User guide
Contents
1. and zs ys containing beta functions and phases of the The 2nd order sextupole cross talk terms contributing to the octupolar resonance m m are given for one period by TE gt with A a scalar factor 6 For N periods this becomes PR iA Mas gt be 3 8 with a as defined above inserting 7 m for and dz S N M m zF S N m m Stk C N M m aR C N m m Ga 8sinw siny sin Y 4 i S N E r E E E snl PEE and C the same with cos instead of sin N bin For N oo we again neglect the fast varying terms and get oo _ Sin W sin 2y i cos 2 cos 2x b 1 sin w y cue 8sinw sin vy sin w y mn 4sin psin sin y 7 4 2 Touschek lifetime Touschek lifetime is given by 1 2 3 1o ret FC T TT re OO e GiGeae cls Sace 8 YOx 0 S 18 re is the classical electron radius q the bunch charge os the bunch length assumed to be constant along the lattice C the machine circumference a and gy the transverse rms beam envelopes and xo the divergence for x 0 given by Ex H s o epee fe ae 14 2 oe with gs the rms energy spread and H the lattice invariant dacc S is the local lattice momentum acceptance which is the minor of the lattice and the RF acceptance In the linear case the lattice momentum acceptance at s s is given by 6 so min a s Hobels n s where a is the2. If the iteration was successful one may watch the solution show accept or reset it to the initial retry returns to the first screen to change the settings and try again Known bugs Symmetric or periodic option does not yet work well Previously selected inter mediate constraints are not reset on restart write OMK writes the current optics into the optics markers elements which can be selected on a panel that will pop up Print prints the plot stretching it to the available area and refining it to the available reso lution of the selected printer _ Plot writes a graphics file nam _beta wmf with betafunctions resp name _envel wmf if envelope mode was selected txt writes a text file nam _beta txt of plotted data for postprocessing using other tools _ GP writes text files nam _beta out with the beta functions and nam _mcod out with element data to be read by a GNU plot command file nam _beta gp which is also created Running GNU plot on this file outside OPA then will create an EPS file nam beta eps Exit terminates the optics design Note that the question to save the data refers only to an internal save to further proceed inside OPA but does not save the data to the file If optics design ends with a periodic solution the options sextupoles and tracking become enabled There is an embarrassing bug that could not yet be fixed if the
3. The geometric acceptance is modified by setting the apertures as described in sec 2 7 Other parameters are the number of turns and the location of the trackpoint Start starts probing the grid surviving particles are shown in green lost ones in red Ex port writes graphic files name _dynap_xy _xp _yp wmf Double clicking the image copies it to the clipboard In x vs y mode the geometric acceptance is shown as a blue polygon It is given by the common area of the projections of all the elliptical apertures to the track point see appendix 4 5 This geometric acceptance includes non linear and chromatic contributions to orbit and beta functions but else assumes linear transformations In tracking it may happen that particles outside the geometric acceptance survive for two reasons 1 aperture checks are only performed at non linear elements because to speed up tracking series of linear elements are concatenated and stored as matrices and 2 the non linear eigenfigure of betatron motion may be different from an ellipse 2 10 Tracking Touschek lifetime This module for Touschek lifetime calculation proceeds in two steps 1 Work sheet to calculate lifetime related parameters in a linear model one may enter param eters in the left panel and see the results in the right panel and in the plots Available plots include e the beta functions e the lattice invariant H e the rms beam envelopes e the apertures e th
4. angles x y in steps as given in the steps field until the maximum betatron amplitudes given by physical acceptance are reached The first third series goes in horizontal vertical direction up to the maximum betatron amplitude with a tiny vertical horizontal amplitude in order to excite coupling The second series sets the initial coordinates for a constant coupling Coupling and maximum amplitudes are defined in sec 4 5 The identified tunes are marked during execution in the tune diagram and afterwards they are plotted vs betatron amplitude or vs ping i e the initial kick angle The three series correspond to the lines blue X lilac X both showing Av vs 2J and purple Y showing Av vs 2J in the left diagram and to the lines lilac X showing Av vs 2J purple Y and red Y both showing Av vs 2J in the right diagram Since the amplitude is derived from the height of the fundamental peak in the Fourier spectrum it may happen in case of very strong non linearity that the curve returns towards the origin if a harmonic peak grows on expense of the fundamental peak It may also happen that the tune gets stuck on a resonance i e the particle is trapped in an island in phase space and the tune shift vs amplitude shows a flat line If theoretical amplitude dependent tune shifts have been calculated previously in the sextupole module they are shown as dotted line for comparison 2 8 Tracking m
