects ECOOL Ring Task 2458 32 ln 0 1 0 Fig 1 Main interface window Electron cooling effect thereinafter Ecool implemented in BETACOOL is the most developed effect and has rather complicated structure That s why it is excluded from the effect list Menu Item Effects and a special Menu Group ECOOL is dedicated to the setting of electron cooling User must use this menu item and step by step to set parameters of the cooler electron beam friction force etc This procedure is give
70. ka Number of steps 200 Humber of steps fao T Nonlogarithmic term Fig 11 ECOOL Friction force TabSheet Magnetized When Numerical integration is chosen here user also has a choice which formalism to select for integration Item of RadioButton Derbenev s integral or Pestrikov s integral For each integration method user has to determine Number of steps If CheckBox Nonlogarithmic term is switched ON then plasma wave irradiation is taken into account 3 4 Parkhomchuk s model If Parkhomchuk model for the friction force calculation is chosen user via Parkhomchuk TabSheet Fig 11 can define parameter Effective temperature eV or it can be interpreted as Angular spread rad which is used in Parhomchuk formula 3 5 Erlangen model ioxi C001 Friction force E Model Non magnetized Magnetized Farkhomchuk Erlangen Electron array Model Non magnetized Magnetized Parkhomchuk Erlangen Electron array Number of integration steps E Nubmer of integration steps Over longitudinal velocity 44 SA z Fast ver longitudinal velocity Boo o 15 Tight Over transverse velocity 44 Analitye density Over transverse velosity 15 Stretched Over azimuthal velocity 33 Over azimuthal velocity 15 Fig 12 ECOOL Friction force TabSheet Erlangen Electron array TabSheet ECOOL Friction force Erlangen 3D Fig 12 lets user to specify parameters for the model of friction
71. l VIII Intrabeam Scattering Last update 30 Sep 2007 The models Piwinski Jie Wei and Gas relaxation Fig 5 are valid only when a storage ring 1s operated above transition energy The model Detailed is used in Model Beam algorithm and for the rate calculation can not provide an accurate result Effects Intrabeam Scattering i Ioj x Martin Jie wei Gas relaxation Ejorken IBS model a Integral divsion mu 20 ru 20 z 20 Integral over z Martini Coulomb logarithm Coulomb logarithm 40 Gas relaxation Tl Biorken Mtingwa Fig 5 The visual form for choice of the IBS model ComboBox IBS model When alpha function and dispersion derivative are equal to zero the 3D Martini integrals can be reduced to 1D integral as it was shown for the first time in the article A Piwinski Proc 9 Int Conf on High Energy Accelerators p 105 1974 This integral is calculated in Betacool with rectangular method the model is called Piwinski Number of the integration steps has to be input in the TabSheet Martini in the edit window Integral divisions mu Fig 5 This number has to be adjusted manually Calculation of the IBS rates using Piwinski model does not require the ring optic structure For the rate calculation the program uses mean lattice functions that output in the tab sheet Mean params of the Ring Parameters visual form Fig 6 Ring Parameters Ioj x lon kind Lattice Mean para
72. lar momentum variation the diffusion is simulated using random number generator Tracking provides a tracking of a particle array along the ring circumference with arbitrary step using Molecular dynamics technique for intrabeam scattering simulation The software is divided in two independent parts physical code BETACOOL which is written using only standard C syntax and interface part which is an executable program working under Windows environment BOLIDE Connection between two parts of the program is provided using three types of the files input output and file used for control of the calculation process Such a structure on the one hand allows to use the program on PC to control and analyse results during simulations From the other hand the physical part of the program compiled for UNIX operation system can be used for calculations independently on interface BETACOOL User manual Introduction Last update 08 Nov 2008 Contents MTT nc 6 o E sent ere Tee Mere emery yen eee nee Sere ery 6 L Work without graphical traia a 7 1 1 Starting the calculations control of the calculation prOcessS oooccccccccconnnoocnnnnnnnnnnnnonannnnnos 4 t2 DE VAC OO LL Proc US y E 8 SA A O RIO 8 LAO te oo 9 2 Working With Windows Interlace idas 10 2 1 Load input file check its validity import of absent parametefPs cccccccccccessseeeseeeeees 10 2 2 Parameters of calculation for Windows Interface ccccccoooooonncn
73. locities As a result 2 files table lvt and table tvt will be automatically created in the current folder If user want to use pre generated tables for electron cooling effect calculation or for drawing the 3D friction force shape it is necessary to 1 choose the model Tabulated in Ecool Friction forcel Model 2 Specify 2 files with tables using at Ecool Tabulated Control 7Browse components for files 3 Choose at Ecool Tabulated Interpolation a method for interpolation for calculation of friction force values using the table 75 BETACOOL User manual XII Gated Stochastic cooling Last update 08 Nov 2008 XII Stochastic cooling 1 Standard Stochastic cooling 1 1 Transverse degrees of freedom For each transverse plane the program uses standard set of input parameters for the cooling chain description Fig 1 that are listed in the Table 1 Effects Stochastic cooling e Oj xj Horizontal Vertical Longitudinal Common parameters M Use Lower frequency ja GHz Me liae E B220 Upper frequency fe GHz fe logarithm fao dE Electrode length E Em Optimum linear gain 115353 3095 Pick kicke Electrode width Electrode width j E em Gap height Gan height fi E jem Humber of loop pairs Number of loop pairs 32 Beta function E Zj m Beta function ps O S m Approx length Ba 000 m Approx length ure m Sensitivity ost ALIS Sensitivity os 71523357 Thermal noise power 0 008836277255 Wl Schottky powe
74. mediately will shutdown with correct saving all the calculated results All those buttons are duplicated as menu items in Main menu To check a validity of the input file one needs to use menu item TasklParameters and push the button Open at the TBrowse component Check parameters Fig 3 This component starts Betacool without parameter The program reads input file and generates list of parameters skipped in the input file and their default values and saves it in the Betacool war file aa MEETS lala Save Results to EFolder Number of skip points Find save bat fo Size of cumes Auto Saving Interval 2000 fa sec W Auto akip of points Check parameters Check parameters Find betacool exe Find betacool exe Fig 3 Window Task Parameters To read the Betacool war file one can use menu item FilelEditor or corresponding button from the toolbar The internal editor 1s generated to open the Betacool war file If the input file contains total set of input parameters the warnings are absent Fig 4 11 BETACOOL User manual Interface Last update 30 Sep 2007 HF oax AA START 2006 11 24 17 D sao GSI 2006 betacool GSI_v2 betacool exe EDMD bld Input parameter initialised with default value O Input parameter initialised with default value Input parameter initialised with default value Input parameter initialised with default value Input parameter initialised wi
75. ms RF system Injection point B arrier bucket Mean ming parameters Mean radius Horizontal beta function 21 6527015 rn Vertical beta function 20 31043364 rn Dispersion 07683740775 im Revolution period 1 270007 005E 5 sec Off momentum factor 0 001 os a Ed Fig 6 Mean lattice parameters using for IBS rate calculation in the frame of Piwinski model Above the transition energy and under a few additional assumption the Martini integrals can be reduced to elementary functions as 1t was shown in 57 BETACOOL User manual VIII Intrabeam Scattering Last update 30 Sep 2007 Jie Wei Evolution of Hadron Beams under Intrabeam Scattering Proc of PAC 1993 p 3651 To calculate the growth rates in accordance with Jie Wei model one needs to input Coulomb logarithm value in the corresponding tab sheet usually the log is about 20 Additional simplifications are related with high energy approximation and neglecting of dispersion The Gas Relaxation formula is based on additional assumption that the beam has a flattened velocity distribution so that the temperature of longitudinal degree of freedom is sufficiently less than transverse one 4 Summary how to provide a choice of IBS model Initially one needs to choose Martini model and Integral over z Numerical Thereafter by a few consequent calculations of the growth rates the Integral divisions have to be adjusted to required accuracy typical number o