5. by ZAP are not included 2 11 Extra Geometry A plot of the lattice layout press and hold the left mouse button to mark a rectangle to zoom in The curved arrow buttons on top will follow the lattice back or forth the third button zooms out again If there are marker elements named center in the lattice the plot will be centered at the center of gravity of these markers Unchecking the fix aspect ratio box stretches the plot horizontally and vertically to the canvas otherwise default same scales are used horizontally and vertically Parameters in the table control width and length of some elements wmf writes a file file _geometry wmf data writes three files named markers txt devices txt and orbit txt containing data of points where a new straight or curved sec tion starts the data of the ploygons relative to the markers and the data of the orbit Markers and orbit can be visualized by checking the corresponding boxes 2 12 Extra Orbit If monitors horizontal and vertical correctors have the special names MON CH and CV the family is expanded in single elements names MONnnn etc where nnn is a number Only these elements will be used for orbit correction Correctors or monitors with other names remain families and can only be used manually Monitors and correctors will show on the Orbit panels as green blue and red objects Correctors can be dragged to knobs to use them manually a monitor can be drag
6. helped to find several bugs 1 4 Capabilities and limitations OPA includes the following features e Human readable lattice input output and robust lattice reader Text editor and modular editor for elements and segments Interactive graphical design of linear optics with many convenient functions as knobs zoom matching tune diagram etc Calculation of momentum dependent lattice parameters Interactive optimization of sextupole and octupole Hamiltonian in 1 and 24 order Tracking with FFT Poincar plots resonance guesses and amplitude dependent tunes Tracking of dynamic apertures Tracking of Touschek lifetime Display of lattice geometry Orbit distortion and correction Calculation of magnet currents and export of EPICS snap files Export of TRACY MAD X and ELEGANT lattice files Several ways to export graphics image snapshots export as wmf file export of gp file for GNU plot Export of data in text files OPA has the following limitations 2 2 1 Only correct for rings with large circumference and high energy High relativistic approximation y gt 1 Paraxial approximation x dr ds lt 1 Large curvature approximation x lt p bending magnet radius Exactly correct only on energy i e Ap p 0 since it uses internally x instead of the canonical coordinate py No betatron coupling and no skew elements included i e it allows only flat lattices 224 order symplectic integrat
7. horizontal aperture In the non linear case it is obtained from tracking The Touschek function F is defined as FQ i ue i eS du For small arguments lt Csman 0 0013 the asymptotic expression F In E 3 2 is used with EF 0 5772 Euler s number For large arguments F becomes very small and is dominated by rounding errors so for gt Cbig 22 8 it is set to F big 10 1 usually lattice locations where this happens are irrelevant anyway for the final lifetime result For Csman lt lt 10 a fair approximation is given by a 7th order polynomial 7 A 3 10811 2 19156 0 615641 F C exp gt A Ind with 0 160444 0 0460054 0 0105172 k 0 1 31192 10 3 6 3898 10 5 The agreement within 2 5 compared to the integration is acceptable considering that the integral itself deviates up to 10 from detailed Monte Carlo simulations of Touschek scatter ing 4 4 3 A simple undulator model The alternating field of an N pole wiggler or undulator can be well approximated by a series of 2N rectangular dipole magnets where the end poles on both sides are attenuated The field of half pole k is By pB with the maximum field occurring in the central poles only and 1 3 3 1 Hee ea Ae eA aA Pk fi Jro Lae z 19 for optimum centering of the wiggling motion of the electron beam A general filling factor i e the ratio of rectangular bend l
8. optics plot window is covered up many times by other panels Windows runs out of memory probably due to some OPA bug in repainting the plot window and every user action will repeat this error In the worst case OPA has to be killed using the Windows tasks manager 2 5 Tune diagram The tune diagram pops up when a periodic solution is found it shows the working point at the centre and the resonance lines in the neighbourhood The lines aQ bQ c to be shown are selected by the order buttons and the checkboxes e Order buttons select a b lt order e nsys not checked selects only systematic lines where c mod P 0 with P the period icity of the lattice e skew not checked selects only regular lines where b mod 2 0 Buttons at bottom modify the plot range Export writes a graphics file nam _tuneplot wmf Double clicking the image saves the bitmap to the clipboard this works for all plots in OPA except the Optics Design plot 2 6 Design sextupoles Sextupoles octupoles and decapoles may be used to optimize the dynamic aperture after chro maticity correction The modes of the sextupole Hamiltonian are calculated in first and second order see sec tion 4 1 there are 10 terms in first order 2 linear chromaticities and 8 resonances and 13 in second 2 quadratic chromaticities 3 amplitude dependant tune shifts ADTS and 8 octupolar resonances The first order modes of the octupole Ham
9. OPA version 3 39 Andreas Streun PSI March 14 2012 1 Introduction 1 1 Status OPA is under continuous development but some colleagues all over the world like to use it therefore these instructions have been written Incomplete features or known problems are described using italics 1 2 General information OPA s main purpose is to support the development of electron positron storage rings Em phasis is on visualization and interactivity OPA is in particular useful for designing high brightness light source lattices but may be used for transfer lines and other types of lattices as well Storage ring design with OPA starts from scratch and ends at a bare i e error free lattice with optimized 2D dynamic apertures to be passed on to other codes like TRACY or MAD which use more complete models 1 3 History and acknowledgements OPA is based on the code OPTIK from Klaus Wille DELTA Dortmund who started in the 80 s already to work on a design tool for electron rings In 1993 he kindly passed it on to the author who developed it further and heavily used it for the design of the Swiss Light Source SLS Algorithms for sextupole optimization and signal processing were contributed by Johan Bengtsson now BNL Simon Leemann MAX Lab did a lot of tests and suggested many extensions and changes during the design of MAX IV Michael Borland APS tested the module for non linear optimization for consistency with the ELEGANT code and
10. and lattice invariant H to calculate the contribution to radiation integrals Multipoles of zero length are ignored of course This approximation is very rough and will not exactly reproduce results obtained by codes using more complete models based on calculation of the field perpendicular to the beam and its contribution to radiation integrals in both transverse dimensions But it is helpful for example to detect possible loss of damping beyond some momentum deviation which has to be checked then using a code like MAD or TRACY 20 4 5 Calculation of geometric acceptance A particle touching an elliptical beampipe of half axis a and a fulfills the condition est VEE E az diy o is the horizontal closed orbit in the error free perfectly linear lattice given by dispersion Yo 0 due to OPA s restriction on flat lattices but generalization is straightforward Betatron amplitudes are given by Az Yalt To 2a x o x x Balz x with the corresponding formula for y Betatron amplitudes thus are given by the starting conditions of the tracked particle For coupled motion at a given and constant ratio of betatron amplitudes x with A As A A KA A 1 amp A i e k 0 pure horizontal x 1 pure vertical oscillation the maximum total amplitude A x accepted by the lattice is the minimum of the limitations from all the elliptical apertures of the machine Alk min p
11. and the element apertures Dispersion is included in the horizontal beam size its contribution shown as a dashed line Momentum displays the optics for Ap p and on momentum One may select to include sextupoles or not Click Momentum again to switch off this mode Note that a sextupole connected to one of the knobs of course can only affect the of momentum curves Tune Matrix gathers quadrupoles in two groups depending on the sign of the k value and establishes a sensitivity matrix for a relative change of strength This allows relatively smooth tuning of the lattice within a small range Matching opens the panel for iteratively adjusting beam parameters Matching can be done from any location to another in the lattice i e begin end or optics markers Constraints at an intermediate marker may be added On the left panel select parameters to adjust and enter target values On the right panel select elements to be used for matching If the number of elements is equal or larger than the number of constraints the go button is enabled and matching may start The algorithm is a Newton search using the inverse square sensitivity matrix of the most effective knobs as tangent for extrapolation see K Wille s book This method converges quadratically but is rather fragile Reducing the fraction of iteration to be applied stabilizes Other pa rameters are number of iterations and required precision for termination
12. and to set its parameters see sec 3 3 for element properties The segment editor allows to type in the line up of elements Insert and Delete keys may be used Undefined elements are shown in red before saving the segment they need either to be deleted or to be defined using the element editor The periodicity field stores a number of repetitions of the segment for example used to calculate tunes etc Invert dipole polarities inverts the polarity of all dipoles and combined function magnets in the lattice Set all element apertures overwrites all element apertures with the values given in the input fields Warning all individual aperture settings if any will be lost The text editor shows the file exactly as it will be saved to disk see sec 3 1 for explanation The test button performs a syntax check 2 4 Design optics The lattice structure appears on the optics panel and a menu to select constraints pops up e periodic will try to find a solution with same parameters at both ends e symmetric will try to find solution with a a 7 0 at both ends so appending the mirror image makes it periodic e the single pass options calculate the optics starting at its left or right end or from one of the optics markers if any If periodic or symmetric fails the single pass solution from initial left values is calculated If the periodic solution was found the tune diagram pops up see be
13. any further This is typically the case if there are less correctors than monitors no convergence failure too many iterations the orbit loop did not converge failed complete failure beam ran off The buttons Corr 0 and BPM 0 set all correctors resp all BPM references to zero The figure displays the SVD weight factors where the excluded zero values are shown darker The small button toggles X and Y and the slider allows to reduce the weighting factors OPA may crash and get stuck on orbit correction if the orbit is very sick catch still missing In case of lattices without correctors or BPMs orbit correction can be started anyway and produces an error catch missing Orbit corrections works yet only for periodic solution implementation for single pass would be straightforward but 1s not yet done 2 13 Extra Currents If allocation and calibration files were given in the lattice file see sec 3 1 the magnet currents are calculated and shown Power supply is the name of a magnet family N is the number of magnets in this family and Current is the current which is the average of the current calculated for the single family members differences may be due to different magnet types connected in a family Clicking a field shows at right the family member data Snap export writes file snap for uploading to EPICS control system 1 3 Data 3 1 The input o