76. n barrier height Amplitude kV defines the amplitude of the barrier RF duration barrier width in the circumference unit Gap duration distance between barriers in the circumference units Barrier height dp p calculates the barrier height in the momentum spread units RMS amplitude dp p momentum spread after fitting in the accordance with barriers parameters can be substantially less than input momentum spread Bucket length m RMS bucket length Synchrotron period sec synchrotron period of RMS particle Stationary bucket Stationary Bucket File Fig 5a has two columns first is position of barrier in the unit of circumference second is amplitude in volts First barrier always start from position 0 5 and file can not have position 0 5 If barrier position 0 5 is not included in the file it means that last barrier has position 0 5 with zero amplitude Red line Fig 3b is amplitude distribution blue line is integral of barrier amplitudes kV m It can be normalized on the maximum amplitude of barriers if Normalize Potential Integral options is chosen Fig 4 46 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 E m SHPlo RQF AA Row 1 8 Col 1115 E Fig 5 a File for definition of stationary BB b amplitude and integral distributions The particle distribution and barrier positions in the longitudinal phase space are shown on Fig 6a T
77. n in details below As a matter of fact if user wants to switch ECOOL effect as active into simulation it is necessary to switch step multiplier corresponding to the Electron cooling on the Form Task Growth Rates Fig 2 to non zero value for details please look for Numerical algorithm manuals iol xi step multiplier Rates Evolution Horizont Vertical Long 3D rate Horizontal 0 02728357785 1 sec Wertical 0 0061 36204922 1 zec Electron Cooling Rest Gas Internal Target Collision Point Longitudinal 3504746198 5 sec Particle number ja sec Calculate Find betacoolexe e Draw Evolution of Fates Particle Losses Intrabeam Scattering Additional Heating Stochastic Cooling shhh Optical Stoch Cooling a di Laser Cooling Fig 2 Effect switching panel One needs to choose menu item Ring submenu item Parameters For Ecool effect all the parameters have to be defined depending on the algorithm chosen How to set the Ring parameters please look RING manual Parameters of six dimensional phase volume of the beam required for Ecool rate calculation are set in the TabSheet Emittance of the Beam Parameters visual form For more detailed description of beam parameters definition please look BEAM Manual 1 Electron cooler In this BETACOOL version electron cooling is treated as an Effect acting on the r m s parameters of the ion distribution function and changing t
78. ndition is Input MAD format must be chosen in Lattice structure File RadioGroup 50 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 A table below presents different modes of usage the Ring Lattice Structure Lattice Filename RadioButtons for selected tasks for details see description of Task Algorithm Radio button INPUT No optics COMMENTS MAD FORMAT in case when Piwinsky model of IBS calculation was chosen Model Beam if chosen No optics user y y y has to fill type in the ring transformation matrix Ring Lattice Structure Lattice Filename Output MAD format Column Positions of Lattice Functions MAD User definition of Column Positions dist beta jer les beta y alta fo fe alta y Ml atri Complex value C Optics Index f Real Abs f Ring jo ul C Imag Arg Sa As Sa a i 8 591 085621E 10 1 Det Fig 12 Window of the Ring Optic structure menu item TabSheet Matrix The next TabSheet Matrix see Fig 12 is useful tool for looking at the transformation matrix of the whole ring or selected optic element One can choose to look at either transformation matrix of the whole ring Ring or selected element from optic structure Optics by choosing its number with Index Counter Here complete transformation matrix is visualized There is an option to look at any part of numerical appearance of matrix elements if it is introduced as complex o
79. ne One can choose the representation by switching Real Imag Abs Arg RadioButtons Here EditWindow 1 Detl introduces the precision of calculated matrix determinant 2 3 Checking of input files To check validity of the MAD file specification one needs to start Betacool using button Open of TBrowse element Calculate Lattice in the left bottom corner in the Fig 9 This button starts Betacool with parameter lattice Betacool reads MAD file in accordance with specification at the tab sheet Output MAD format Fig 10 If the positions of the lattice functions in the file correspond to the specification Betacool outputs the lattice functions into corresponding cur files BetaX cur BetaY cur DispX cur AlfaX cur AlfaY cur DispX_ cur these curves are shown in the TabSheets beta functions and alpha functions of the Form Ring Lattice Structure Fig 9 Betacool stops the calculation after without any warning see example in the Fig 13 If the lattice function positions do not correspond to the specification Betacool generates the following warning 51 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 START 2007 7 27 2Zoa 17 9349 D betacool betacool exe esr BLD lattice Error in Lattice Structure file esr tis Press Enter to continue and stops the calculation after pressing Enter The warning is saved in the Betacool war file and can be read using Bolide text editor menu item File submenu item Edi
80. ned as 95 normalized emittance and momentum spread is defined in absolute value GeV c User can input transverse emittance and momentum spread in the 37 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2007 format of the BETACOOL definition and check these parameters in other units Fig 1 Normalized emittance is calculated from one sigma un normalized emittance as Enorm PYAGSE rms gt where fy relativistic factors ng 2 In 1 a 100 number of sigma calculated via percents of the particle number a for the Gaussian distribution For Recycler measurements usually a 95 which is corresponds to n 5 991 rms sigma The momentum spread in the absolute value can be calculated from the relative momentum spread as Ar al M GeV c Fo P abs 0 rel where M is the particle momentum in GeV c Fig 1 4 The energy spread is defined as AE y l AP o abs Y Fo rel where K particle kinetic energy If the kinetic energy was defined per nucleon then energy spread will also defined as GeV u K GeV Beam Parameters IOl x Beam Parameters Oj xj Emittance Injection Stability Bunch Characteristics lon beam Barier bucket Ime un normalized and normalized 95 5 991 me Horizontal 0 02 11138472789 pimm mrad peromemrad Vertical 0 02 EE 11138472789 momentum and kinetic energy spread Longitudinal 0 0002 1 77 Meve ion beam model particles Fa
81. nformation about setting Ring parameters please see RING Manual Step 5 Setting beam parameters One needs to choose Menultem Beam Parameters Fig 7 Use Emittance TabSheet to set up Ion beam state Horizontal emittance Vertical emittance Momentum spread and Number of particles Here number of particles means number in the main not modeled beam and this number is used for particle losses calculation evolution of beam particle number Model particles 29 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 number we recommend to set it not less then 1000 but the time of calculation depends proportionally on the number of particles both as accuracy Model particles will be generated in concordance with indicated emittance values and type of Emittance definition Beam Parameters IOl xj Beam Parameters IOl x Initial distribution Gaussian a FF Injections with interval sec 10 4 Number of injection cycles E File with initial distribution Find fleir2 inj Draw initial distribution Find betacool exe lon beam state Coasting Horizontal emittance 150 pi mm mrad Vertical emittance 50 pi mm mrad Momentum spread 0 001 Number of particles 1E9 Ey Model particle number fi 000 rr i FE Ramee eC CARI Root Meam Square E MECA Momentumn spread shift o ai e Horizontal shift m o E Enclosed Persents Transverse E 35 Vertical shift m o
82. ntal beta function 10 39 703071 m BE voltage k 50 Vertical beta function f 1 04684513 Im Separatris size 100 E Dispersion 3 057350208 rn Revolution period 8 922795638E 7 sec Saparatrix length m fi 1 1055 Off momentum factor 0 28021 45673 Synchrotron tune 0 0381 4866195 Induction acceleration f 0 3 Fig 2 Window of the Ring Parameters menu item TabSheet Mean params RF system 44 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 1 4 RF system for bunched beam If the beam is bunched one needs to set RF harmonic number and amplitude of the RF voltage in the TabSheet RF system Fig 2 The Separatrix size parameter is used for the particle loss simulation and it can be arbitrary positive number Separatrix length and Synchrotron tune are output parameters The check box Induction acceleration has to be not checked Variable caption Harmonic number J Jooo O RF voltage RV ae Ue of particles involved into longitudinal invariant Induction acceleration __ boolean Used if induction acceleration is presented Induction acceleration voltage Amplitude of the induction acceleration field Separatrix length Lsep CIN Synchrotron tune o 1 5 Reference point The TabSheet Reference point Fig 3 is used for matching of the particle array with the ring optic structure in the frame of Model Beam algorithm For the rate calculation the lattice functions in injection p