14. ars besides the 2nd order chromaticities and amplitude dependant tune shifts Checking these boxes activates a singular value decomposition SVD routine 7 which is controlled by the buttons appearing underneath the octupoles The Condition and Nweight labels shows the ratio of smallest non zero to largest value of the weight vector and the number of non zero values The buttons may be used to filter these values and improve the condition The SVD button performs a calculation which can be canceled using the undo button Checking the auto box enables automatic SVD after each change of a sextupole SVD uses all available octupoles but checking the lock box at an octupole excludes it If there are decapoles in the lattice they will be shown underneath They only affect the cubic chromaticites and may be modified manually only A cubical fit for the momentum dependant orbit length longitudinal chromaticity is given at the bottom numbers given are the first three orders of the momentum compaction factor multiplied by the lattice length start starts the minimizer which uses the Powell algorithm 7 The initial step size for sextupole variation may be set The minimizer will inform on its progress by listing the current value of the penalty function normalized to its start value and also by writing messages to the message window on the OPA main panel After successful termination the penalty functi
15. bitXP 0 000 OrbitY 0 000 OrbitYP 0 000 OrbitDPP 0 000 Solenoid K is solenoid strength B 2Bp incomplete beam rotation contribution to 2Q resonances to path length and to radiation integrals are not included better don t use it S01 Solenoid L 0 200000 K 0 50000 H corrector DXP is horizontal kick in mrad however it has only effect in the orbit module is ignored elsewhere If the name is CH it will be used for orbit correction V corrector DYP is vertical kick If the name is CV it will be used for orbit correction Monitor no parameters If the name is MON it will be used for orbit correction Other elements are infrequently used and may be seen in the OPA editor 16 3 4 Segments A segment is a line up of elements and segments Many segments may be defined the segment to be used to built the lattice is selected interactively later A minus sign reverses the segment A factor repeats it Correct direction of bendings with different edges is taken care off internally In the example below underlined names are segments the others are elements Segment hier archy requires that sub segments to be used by a segment have to appear earlier in the file otherwise it is an error This also avoids circular references MS DS1 SSA DSX QSE DS2 QSF DSX SSB DS3 QSG DS TMS TS MS TEST TML TMS 3 HUGO QF 5 XYZ The field nper n appearing somewhere in a segment line up defines
16. de of the peak in order to identify guess the underlying resonance 5 Results are shown in the lower panel The tune considered as the fundamental is also marked in the tune diagram The param button opens a panel to set parameters for resonance guessing fundamental tune range sets the maximum deviation of the guessed tune from the linear tune peak identification tolerance sets a parameter p defining AQ p c as the maximum tune deviation with c the order of the resonance The two filter levels are for accepting peaks and for the range of the plot By default tracking uses the apertures of the elements to test on particle loss By unchecking element apertures the apertures in the Ax Ay fields are used instead Aperture check assumes an elliptical beam pipe and tests for 1 a y ay lt 1 Note that the aperture check may underestimate losses because internally sequences of linear elements are concate nated into matrices at start Aperture checks are only done at locations of nonlinear kicks and at the track point Therefore particle tracking may also paint outside the linear acceptance ellipse The trackpoint by default is at the begin end of the lattice but the field trackpoint allows to select any location The ellipses indicating the physical acceptance will change accordingly The amplitude dependent tune shifts panel performs three series of trackings stepping up the initial
17. e bunch volume 11 the momentum acceptances from RF green and from apertures brown the parameter for the Touschek function see section 4 2 the local loss rate in linear scale and the local loss rate in logarithmic scale 2 Tracking for local dynamic momentum acceptance after pressing track the program will step along the lattice in steps of As and start particles on axis but with momentum deviation Ap p to simulate Touschek scattering A binary search on Ap p determines the minimum and maximum values of Ap p accepted at the particular location Only locations where H and its nonlinear equivalent has changed need to be tested therefore the loop jumps over non dipole elements and just copies the previous momentum acceptance data During execution the plot will switch to momentum acceptance to show the progress of the calculation Break allows to interrupt When done all calculations for loss rates and lifetime like in the linear case are done and the results are added to the plots In the plot 2 additional lines for positive red and negative blue dynamic momentum acceptance will appear In the loss rate plot it is only one line for the total losses pos and neg Input parameters e Energy may be changed for testing but the original value will be restored on exit e Coupling is the emittance ratio e Total beam current in the machine and e number of bunches give the charge per bunch e T
18. e removed 3 3 Elements Description of elements meaning of the parameters and how they appear in the input file examples All parameters can be seen in the OPA Editor All elements have a length L m 0 in some cases and horizontal and vertical apertures Ay A mm half apertures internally assumed rectangular not elliptic e Driftspace D2 Drift L 0 200000 Ax 35 00 Ay 17 00 e Quadrupole K is strength b B Bp m K gt 0 horizontally focusing Q1 Quadrupole L 0 200000 K 4 350000 e Bending magnet angle T in out edge angles T1 T2 and corresponding fringe field parameters K1IN EX K2IN EX 8 gap GAP mm and gradient K like quadrupole Angle can be positive or negative depending on bending direction An edge angle of same sign like the bend angle makes the bend vertically more focusing i e a rectangular bend always has T1 T2 T 2 no matter if T is pos or neg B1 Bending L 1 000000 T 45 00000 K 0 000000 T1 22 50000 T2 22 50000 Gap 0 00 K1IN 0 0000 KiEX 0 0000 K2IN 0 0000 K2EX 0 0000 15 Sextupole if L gt 0 K is the sextupole strength b3 m if L 0 K is the integrated sextupole strength b3L m K gt 0 is horizontally focusing for x gt 0 Sextupole strength is defined as bs B Bp 2 Byotetip R Bp N is only meaningful for L gt 0 since the sextupole is modeled as Nx driftspace L 2N thin sextupole kick b3L N dri
19. eans oo and is applied only to the resonant terms of course The bars are for comparison and visualize the contribution to the minimizer s penalty function they are products of the modes absolute values hjximp with relevant amplitudes 2J 2J and 6 and weighting factors the relevant betatron amplitudes and momentum range are given by the fields at bottom practical units here are mm mrad and Another empirical factor applies to the resonant terms to make them comparable otherwise they would be invisible compared to the chromaticities The weighting factors are given by 2 1 with w stepped up down by the and buttons For non resonant additive terms like chromaticities and tune shifts a target value can be set The check boxes in the inc row include exclude the related quantities to the minizer The penalty function is calculated as 2 F pia 2 ONI NE amp Poio Tjing jklmp For the non resonant mode where S h 0 a target value tjkimp can be given which is always zero for the resonant modes For the resonant modes a general weighting factor Wr is given in the fifth field at the bottom of the panel to increase their weight because due to interference they are smaller numbers than the additive non resonant terms but due to resonant amplification they may be more harmful 7 The right side of the panel shows the integrated strengthes of the related sextupole resp combined function
20. ength to half pole length 2 is defined by f 1 T B s AJ where f affects the orbit and fo f damping partitions emittance and energy spread An ideal sinusoidal wiggler has ds 2 1 4 fi 0 637 fo 0 5000 fs z 0 424 T 2 on Taking into account that the variations of beam functions within a half pole of a wiggler are rather small defining h B Bp the maximum curvature and further assuming that a wiggler usually has no gradient would affect I only the contributions of half pole k to the synchrotron radiation integrals 9 are approximately given by 2 a A a Ah f 1 ds fil Nye pr Alox fo prh 0 P 2 2 A A A a Als fs a Ipeh Alan fs gt ne prh Als fs 5 H i pe h 4 4 Approximative calculation of dipole down feeds For an off momentum orbit following a dispersive periodic solution all multipoles act like small dipoles dipole down feed and thus contribute to the radiation integrals affecting emittance damping partitions etc Since OPA knows only flat lattices the mosts simple model treats each multipole as a small bending magnet of angle Ag ziu Zip curvature h Ad L with L the length of the element and gradient k n 1 bn Z for n gt 2 where the average horizontal offset is taken as the mean between offset before and after the multipole Z Zou vj 2 Same simple averaging is used for optical parameters like dispersion 7
21. ftspace L 2N SD Sextupole L 0 200000 K 10 000000 N 4 Combined function magnet has the same parameters like the bending magnet except K2 fringe field parameters In addition it also may contain a sextupole strength M b3 m and the corresponding number of subdivisions N Bend angle T 0 is allowed and describes a quadrupole sextupole combination Q3C Combined L 0 400000 T 0 00000 K 4 350000 M 12 000000 T1 0 00000 T2 0 00000 K1IN 0 0000 K1EX 0 0000 Gap 0 00 N 5 Undulator period Lamb m peak field Bmax T Note since the peak field is explicitly given the undulator is the only element where the optics changes with beam energy whereas all other element are described energy indepently filling factors F1 2 3 4 3 and Gap mm Internally the undulator is represented by a series of rectangular dipoles where the two end poles have 1 4 3 4 of peak field to center the trajectory Only planar undulators with vertical field are possible U19 Undulator L 0 912000 Lamb 0 019000 Bmax 1 000000 Fi 0 636620 F2 0 500000 F3 0 424413 GAP 5 000 Ax 50 00 Ay 2 00 Marker no parameters Optics Marker useful to store beam parameters and for matching from to OM1 OpticsMarker Ax 35 00 Ay 17 00 BetaX 7 657791 AlphaX 0 000000 BetaY 0 723110 AlphaY 0 000000 EtaX 0 123958 EtaXP 0 000000 EtaY 0 000000 EtaYP 0 000000 OrbitX 0 000 Or