83. nterval number of injection cycles indicate file with pre generated array of injected particles Shift of longitudinal momentum Momentum spread shift Shift of horizontal and vertical positions of the injected beam Horizontal shift Vertical shift Horizontal and Vertical acceptances at injection Horizontal acceptance Vertical acceptance To adjust RF system parameters to the required bunch length in the case of bunched beam the TabSheet Bunch can be used Fig 8 This tab sheet contains one input parameter Number of bunches This parameter is necessary for luminosity calculation only and in IBS rate calculation it does not play a role It can be arbitrary positive non zero number After starting Betacool the program outputs rms bunch length corresponding to relative momentum spread of the bunch and RF system parameters By a few subsequent runs of simulations one can adjust RF voltage or harmonic number to have required rms bunch length 30 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Beam Parameters 2 Oj xj Beam Parameters lOl xj z i 0 056395126589 Number of bunches HE sust tal m Longitudinal form factor 2 969620885 RMS bunch length f em Space charge impendances Maximum particle number fi Longitudinal 11830 60357 Ohm Stella WE f Transverse 166005092 7 Ohm m Bunching factor f Peak current 0 002508273678 4 Fig 8 Beam Parameters Bunch amp Characteristics The TabS
84. oint can be arbitrary It determines parameters of some Ring point it can be point of beam injection or just a reference point for dynamics calculation Here a ComboBox Lattice functions at point is intended for the selection of lattice parameters at reference point To avoid errors at initialization of the program variables the beta functions have to be nonzero positive Unit Alpha Horizontal and vertical alpha functions m Dispersion derivative Horizontal and vertical Dispersion Derivatives Ring Parameters Ioj x Lattice functions at injection User User Lattice functions Horizontal Vertical Beta rn fro 22 Alpha o o Dispersion m jo o gt Fig 3 Window of the Ring Parameters menu item TabSheet Reference point amp Burrier Bucket There are the following 3 Items are presented Mean Ring when mean Ring lattices are taken for calculations First Optics when lattices of the first optic element are taken from file with lattice 45 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 structure User when lattices at reference point are taken in accordance to user definition which can be made using EditWindows at the current TabSheet below presuming the following input and output variables 1 6 Burrier Bucket model Parameters of barrier bucket BB are defined in Form Fig 4 Three options of BB model are realized in BETACOOL
85. on are set in the TabSheet Emittance of the Beam Parameters visual form For more detailed description of beam parameters definition please look BEAM Manual 1 IBS parameters The menu item Effects submenu item Intrabeam Scattering is used to provide a choice of the model for IBS rate calculation The corresponding visual form Fig 2 contains ComboBox IBS model check box Average transverse and four TabSheets for input parameters of different models Effects Intrabeam Scattering Ioj x Martini Jie Wei Gas relaxation Ejorken IES model Integral over z Martini Numerical ag Coulomb logarithm Fig 2 The visual form for choice of the IBS model The current version of Betacool calculates the IBS growth rates for uncoupled transverse motion only In the case of residual coupling or at work near coupling resonance the transverse rates can be averaged using the check box Average transverse If it is checked the program calculates the transverse rates for uncoupled motion thereafter calculates mean value and the both horizontal and vertical rates are put to be equal to this mean value This option is used for instance for RHIC 54 BETACOOL User manual VIII Intrabeam Scattering Last update 30 Sep 2007 simulation when the coupling is introduced to have a round beam in the collision point In the general case this check box has to be not checked A few analytical models proposed for IBS growth r
86. on type atomic mass charge number lifetime on the TabSheet Lattice circumference gamma transition horizontal and vertical tunes chromaticities acceptances longitudinal acceptance on the TabSheet RF system harmonic number RF voltage separatrix size induction acceleration 1f needed More detailed description of this Form is given in Ring Manual Note if IBS effect is chosen user must check how to specify Ring lattice If Piwinsky model of IBS is chosen Form Effects Inrabeam Scattering IBS model user has nothing to do with ring lattice and setting parameters in Ring Parameters Lattice is enough If another IBS model is chosen it is necessary to load a file with ring lattice structure One has to call Ring Lattice Structure and specify a file with lattice in TabSheet Lattice Filename TBrowse Output MAD filename For detailed description of IBS effect setting up please look IBS Manual By next step user must specify parameters of GR using Form Task Growth Rates Fig 1 If user wants to calculate only immediate rates one has to use TBrowse component Calculate which starts the calculations This Form contains four edit windows for representation of sum of the rates of corresponding rms beam parameter In case of successive calculation the program does not generate any warning and stops the calculation process The Betacool war file contains only information about calculation time Fig 4 16 BETACOOL Use
87. or transverse and longitudinal components Equilibrium point can be found if one overlaps these pictures each other Fig 9g Position of this point does not depend on initial coordinate For very complicate pictures more then one equilibrium points can be found In this case the equilibrium parameters can depend on initial values Fig 9g shows the dependence of the transverse emittance on the momentum spread during cooling process for r m s dynamics on Fig 7 Initially the electron cooling force achieves the equilibrium with transverse component of IBS During this process the emittance and momentum spread are decreased evolution from start point on Fig 9 Then cooling process continues and beam parameters change in accordance with the equilibrium boundary of transverse component Momentum spread continues to decrease but transverse emittance begins to increase When the cooling force also reaches the equilibrium with longitudinal component of IBS beam parameters achieve the equilibrium point which does not depend on initial parameters end point on Fig 9 r m s dynamics is rather different and the cooling time can change very strong It means that initial parameters of ion beam don t influence on the equilibrium point but they have a strong influence on the cooling time 19 BETACOOL User manual Il Growth Rates Algorithm Last update 30 Sep 2007 IBS IBS ECOOL 10 10 10 Horizontal Emittance pi mm mrad 0 1 Horizontal Emit
88. p O 000000 Syd F Super 1 ELEMENT SECUENCE HORIZONTASL pos element acc dist 1 hetax alfax mux x co pxicoj Dx Dpx I betay 001 begin MAFM 1 a 7 1 a o o 5 o 7 1 DRIFTS 1 0 710 5 720 0 669 0 018 0 0000 0 000 5 363 0 000 6 499 2 DRIFTS 2 1 420 4 615 0 667 0 040 0 0000 0 000 5 363 0 000 5 765 3 DRIFTS 3 130 3 526 0 444 0 067 0 0000 0 000 5 363 0 000 5 246 4 DRIFTS 4 2 540 3 353 O 222 0 099 0 0000 0 000 5 363 0 000 4 933 5 DRIFTS 5 3 550 3 195 0 000 0 133 0 0000 0 000 5 363 0 000 4 525 6 DRIFTS 6 4 3 a a o 0 000 5 363 0 000 4 033 E Row 1 31 Col ii Lae re Fig 10 Example of output MAD file Another 7Browse component at the Form Ring Lattice structure Fig 9 is Make output MAD file which allows to launch MAD application in the framework of BETACOOL and to create file with lattices in format of MAD output file Here user must indicate MAD input file with find Input MAD file component and then to launch TBrowse component Make output MAD file to start MAD program generate output file with tracked lattices Input MAD format is used for choosing the input file name for multi particle tracking BETACOOL program can read optics and lines from the standard input MAD file and translate to the optics structure of the storage ring Fig 11 Input MAD file is needed to provide tracking using Molecular Dynamics algorithm Betacool translator does not support all the possibilities of MAD input file syntax and sometime
89. pi mm mrad 0 0016 Momentum spread 100000000 Number of particles O bunched 0 coasting 1 O Collider regime 0 1 0 008281840936 Mean beam radius m LO of 0 Longitudinal Torm tactor 746 4608902 Longitudinal space charge impendances Ohm 87519902 22 Transverse space charge impendances Ohm m 0 0006055379817 Peak current A S EMELE ance definition RMS0 CSC FWHMC2 yo 3 35 Percents for transverse degrees of freedom 68 Percents for longitudinal degree of freedom 1 Mean Longitudinal Invariant In the bld file names of files required for calculations in specific cases are also specified In the example below the parameters nesr_p034a tfs r005 mad and rhic red are the filenames of output MAD input MAD files and file describing procedure of the lattice structure reduction correspondingly If they are necessary for simulations they have to be saved in the same folder with Betacool exe row 13 Ring Lattice Structure Lattice Filename O Lattice File Output MAD 0 Input MAD 1 No file 2 2 Lattice Structure Reduce 0 Extend 1 No changes 2 l Extend step cm nesr_p034a tfs Output MAD Filename O Auto skip of points 0 1 r005 mad Input MAD Filename fe rhic red Reduce Filename 1 4 Output files As a result of simulations BETACOOL modifies the input file bld format and creates a few files from the following list The files cur as a rule contain time dependencies of the beam param
90. pm bld 2 5LSR p BLD ESR BLD 2 NESR bld 2 TARN2 BLD hesr bld 2 RECYCLER BLO 2 USA bld File name JESR BLD Files of type BOLIDE s File bld hi Cancel Zi Fig 2 File open window Step 3 Setting of the ring parameters One needs to choose Menultem Ring Parameters Fig 3 It is necessary to set Reference Energy on TabSheet ion kind Fig 3 Energy can be set in four ways Lorenz factor y Gamma Particle velocity in the units of the speed of light Beta Kinetic energy Kinetic Particle momentum in GeV c Momentum Ring Parameters Oj xj Reference Energy C Gamma 400 mewu y josia Gev Atomic mazs j A Charge number fi Life time Decay MEE sec Beta Kinetic C Momentum Fig 3 Ring parameters In addition it is necessary to set up Atomic mass Charge number and Life time For references the parameters of chemical elements are collected in the periodic table Menultem File Periodic 2 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Table If the beam is bunched one needs to set RF harmonic number and amplitude of the RF voltage in the TabSheet RF system Fig 4 Ring Parameters E ES lori kind Lattice Mean params FP system Reference point sl Harmonic number 1 p RF voltage kv 5 mj aa mj SEparalile S126 Separati size 100 z Saparatris length m Synchrotron tune 0
91. program or assembled in accordance to the input MAD file standard No file option is chosen when user does not need Lattice file ComboBox Lattice Structure has also three possible selections reduce filename extend step cm no changes Here choice of active option depends on the definition made in described above Lattice structure File ComboBox Ring Lattice Structure Lattice Filename Output MAD format Lattice Structure File Input MAD file Dutput MAD filename _ Find sis18 tfs _ Open Input MAD filename Find fsist mad _ Open Modify Lattice Structure No Changes gt Reduce filename Find fo Open Extended step crn eO Auto skip of points Calculate Lattice Make output MAD file betacool exe madSrin bat Open Fig 9 Window of the Ring Lattice structure menu item TabSheet File names Circumference m 48 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 In this TabSheet in the combo box Lattice Structure File the option Output MAD file or No Files for Piwinski model has to be chosen The file name has to be pointed in the TBrowse element Output MAD filename Fig 10 The button Open of this TBrowse element starts internal BOLIDE text editor and pushing this button user can check existence and validity of the chosen file AA lx SAF oR AA l NAP M Reconstructed by A Smirnow Linear lattice functions TWISs line NAF range Deltalpl
92. put files with table of longitudinal components of the electron cooling friction force mad input files in the format of input MAD8 program pat input files of painting procedure for electron beam shift red input files of positions for the reduction of lattice structure tfs input files with lattice structure in the format of output MAD8 program tvt input files with table of transverse components of the electron cooling friction force cur output files with 2D graphs see Appendix for details srf output files with 3D graphs see Appendix for details use output files with lattice structure The software also includes the total set of BETACOOL source codes cpp and h files project files for compilators betacool dsp and benacool dsw MS Visual C Windows betacool bpr C Builder Windows betacool cbx BuilderX Windows LINUX makefile and objects for GCC compilator LINUX backup bat and upload bat command files for saving of BETACOOL package save bat command file for saving of current 2D and 3D graphs in separate folder mad8win bat command file for run MAD8 program mad8 exe MAD8 program mad8 dic dictionary of MAD8 program The first part of this guide describes structure of input and output files of the program procedures which can be executed with the program files for the calculation process control This part contains mainly background information and to
93. r 0 076272644936 Wwe Equilibrium emittance 10544721 21E 10 pmrad Cooling rate 0 004647370273 3 jaso27720063 We Optimum cooling rate 0 006691 806406 ai Fig 1 Visual form for input and output parameters for transverse cooling chain Total power Table 1 Input parameters for the cooling chain description Lower frequency fma G Upper frequency faw G Electronic Gain Ga Dimensionless or in dB G dB 20logG iin Loop length Pickup and kicker parameters Electrode width IO E ap height __ height 2 Number of Number of loop pairs pairs Se Nk Beta function in the pickup Po Pr and kicker positions For the pickup and kicker the program calculates the following output parameters sensitivity Op x 2 in accordance with the formula G IV 2 8 approximate length of the electrodes in accordance with a Ny k cop T lem electrode For the equilibrium emittance cooling rate and consumption power calculation the program uses the following input parameters common for both transverse planes Fig 2 Table 2 76 BETACOOL User manual XII Gated Stochastic cooling Last update 08 Nov 2008 Effects Stochastic cooling IOl xj Horizontal Vertical Longitudinal Common parameters Total width of momentum distribution a j loma Pickup effective temperature E y E Preamplifier temperature En j E Charachteristic impedance Eo 3 Ohm Losses in combiner fe ial dE fi
94. r manual Il Growth Rates Algorithm Last update 30 Sep 2007 iolxi oHPFliotse OE A ETART 2007 2 26 139 54 3 D sa0 betacool betacool exe RHICmbh BLD rates END 2007 2 26 13 54 35 Row age Col 11 36 Modified Fig 4 Betacool war file after successive calculation of the growth rates If user wants to calculate evolution of growth rates and to look over the dynamics of this process one must check CheckBox Draw Evolution of Rates Fig l which switches ON OFF drawing of Evolution of Rates plot Fig 5 and run RMS dynamics calculation Task RMS Dynamics Parameters of the evolution calculation time step etc can be defined inhere lolx step multiplier Rates Evolution E a Long 3D rate Electron Cooling Ta 0 i w o Fest Gas i fo Internal Target E al i 4 rt I fo Zj Particle Losses z o E immaansctaes il ike u ME li a fo Additional Heating at mun fo 1 Stochastic Cool Stochastic Cooling a 2 3 Reference time sec Fig 5 Task Growth Rates Evolution To calculate 3D plots of the growth rates vs transverse andlor longitudinal emittances one should use TabSheet 3D rate Fig 6 which determines the parameters of the visualization Here one can set minimal and maximal emittance value for plots and range division The same parameters are specified for momentum spread To calculate and draw necessary 3D diagrams user must use TBrowse Calculate 3D rate her
95. rabolic 2 5 From file The distribution of the electron beam on the radius can be calculated in other program and result of the calculation can be read into BETACOOL program as text file TabSheet File for reading of the external file with radial distribution of electron density and transverse gradient is shown on Fig 9a Fist column of the file is the radial coordinate in mm second column is the electron density in A cm and third column is the transverse gradient G in l sec If the third column is absent in the file then the constant transverse gradient will be used from window Fig 8 Example of the text file with the electron beam density is shown on Fig 9b ECOOL Electron beam O xj HT onon ks seael A H 5 x Radial density and Find res cler den Open transverse gradient E ri mm 41 Aem z 1 14 mm J2 8 4cm2 Va Wtr gradient 12 o Electron current 01 044860687 Central density 1 m 3 21 12534413813 00000000500 00000 025403701 05792085 089731939 12015566 1456935503 174933916 198469241 2 1874152 235665254 OD rasa 255109564 265558697 266978687 2 Pe OSs26 264046512 963802326 963313953 Ab 703406 26197093 261116279 960261628 95952907 255674419 2550063953 957697674 957331395 9572093042 956595537 Fig 9 ECOOL Electron beam TabSheets File and example of input file 3 Library of the friction forces 3 1 Models of friction forc