22. ged to the BPM field It will show its reading there By switching from actual to Reference a target value can be entered for x and y and is written to the BPM after pressing set The status statistics panel at lower left allows to set the starting point and to include or exclude nonlinear elements The statistics panel shows mean rms and max values for orbit relative to reference BPM for absolute orbit at all elements all or for the corrector kicks Corr press to toggle The plot panel at lower right allows to choose between corrector and orbit BPM plots If keep max is checked no autoscaling of plot is done The misalign and correct panel sets misalignments and performs orbit corrections Misalign 13 ments are entered in micron and will be applied to all magnets not the correctors as Gaussian distributed random numbers with the given cut off in sigma seed determines the series of random numbers Set applies the misalignments zero sets them to zero and re set applies a previous setting again to save retyping the input fields Corr calculates the response matrix sets up the SVD and performs orbit correction The results as shown below the Corr button are COD no correction done zeroed success orbit agrees with reference minimized success orbit does not agree with reference but does not converge
23. he cavity voltage defines bunch length and RF momentum acceptance If it is lower than the energy loss per turn the bunch length is set to the ring circumference and the momentum acceptance is zero e The harmonic number contains RF wavelength The number of buckets can not be higher than the harmonic number this is checked e The longitudinal resolution defines As for tracking along the lattice e Momentum resolution defines the precision of the binary search e Numbers of turns to track to decide on loss or survival e Residual gas is defined by atomic number atoms per molecule and partial pressure The gray fields show quantities derived from the input values which can not be modified Track starts the tracking which is a 4 D tracking i e keeping the momentum constant Track sync is an improvised 5 D tracking varying the momentum deviation 6 Ap p in turn k simply as k 6 cos 27v k with vs the synchrotron tune The implementation is very inefficient and therefore this tracking is rather slow 12 Export plot writes a file name _touschek_N wmf where N 0 8 is the number of the plot N 0 for beta function plot etc Export data writes a file name _touschek txt with all plotted data ZAPLAT writes a file name _zaplat dat to be used as input file zaplat dat by the ZAP code 2 for calculation of intra beam scattering Note that aperture data as needed for Touschek lifetime calculations
24. iltonian are calculated and added to the 13 second order sextupole modes Also cubic chromaticities are calculated Chromaticity and path length calculation is done by numeric differentiation of the dispersive orbit whereas all other quantities are calculate analytically All Hamiltonian modes are normalized to betatron amplitudes of 2J 1 and a relative energy deviation of Ap p 1 ADTS values are displayed as 0Q 0 2 J As much as possible is calculated only once at start of the sextupole module This may cause some delay depending on the total number of sextupole kicks in the lattice which depends on the number of slices per sextupole etc But afterwards the iterations will be fast A tune diagram will also pop up In addition to the tune diagram opening with linear optics it shows the expected tune spread of the beam the magenta cyan parabola shows the tune variation due to chromaticity and the green straight lines due to betatron amplitudes The sextupole panel lists at left the 25 Hamiltonian modes plus a sum of total sextupole strength The numbers are the absolute value of the complex mode and given in SI units To each resonant mode exists a complex conjugate which is not shown The periods field will be set to the number of periods of the lattice but may be changed to study how the resonant terms vary due to interference For the non resonant terms the period number is just a scalar multiplication factor A value of 0 m
25. is located so it does not run from a CD Table 1 gives an overview of files read or written by OPA 2 2 Start The OPA menubar gives access to all functions The large buttons on the GUI access only the most used functions If functions are not available because a prerequisite is missing e g periodic solution for tracking the buttons are disabled and shown in gray Active file shows the selected lattice file opa A lattice file contains a list of elements magnets and a list of segments A segment is a series of elements and segments see section 3 for definition of elements and segments The active segment is selected from the segment list on the GUI From this segment the lattice is built by recursive expansion of the segments to get the elements line up which is shown in the message window when pressing show lattice Upon start only the File and Edit options in the menu bar and the corresponding buttons are enabled One may either read a opa file or create a new one by using one of the two editors 2 3 Editor There is the OPA editor and the text editor New users may prefer the OPA editor advanced users the text editor The OPA Editor shows a list of elements and of segments and further has input fields for beam energy element apertures and for a comment text The functionality is quite obvious and does not need much explanation The element editor allows to define the type of element