96. rame hy e EA A A O oa eee TORE Tce een eR ae eT ee 37 1 Emittaices and particle UMD cas i 37 12 Parameters or Aec ON ias 38 SAO DUNCA parameter ib ii di iia 39 1 4 Calculated Character SUC sist os 40 Ze VASUA MZA COnOr Dean parameters is di 40 ZA EVON OL Sea E E aed ianauace tues eecee 40 Zola Nase space Ol model parco 41 2 5 WIS ton ot PrOMles a a ivan 41 BETACOOL User manual Introduction Last update 08 Nov 2008 Vil tora mie O Dionne ad 43 lo era te etsy Olly Me nas da a 43 ll Setting Ol 10n kind paramotor ia a ias 43 1 2 Latice parameters Ol ROO dada dales 44 SA A EAN 44 LARP system Tor bunched DCAM A AAA AA 45 keds IR CTCECMCC PON cs 45 16 Bumer Bucker mola SAA 46 PE NS 48 Ze oput nies ita latice SUCU saccra A vaca 48 2 2 Parameters OL latice struc Ur calas 50 PS Ele KIO A a a a a 51 VII Miitrabeami S Catteries t26 torceteens he toice iia ian ter atv albeit aaa eg eis eee a ea 54 cla Ss Palate leks rn a sl E 54 2 Marini mode ll is cicene ain arta ina 55 SOME mode Ieor B Siasea isa 56 4 Summary how to provide a choice of IBS model esrsesanicnii an 58 IX enal Parce EEC sida ct ee rer oe rR ee tod 59 E Maternal or tar oteren idee a SG wee apenas wo ene aie aan 59 Z Rarameters OL mternal ta olonia iaa 59 atte TACA ONS o iiO di arco iio 60 A pE eda a e anaes Aiwa nduduntn a pares diya ndetes ind adaelwasdaaeeene dees 60 Sy lV MAR BOC ars seca tala e ee lar alta gece nas cabot eweeass 60 OP AI CLC MOSS A O een eter NS 61
97. rent Form which correspond to their Checkboxes User must check plots which are needed to be redrawn on line and or check out other plots More detailed description is given in Beam Manual Beam Evolution I Horizontal emittance 3D Phase Diagram j Vertical emittance Gamma Criterium l Momentum spread Temperature Equilibrium Particle Number Footprint of invarinats 15 Reference time sec Fig 14 Window of the Beam Evolution menu item Note Instructions for working with the 2D and 3D plots are presented in the file Bolide doc 34 BETACOOL User manual V Particle Losses Last update 30 Sep 2007 V Particle Losses One needs to choose Menultem Effects Particle Losses on the MainForm Fig 1 F Pivin GSI_betacool_ 1 2 E5R 6LD p El x Fie Beam ECOOL Ring Task Effects CGulB S HliaeK Internal Target Additional Intrabeam Scattering Rest Gas Stochastic cooling Particle Losses Fig 1 Main Form Window of the Effects Particle Losses allows you to activate effects which will influence on particle number in the beam Fig 2 Effects Particle Losses l 2 aj x Active Effects Additional Losses Electron Capture in ECOOL Life time Decay e Scattering on Rest Gas Acceptance Separatris length Generate model particles on losses with distribution Rea Fig 2 Particle Losses options One has to set additional parameters Fig 3 of los
98. rocedure then longitudinal coordinate and momentum spread shifts are calculated as A dp p Aldp p Aldp P in ACAD p XR AS AS As 4 Si x R 2 3 Electron beam shifts can be read from the file for the painting procedure if parameters Painting is enabled This file includes 6 columns which correspond to vector of current shifts Number of rows equal to the period of the painting procedure and each row corresponds to the current step of the integration process Scaling parameters Painting x __ can increase positive value or decrease negative value a speed of the painting procedure For example if scaling parameters equal 2 it means that only each second row is used in the painting procedure If scaling parameter equal 2 it means that each row is used twice User can change all parameters on the TabSheet Shifts during simulation and even change data filenames with solenoid errors or painting procedure 1 5 Space charge of electron beam TabSheet ECOOL Cooler Space charge Fig 5 gives a possibility to draw beam potential distribution and real particle distribution for model beam To launch the visualization drawing user can use TBrowse component Redraw Space Charge If it is necessary to monitor paricle dynamics on line there is a CheckBox Show particle dynamics which must be ON in that case iol xi Cooler lon Beam Lattice Shifts Space Charge Redraw Find betacool Open W particl
99. rs Smooth rho_max is used for maximal impact parameter calculation either via plasma period or time of flight rho_min via rel U minimal impact parameter is calculated via RMS electron velocity spread or velocity of individual electron rho_min Plus e_rms minimal impact parameter can be calculated either via sum of electron and ion velocities or via ion velocity 3 3 Magnetized model of friction force The TabSheet ECOOL Friction force Magnetized Fig 11 is used to determine and define parameters for the Magnetized friction force model calculation Here user can change the following parameters on the corresponding Panel When Derbenev Skrinsky Meshkov model is chosen user can choose calculation method for it s realization Numerical or Asymptotic one and define so called Smoothing coefficient coefficient proposed by Meshkov to smooth the friction shape 70 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 ECOOL Friction force O xj Model Non magnetized Magnetized l Parkhomchuk Erlanger Electron array ECOOL Friction force 2 Oj xj Model Non magnetized Magnetized Parkhomchuk l Erlanger Electron array Derbenev Skringky Meshka f Numerical Asymptotic fi Smoathig coefficient Humerica Parkhomchuk Angular spread rad o oo i Effective temperature e 0 005235876 i Derbenev s integral i Pestirkoy s integral Derbene Pestri
100. rsents 35 Transverse Longitudinal 65 e Mean Longitudinal Invariant Fig 2 Beam Parameters Emittance 15 BETACOOL User manual Il Growth Rates Algorithm Last update 30 Sep 2007 Here only the following parameters must be set ion beam state horizontal emittance vertical emittance momentum spread and number of particles More detailed description of this Form is given in Beam Manual For the ion ring user must set corresponding parameters in Form Ring Parameters fig 3 Ring Parameters Ring Parameters Ring Parameters Lattice Mean params RF system Reference point lonkind Lattice Mean params RF system Reference point Reference Energy i 3 Circumference IEEE m Gamma 1 429414 al T 7 Beta 0 71455 Gamma transition 12 7824 M Imagenary f Kinetic 400 MeV u y Horisontal Vertical Harmonic number ica a AF voltage kW E E Separatrix size ho Saparatrix length m 1 08 3601 Synchrotron tune 0 0006470272494 Induction acceleration Y 0 3 Momentum 0 95142 4 GeV c Tunes 2 2352 2 266 ans Atomic mass 1 Charge number 1 Life time Decay 1E6 Longitudinal Acceptance 10 003 Chromaticity 2 5511 2 3715 Acceptance 0 00025 0 00015 m rad Fig 3 Ring Parameters Here the following parameters must be specified on the TabSheet Ion kind reference energy depending on the presentati
101. rticle number 1 88812 2000 Mero Ermmmitance definition p ont pa 5 A a ar Initial distribution Gaussian i FF Injections with interval sec 10 4 zj Number of injection cycles 5 File with initial distribution Find leir2 ini Draw initial distribution Find betacoolexe Momentum spread shitt 0 Horizontal shitt m 10 Enclosed Persents Vertical shitt m Transverse E 38 Longitudinal gg Horizontal acceptance m rad H Mean Longitudinal Invariant Vertical acceptance m rad a a E Fig 1 TabSheet Emittance amp Injection of the menu item Beam Parameters 1 2 Parameters of injection The TabSheet Injection Parameters Fig 1 includes the following input and output variables Initial distribution Choice of initial distribution type Gaussian Flattened form file Number of injection Number of injections cycles distribution Momentum spread shift Shift of longitudinal momentum 38 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2007 Here a TBrowse component Draw initial distribution is intended to visualize an initial distribution of model particles which is generated in accordance to the user defined choice Initial distribution gaussian flatten from file User can watch the distribution on different phase space at Form Beam Real Space 1 3 Ion bunch parameters To adjust RF system parameters to the required bunch leng
102. s it is necessary to modify the input file manually Therefore for IBS rate calculation it is easier to use output MAD file To provide a choice of the lattice file name and its specification the menu item Ring submenu item Lattice Structure and corresponding visual form Fig 9 are used kk i loxi b HF n BAE AH WAP M Reconstructed by A Smirnov EEE COHETES drift drift SBEND L 4 7124 iANGLE 1 5708 El 0 415 E2 0 415 gt line driftl1 sbendli line 4 50PER ae ae lou tw ou e w On line sbendl1 drift2 xecool driftz sbendl driftl shendl drift1 sbendl drift1j save PLOT T amp BLE TWISS HAaAXIS S SPLINE VaAxXIS1I BETZ BETY DE Fig 11 Example of input MAD file The result of translation is saved to file with same name as MAD input file and extension use BETACOOL can translate the following elements from MAD file DRIFT SBEND ANGLE bend angle El and E2 edge angles 49 BETACOOL User manual VII Storage Ring Object Last update 30 Sep 2007 QUADRUPOLE K1 quadrupole gradient TILT rotation SEXTUPOLE K2 sextupole gradient RFCAVITY FREQ RF frequency V RF Voltage SOLENOID Ks solenoid gradient LINE USE All the elements have obligatory parameter LENGTH Depending on the task the BETACOOL program can be a very powerful instrument for processing of ring lattices and or transformation matrices of optics element If user has a
103. s the name of input file At usual setting the interface opens input file used in previous run To open new file one needs to use menu item File submenu item Open or corresponding button in the toolbar It opens a new input file using the standard MS Windows dialog DB Smirnov betacool sis18 bld E oj x File Beam Effects ECOOL Ring Task cH m l ln i 1 oD Fig 2 Main window of the BOLIDE interface for BETACOOL program Main window has the following buttons for working with interface lar _ open the input file with using Windows Open dialog lel _ save input file 10 BETACOOL User manual Interface Last update 30 Sep 2007 Ed _ calculator tool periodic table of chemical elements text editor by default open betacool war a _ setup dialog window of the interface program n dialog window for elaboration and editing of exterior i _ redraw all graphics 0 restart calculation with new parameters o start calculation process a pause calculation process Om restart with changed parameters If some changes of parameters in input file via interface during calculation were made by user then program will reread initial file and will continue calculation with new parameters Op stop calculation To stop the program with correct OS memory cleaning we advise to use this item In this case a special file marker will be created in the current directory and as soon as program will find it then it im
104. s when array is nearly to be overfilled every second cell in it will be released In ComboBox Modify Lattice Structure the option No Changes has to be chosen All other parameters do not play a role in calculations but it is better to input where required the names of arbitrary files existed in the current folder Reduce filename Fig 9 is useful option foreseen for large lattice optics structure Here one must built a special file red with reduced structure of the ring User has to leave only optical elements and corresponded which he wants to be taken into account for calculations and visualization Here the following algorithm takes place for the tracking using matrices the whole structure is taken into account However necessary matrices will be built only in user selected points by multiplying all the intermediate matrices between selected points Then only these matrices will track the beam And IBS effect will be calculated only in these points Finally lattices in selected points will be plotted So the calculation time may be sufficiently reduced Extend step cm Fig 9 this option is used only when Tracking algorithm is presumed and Molecular dynamics technique is used Here the step over longitudinal coordinate is defined between points where transformation matrix is calculated This choice is active when option Matrixes is switched on in Task Algorithm Tracking Equations of motion window The second necessary co
105. ses 1f Scattering on Rest Gas or Internal Target were chosen Effects Rest Gas Of x Effects Internal Target oO x E Electron capture e Single scattering lv Single scattering M Nuclear reaction Interaction event e Nuclear reaction Cross section barn 0 04 re Mean vacuum chamber radius cm Luminosity 1 4cm cem s 5 892709482E 27 100 Fig 3 Particle losses in Rest Gas and Internal Target Also one has to choose how lost particles will be recovered in the test beam in accordance with defined distribution from the list Fig 4 35 BETACOOL User manual V Particle Losses Last update 30 Sep 2007 There are 4 options Gaussian re generation according to the Gauss distribution Real re generation according to the real distribution None lost particles will be not recovered in model array but will reduce whole number of particle in the beam Off model particles don t lost for example beam decay but will reduce whole number of particle in the beam Effects Particle Losses Ioj x Active Effects Additional Losses Electron Capture in ECOOL Life time Decay e Scattering on Rest Gas Acceptance e Internal Target TT Separatris length Generate model particles on losses with distribution Real Fig 4 Particle Losses form Finally one has to switch ON all other used effects Fig 5 User can push Open on the Form Task Growth
106. start simulations on PC one can start directly from the second part The second part describes a structure of the Windows interface and contains simplest examples of input file preparation and simulations with general procedures of the program using the interface BETACOOL User manual Interface Last update 30 Sep 2007 1 Work without graphical interface 1 1 Starting the calculations control of the calculation process The simplest way to start a work with BETACOOL program is to save the Betacool exe file file of input parameters bld format other required input files from archived Betacool kit download from website http lepta jinr ru betacool and SAVE bat file into the same folder To start the BETACOOL program one needs to type in the command line the following command lt path gt betacool exe lt inputfilename gt lt parameter gt The parameter lt inputfilename gt is obligatory If this parameter is skipped the program generates in the output flow the warning message presented in the Fig 1 and stops the calculation after press Enter cs DA saot 6512006 betacool GSI Y2 BETACOOL exe START 2006 Mo IA 24 13 15 18 Use DissaoA65 1520065 betacoo1_G51 y2XBETACOOL exe inputfile parameters Press Enter to continue Fig 1 Betacool output in the case when lt inputfilename gt parameter is skipped If the specified file is absent in the current program folder the program generates the followin
107. stimations by the order of magnitude using mean ring parameters All other IBS models require to import a file containing the ring optic structure 58 BETACOOL User manual IX Internal Target Last update 30 Sep 2007 IX Internal Target Effect One needs to choose Menultem EffectslInternal Target on the MainForm Fig 1 F Pivin GSI_betacool_ 1 2 ESR 6LD File Beam ECOOL Ring Task Effects ca E Es PES i El Internal Target Additional Intrabeam Scattering Rest Gas Stochastic cooling Particle Losses Fig 1 MainForm Window of the Effects Target includes five TabSheets Material Params Lattice Type Pellet and Losses 1 Material of target Effects Internal Target Materials One needs to set Mass number and Charge number of the target atoms Length and Density of the target on the TabSsheet Material Density can be set as gram cm 3 as atom cm 3 Calculate from material Mass number 4 1 lw Charge number lt fi Density atomecm 2 1 85E19 Length mm ls a Ame scattering angle i T6305245E 5 Densit gam cm 3 jen 43995E 5 Energy straggling ev 2705 847912 e atom cm 3 47E19 W Energy loss e 195 7009857 Fig 2 Material amp Parameters 2 Parameters of internal target TabSheet Params Fig 2 shows parameter of the target which can be calculated from Material if Checkbox Calculate from material is switched ON Checkbox Energy loss indicates usage of th
108. tance pi mm mrad 0 1 0 001 Horizontal Emittance pi mm mrad 0 1 0 001 0 0011 1E 5 0 0001 0 001 0 0001 0 001 1E 5 0 0001 0 001 0 01 Momentum Spread Momentum Spread Momentum Spread 10 10 10 Horizontal Emittance pi mm mrad 0 1 Horizontal Emittance pi mm mrad 0 1 0 001 Horizontal Emittance pi mm mrad 0 1 0 0011 0 001 1E 5 0 0001 0 001 0 01 1E 5 0 0001 0 001 0 01 1E 5 0 0001 0 001 0 01 Momentum Spread Momentum Spread Momentum Spread 10 0 1 0 01 0 001 0 0001 1E 5 1E 6 1E 7 1E 5 1E 9 1E 10 Horizontal Emittance pi mm mrad 0 1 0 001 1E 5 0 0001 0 001 0 01 Momentum Spread Fig 9 Phase space diagram of growth rates sec for HESR a b transverse and longitudinal components of IBS growth rates c d transverse and longitudinal cooling rates of EC e f summary of cooling and heating rates g overlapping picture f over e and r m s dynamics in accordance to Fig 1 2 20 BETACOOL User manual III RMS Dynamics Algorithm Last update 30 Sep 2007 HI RMS Dynamics Introduction RMS Dynamics is algorithm included in BETACOOL This algorithm allows to analyze evolution in time of r m s ion beam parameters under a common action of a few heating or cooling effects which are described in terms of characteristic times of the beam r m s parameter variation This model presumes Gaussian distribution of the ions in all degrees of freedom Step 1 Lunch