26. king the box after the name of the parameter It then appears as a button label in the minimizer panel at bottom Clicking this button shows the parameter in the plot and allows to edit target values as polynomial coefficients in the fit panel at right which are shown in pink in the plot The minimizer is of Powell type 7 and works on the penalty function ee f 5 fr 9 7 with the array of momentum values covering the selected range f the momentum dependent parameter fr the target for this parameter and wy a weighting factor The latter is entered left of the button Only nonlinear elements are available for minimization the minimizer knobs are 10 the strengths normalized to the initial values Optimize starts the minimization Break in terrupts it Reset restores the initial values Plot absolute relative toggles between showing parameter and target or the difference between both Target values are saved on exit however this has been implemented yet only for tunes and path length up to 12th order 2 9 Tracking dynamic aperture There are three modes x vs y x vs Ap p and y vs Ap p When selecting the first a Ap p offset may be given for the others it is a Ap p range The plot will show the geometric acceptance based on linear beam dynamics and the grid for probing stability by starting parti cles at these locations Grid parameters may be stepped up and down by the cells buttons
27. low Beta functions and dispersion will be shown 3 in blue 3 in red 7 in green The table at right gives in its upper part total values of the lattice some of them only valid of course if the lattice would be repeated periodically In the lower part local optics values are displayed The location can be selected by right clicking on the plot Moving the mouse over one of the elements displayed at the bottom of the figure shows its name Left click on an element and releasing the mouse button after moving to one of the knob fields connects the most important parameter of this element to the knob Variation by moving the slider or entering numbers changes the optics The range of variation is given by the fields at the bottom of the knob which are adjusted automatically but can be changed using the lt gt and gt lt buttons Left double click on an element opens the panel from the element editor which allows to change all parameters Buttons at the top of the plot allow to zoom in calculation through elements proceeds in slices of length corresponding to 1 pixel on screen The button field at lower left Start again selects the constraints Envelopes is for showing the beam size if the equilibrium values of the lattice are used an emittance coupling factor has to be given since there is virtually no vertical emittance in an ideal flat lattice The envelope plot will show the 1 sigma beam size
28. magnet families Maximum strength and step size for pressing the gt and lt buttons are given below gt gt and lt lt buttons apply 20 steps off sets to zero res restores the initial value The lock check box excludes the family from the minimizer Underneath are windows to set maximum strength and step size For automatic adjustment of linear chromaticities to the target values two sextupole families have to be selected by clicking the check boxes in the row labeled If these sextupoles have no dispersion chromaticity correction will be impossible and an error message is shown There may be a small deviation from the target value of chromaticity This is due to the fact that linear quadratic and cubic chromaticities are obtained from numeric differentiation whereas the chromatic sextupole values are calculated using the simple 2 x 2 matrix containing the well known sums over beta functions and dispersion The select button launches a window for visualization of the first order resonances it displays the sextupole kick vectors in the complex plane Pressing select again toggles between the 8 resonance modes which will be highlighted at left The sum is shown as circle An 8 plot shows the sum vectors of the 8 resonance modes for comparison If there are octupoles in the lattice they will be shown underneath the sextupoles and a row of checkboxes labeled O appe
29. omentum Actually this module does no tracking but calculates the linear optics along the off momentum orbit It works for periodic and also for single pass systems the checkbox at top right makes the selection and is checked at start if a periodic solution was previously calculated The range of momentum variation and the number of steps may be set and if a periodic or single pass solution is requested the corresponding checkbox is set following previous Optics Design calculations Go starts the calculation A tune diagram pops up in case of periodic solution Afterwards several plots may be selected by the radio buttons at left Each curve is fitted by a polynomial the order to be selected by the field at left where also the coefficients will be shown in a table The Units button switches between plot units and SI units for displaying the coefficients In the tune plots first four radio buttons also the theoretical values actually calculated in the same way by numeric differentiation are show by solid lines if the sextupole module was used before The chromatic beam footprint will be shown in the tune diagram _ gt WMEF resp TXT writes a graphics file resp a text file of the data named name _momentum_N wmf resp txt where N is the number of the plot radio button Double clicking the image copies it to the clipboard Up to four parameters may be selected for automatic minimization by chec