109. tance corresponded to particles inside full width on half maximum of distribution Enclosed Percents emittance occupied by the indicated percent of beam particles The input horizontal and vertical beam emittances correspond to rms non normalized values The relative momentum spread is also set as rms value In the case of bunched beam simulation the Number of particles corresponds to the particle number in a single bunch not in the total ring All other parameters in the tab sheet are used in the Model Beam algorithm and for IBS rate calculation they can be arbitrary The TabSheet Emittance Fig 1 includes the following parameters which has to set Combo Box bunched different state of ion beam O oasting 1 coasting barrier bucket bunched 2 bucket Combo Box Used for Model Beam Algorithm Emittance definition for 0 Root Mean Square Model beam 1 Courant Snyder invariant 2 FWHM 3 Enclosed Percent Enclosed percents for Used for definition of the emittances and trans and long degrees momentum spread enclosed in pointed of freedom percentage of particles Mean longitudinal parameter has to be switched on in the invariant case when the momentum spread has some deviation from the reference energy In the BETACOOL program the transverse emittance is define as one sigma un normalized emittance and momentum spread is defined in relative value AP P Usually on experiments at Recycler the transverse emittance is defi
110. th in the case of bunched beam the TabSheet Bunch can be used Fig 2 This tab sheet contains one input parameter Number of bunches This parameter is necessary for luminosity calculation only and in IBS rate calculation it does not play a role It can be arbitrary positive non zero number After starting Betacool the program outputs rms bunch length corresponding to relative momentum spread of the bunch and RF system parameters By a few subsequent runs of simulations one can adjust RF voltage or harmonic number to have required rms bunch length The TabSheet Bunch Fig 2 includes the following input and output variables Variable lable Number of bunches Used for luminosity calculation R m s bunch length O Maximum particle number N nax 3nZG R rU Synchrotron tune Bunching factor L 8 2 Lsep is the separatrix length Beam Parameters 2 Oj xj Beam Parameters IOl xj Emittance Injection Bunch Characteristics Emittance Injection Bunch Characteristics Number of bunches re E SEINE eI fia Longitudinal form factor 2 969620885 RAMS bunch length E E cm Space charge impendances Masimum particle number fp Longitudinal 11830 60357 O Firm synchrotron tune fi Transverse 166005092 7 Ohm Bunching factor fi Peak curent 0002508279678 A Fig 2 TabSheet Bunch amp Characteristics of the menu item Beam Parameters 39 BETACOOL User manual VI lon Beam Object Last update 30 Sep 2
111. th default value Input parameter initialised with default value initialised with default value initialised with default value Input parameter Input parameter END 2006 11 bd bd d d d d d START 2006 11 f 24 17 D sao GSI 2006 betacool GSI_v2 betacool exe NESR bld END 2006 11 Y 24 17 42 28 Col 1 1 Row 380 380 Fig 4 Betacool war file in the Editor window The warning after two consequent runs of the Check parameters procedure with input file EDM bld and NESR bld In the EDM bld file a few parameters are skipped the NESR bld contains total set of parameters To import the absent parameters into input file one needs to open a file containing total set of parameter and use menu item Filellmport and load required file using the standard MS Windows dialog In the example presented in the Fig 4 to provide simulations with EDM bld file one needs to open NESR bld file and import EDM bld file After the skipped parameters in the EDM bld will be substituted from NESR bld and EDM bld saved with total set of parameters 2 2 Parameters of calculation for Windows Interface Parameters of calculation can be defined on the Form Task Parameters Fig 3 To save results it s needed to push Button Open Save Results to Folder on TabSheet Output All results will be collected to current folder The name of the folder depends of input file name for example for input filename ESR BLD the folder n
112. th mesh parameters and interpolation method which are defined in next Tab Sheets on this window ECOOL Tabulated loj xj ECOOL Tabulated ioj xj File with transverse velocity table Find ftable tvt File with longitudinal velocity table Find table Ivt Bilinear Triangle Generate table with velocities Find betacoal exe Fig 16 Window of the ECOOL Tabulated menu item TabSheet Control 5 2 Interpolation TabSheet Interpolation Fig 16 1s used for definition of the interpolation method for processing of the tables with pre calculated friction force values Here RadioGroup Type is presented and user can choose one of three possible interpolations Linear linear interpolation closest nodes For uniform mesh Bilinear non linear interpolation For uniform mesh Triangle non linear interpolation For arbitrary non uniform mesh 5 3 Transverse and longitudinal velocities TabSheet Transverse Force Fig 15 is used for definition of the parameters of the table for transverse component of the friction force This table is a mesh with friction force values in nodes which is generated versus transverse and longitudinal ion velocity values Mesh for this table has 3 ranges for every velocity with independent splitting in every range Parameters of this mesh are presented on this Tab Sheet 74 BETACOOL User manual XI Electron cooler Last update 08 Nov 2008 ECOOL Tabulated ECOOL Tabulated
113. th rate on time vertical growth rate on time evolution of emittance on momentum drift velocity of electron space charge distribution of electron beam density evolution of profile on time longitudinal electron cooling force transverse electron cooling force longitudinal component of growth rates horizontal component of growth rates vertical component of growth rates 13 Last update 30 Sep 2007 Beam Distribution Coordinate Beam Evolution Momentum Beam Evolution Momentum Beam Evolution Emittance Beam Evolution Emittance ECOOL Draw force 1 D force ECOOL Draw force 1 D force ECOOL Draw force 1 D force Beam Evolution 3D Diagram ECOOL Draw force 1 D force Beam Evolution 3D Diagram Beam Evolution 3D Diagram ECOOL Cooler Space charge Beam Evolution Beam beam Beam Evolution Beam beam Effects Laser Cooling Force Beam Evolution Luminosity Effects Collision point Luminosity Beam Evolution Number ECOOL Cooler Shifts Beam Phase Space Task Growth Rates Evolution Task Growth Rates Evolution Task Growth Rates Evolution Task Growth Rates Evolution Beam Evolution 3D Diagram ECOOL Cooler Space charge ECOOL Electron bunch Array density Beam Distribution Evolution ECOOL Draw forces Longitudinal ECOOL Draw forces Transverse Task Growth Rates Longitudinal Task Growth Rates Horizontal Task Growth Rates Vertical BE
114. this method was made for simulation of IBS in the case of non Gaussian distribution Evolution of the ion distribution function is described by the Fokker Plank equation Friction and diffusion terms in the general case depend on the distribution function However in some cases when the effects acting on the distribution function do not lead to change of its shape the Fokker Plank equation can be reduced to equation for the second order moments of the distribution function In general case the Fokker Plank equation can be reduced to Langevin equation in invariant or momentum space The Model Beam algorithm realizes solution of Langevin equation in momentum space using Monte Carlo method In the frame of this algorithm the ion beam is presented as a particle array Each particle is presented as a 6 co ordinate vector far e A e e e X E Px JE 2 where x and y are the horizontal and vertical co ordinates p and p P P P are corresponding momentum components s so 1s the distance from the bunch center in the case of coasting beam distance from a reference particle Ap is the particle momentum deviation from momentum of reference particle p Action of each effect is simulated as the particle momentum variation in accordance with the following equation Pas P ag Pass A AT Days AT p where ps is the particle longitudinal momentum deviation subscript in correspond to initial momentum value subscript fin relates to final par
115. ticle momentum after action of the effect A and D are the drift and diffusion terms for corresponding degree of freedom AT is step of the integration over time is Gaussian random number at unit dispersion Calculation scheme of the Model Beam algorithm The basic scheme of the algorithm is the following on the first stage a beam is generated with defined parameters in the selected point of the ring in accordance to the current lattices so called kicks from active effects are calculated coordinates and angles of every particle are changed correspondingly obtained vector of coordinates is multiplied Turn step times by the transformation matrix of the whole ring go to the first step Below a step by step instruction for setting and using this algorithm is given 26 BETACOOL User manual IV Model Beam Algorithm Last update 30 Sep 2007 Step 1 Lunch interface Launch file bolide exe As a result the MainForm window is opened Fig 1 F Pivin GSI_ betacool v1 27 E5R 6LD 2 oj xj File Beam ECOOL Ring Task Effects EREGI Fig 1 MainForm Step 2 Open file Open file of input parameters bld format Choose FilelOpen or on the MainForm Fig 1 and choose file Fig 2 open Look in 6 GSl_betacool_w1 2 d fe AE a B CELSIUS ELD 2 HESR_Dag bld 2 RESR bld 3 cosy bld himac bld rhic bld 2 EDMD bld leir bid 2 SLSR Mg BLD 2 ELEMA ELD 2 na
116. tion it is easier to use output MAD file To provide a choice of the lattice file name and its specification the Menultem RinglLattice Structure and corresponding visual form Fig 5 are used 22 BETACOOL User manual III RMS Dynamics Algorithm Last update 30 Sep 2007 Ring Lattice Structure E Ioj x Lattice Filename Output MAD format Lattice Structure File Input MAD file Dutput MAD filename Find ESR tts Modify Lattice Structure ho Changes pir Mil Reduce filename Find JESR RED my Auto skip of points Calculate Lattice Hake output HAD file TA O Find fradiwinbat Onen 0 48 144 200 men m Fig 5 Ring lattice structure In the TabSheet Lattice Filename ComboBox Lattice Structure File the option Output MAD file has to be chosen For IBS calculations using Martini or Jei Wei models one needs to find appropriate lattice structure file Button Find of the TBrowse component opens the file manager window Button Open opens the file using internal text editor The chosen file name is indicated in the edit window of the TBrowse component and saved in the input BETACOOL file This name is used for initialization of the ring structure after start of the program Validity of the file can be checked using TBrowse component Calculate Lattice Button Open of this TBrowse component starts BETACOOL with the parameter lattice At this parameter BETACOOL reads MAD output file transforms lattice parameters in
117. to internal format and saves them into the files BetaX cur BetaY cur DispX cur AlfaX cur AlfaY cur DispX_ cur During this procedure the program checks validity of the data in all positions of lattice structure file in accordance with the description tacking from the TabSheet Output MAD format Step 5 Setting of the beam parameters One needs to choose Menultem Beam Parameters Fig 6 Use Emittance TabSheet to set up Ion beam state Horizontal emittance Vertical emittance Momentum spread and Number of particles Model particle number is used for Model Beam algorithm only lolx lon beam state Coasting Horizontal emittance 150 pi mm mrad E pi mm mrad Vertical emittance 50 Momentum spread pom gt Number of particles js Model particle number fpo Emmitance definition Root Meam Square use for IBS kick Enclosed Persents 35 Transverse E Longitudinal 65 e Mean Longitudinal Invariant Fig 6 Beam parameters 23 BETACOOL User manual III RMS Dynamics Algorithm Last update 30 Sep 2007 Step 6 Setting the active effects To calculate sum of the rates for a few active effects the Menultem TasklGrowth Rates are used Left part of the corresponding visual form contains the list of the effects that can be used in simulations An effect is switched ON in simulations when the corresponding step multiplier parameter has value equal to 1 In the Fig
118. tor or corresponding button in the Main tool bar Example of the Betacool war file generated after three runs of calculations is shown in the Fig 13 O x SH Aio See l A H START 2007 2 4 24 18 43 14 D 1saol betacool betacool exe RHICmb BLD lattice END 2007 2 24 18 START 2009 4 27 24 18 TD sa0 betacoolhetacool exe RHICmh ELD lattice Error in Lattice Structure file rhic4 st tt s START 2009 7 2 7 24 18 D 3a0ibetacoolibetacool exe RHICmh ELD lattice END 2007 2 24 18 44 20 Row 16716 TE TE fe Fig 13 Betacool warnings The first and the last runs of the program have been successive In the second run the positions of lattice parameters in the input file do not coincide with specification in TabSheet Output MAD format Betacool supports three standard of output MAD file 132 columns 157 columns and the output file can be generated by mad8win but file included into Betacool package MAD option The corresponding file specification can be chosen using ComboBox Column Position of Lattice Functions Fig 14 Ring Lattice Structure lOl xj Lattice Filename Output MAD format beta functions alta functions Matrix Column Positions of Lattice Functions User User definition of Column Positions dist beta_x EJ so beta y alfa_x ar je alfa_y mu EE 106 mur y 107 114 y II A ADAL RAVA NAD AN p_x 115 121 py Dx h22 fize
119. tudinal beam profile Beam Distribution Profile dist_1x cur horizontal beam profile Beam Distribution Profile dist_1y cur vertical beam profile Beam Distribution Profile dist_sp cur distribution of momentum spread Beam Distribution Coordinate dist_sx cur distribution of horizontal coordinates Beam Distribution Coordinate 12 BETACOOL User manual dist_sy cur dp2t cur dpmo2t cur ex2t cur ey2t cur falong cur fatr cur flong cur footprint cur ftr cur gamma2 cur gamma3 cur inecool cur kappax cur kappay cur laserf cur lum2t cur lumitest cur nr2t cur shiftNNNecur spaceN cur th2t cur tn2t cur tp2t cur tv2t cur txy2t cur vdrift cur density sur evolution sur fflonf sur fftr sur ratedp sur rateeh sur rateev sur Interface distribution of vertical coordinates momentum spread on time deviation of momentum spread on time horizontal emittance on time vertical emittance on time longitudinal electron cooling force transverse electron cooling force longitudinal electron cooling force particle invariants transverse electron cooling force ordering criteria temperature equilibrium of beam particles in cooler section horizontal beam beam on time vertical beam beam on time laser cooling force luminosity on time test calculation of luminosity particle number on time electron beam shifts particles in phase space horizontal growth rate on time particle number growth rate on time longitudinal grow
120. umber and Life time For references the parameters of chemical elements are collected in the periodic table Menultem File Periodic Table or corresponding Button in the tool bar Using the TabSheet Lattice Fig 4a set up Circumferensce Gamma transition Tunes Chromaticity Acceptance and Longitudinal Acceptance a AE Circumference r 06 3601 m Gamma transition 12 7824 TF Imagenary Lattice functions at point User User Lattice function Horizontal Vertical Betal fsa H ps 4 Apa p p Horisontal Vertical Tunes 2 2352 2 266 Chromaticity 25511 23715 Acceptance 0 00025 fo 00015 m rad Longitudinal Acceptance 0 003 En a b Fig 4 Ring parameters Dispersion m fo fo Dispersion derivative u El c Using the TabSheet Reference point Fig 4b set up Lattice functions at point and User Lattice functions Step 4 Setting of lattice structure If IBS effect 1s included into calculation depending on the IBS model one has to set ring lattice structure Piwinski model needs only mean ring lattice so it is not necessary to set this Form Other models need real or reduced lattice structure of the ring The ring lattice structure can be imported from input or output MAD file Betacool translator does not support all the possibilities of MAD input file syntax and sometime it is necessary to modify the input file manually Therefore for IBS rate calcula
121. w orders less in comparison with cooling time and don t take into account during these simulations An unexpected behaviour of emittance can be explained with 3D phase space diagram Fig 9 These diagrams presented dependence of growth rates on the momentum spread and horizontal emittance The vertical emittance is assumed to be equal to the horizontal one 0 0001925 mm rs T E E E o oc 5 LLI LLI T a T T 400 oO 1200 1600 2000 T 400 oO 1400 1600 2000 a Reference time sec b Reference time sec Fig 8 r m s beam dynamics for HESR under action from IBS and ECOOL effects a transverse emittances b momentum spread IBS growth rates Fig 9a b are calculated in accordance with Martini model Colour areas indicate different values of growth rates White area for longitudinal component means that in this region of beam parameters the momentum spread is decreased and emittances is increased The temperature relaxation exists for large momentum spread and small emittance Beam parameters due to IBS come to the equilibrium temperature between all degree of freedom Cooling rates for EC Fig 9c d are calculated in accordance with Parkhomchuk formula of cooling force Transverse and longitudinal components of cooling rates have approximately the same behaviour Summary of cooling and heating rates are presented on Fig 9e f Boundaries between colour and white areas shows the equilibrium between IBS and EC f

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