30. on is shown in blue after interrupt in magenta The minimizer does not use the octupoles however if the auto option for SVD is activated the octupoles are set after each minimizer step In the same way the chromaticity sextupoles are set Exit terminates the sextupole programs and asks if the new sextupole values should be saved Note that the question to save the data refers only to an internal save to further proceed inside OPA but does not save the data to the file 2 7 Tracking phase space This panel shows Poincar plots of particle motion in horizontal and vertical phase spaces x x and y y it is x y although the axis are labeled ps py The circles or ellipses show the linear acceptance given by the physical aperture When starting a particle the effective apertures are also shown which are reduced due to coupling assuming elliptical beam pipes see sec 4 5 By left clicking in the diagrams or by entering numbers in the centre panel the starting con ditions are selected A momentum deviation may be entered in the dp p field run tracks the particle a number of turns as given in the top panel more adds more turns clear clears the panel exit terminates the program A Fourier spectrum of particle motion is calculated after tracking and shown in the lower diagrams The algorithm used is FFT with sine window and sin x peak interpolation to obtain frequency and amplitu
31. or only Nonlinear elements are treated by a Only planer insertion devices allowed Simple model as dipole array Only 4D tracking no synchrotron oscillations Approximative not exact calculation of path length and dipole down feed from higher multipoles contribution to radiation integrals How to use Installation and files OPA is a Windows program best tested for XP There is no special installation procedure OPA is one single executable opa exe and does not need additional libraries or files to run Table 1 Files read or written by OPA file read write files in the OPA folder opa3_path ini e e remember last used files diagopa txt files in each data folder code development opa3_set ini user settings for this folder name opa lattice files name plot wmf plot export as Windows metafile name _ plot txt plot data export as text file name _ plot out plot data export as text file name _ plot gp GNU plot command file for plotting out name lat TRACY lattice file name mad MAD X lattice file for EPICS export of magnet currents in data folder allocation opa e power supply allocation calibration opa magnet calibrations name snap e EPICS snapshot file name dev e outdated So all to do is to create a folder for OPA and perhaps one or another for the data Note that OPA needs write permission also for the folder where it
32. the periodicity i e the factor n is applied for convenience to tunes sextupole terms etc of the lattice buit from this segment e g ARC HALF XXX HALF nper 6 Note if one likes to split a bend for example to put a marker in the centre and a non zero gap is given then one has to set K1EX 0 0 otherwise the internal edge where the dipole is split will have an effect on the vertical focusing Example BHALF Bending L T Tl T2 0 0 Gap K1IN K1EX 0 0 BEND BHALF BHALF 4 Theory 4 1 The sextupole Hamiltonian Calculations of 1st and 2nd order sextupole terms have been done by Johan Bengtsson 5 6 We add here the multiplication factors for N periods For first order the complex factor ay to transform the Hamiltonian mode for 1 period into N periods i e h ay h is given by 5 1 iNmpt N ina l e ay e D aaa 1 emp with m j k l m the mode of hjj and u 2T Qz Qy the ring tune Defining y mpi 2 this can be expressed as aN siny sin 2N 1 Cos cos 2N 1 w 2sin yY 2sin Y 17 In the limit N oo we may neglect the fast varying term and get 1 1 1 co OO an t cot y an ee ees 2D lan 2sinw revealing the resonance denominator For the 2nd order we define S s Ss s5 S T x 3 NAUNA N 7 S S ilps i p DES cone a Sov reree 9 s 1 s 1 s s s 1 s 1 s 1 i k m with Ts b3 L s bzs Bys sextupole s
33. utput files Files with extension opa are read and written by OPA The syntax is simple look at an example file This is for internal use at SLS and probably would have to be modified for other machines 14 First are the global parameters like beam energy etc 3 2 then comes the list of elements 3 3 and and finally the list of segments 3 4 which will be unpacked recursively to generate the lattice All inputs are optional since OPA may start without lattice as well For parameters of an ele ment not given in the input file OPA assumes reasonable defaults If a parameter is mistyped OPA will ignore it and set it to the default value Text in curly brackets is treated as comment i e ignored by OPA except text bracketed by com com which is the official comment text like lattice title and some notes Further comments visible in the opa file are generated by OPA for the user s convenience Comments written manually into the opa file will be lost To use the option of exporting magnet currents and channel names 2 13 a link to the corresponding allocation and calibration files is required and should be given at the beginning of the opa file allocation allocation file dat calibration calibration file dat 3 2 Global Parameters This is only the comment com com the beam energy optionally the allocation calibration links and optionally explicit initial parameters to b
34. yP a with a2 Cowl VI K Bok G21 Zo Azk py EA N Saale A or asi bodys Nk Nk The contour of the geometric acceptance in the x y plane at the location of the track point t is thus given by k a V 1 KJ K Ba JK wA K By 6 0 1 References men H Bruck Circular Particle Accelerators Los Alamos 1966 LA TR 72 10 2 M Zisman et al ZAP user s manual Berkeley 1986 LBL 21270 wo A Streun Momentum acceptance and Touschek lifetime SLS Note 18 97 4 S Khan Simulation of the Touschek effect for Bessy II a Monte Carlo approach BESSY TB 177 93 OU J Bengtsson Non linear transverse dynamics CERN 88 05 D J Bengtsson The sextupole scheme for the SLS SLS Note 9 97 21 7 W H Press et al Numerical Recipes in Pascal Cambridge 1989 8 K L Brown A first and second order matrix theory Stanford 1967 SLAC 75 9 A W Chao M Tigner Handbook of accelerator physics and engineering Singapore 1998 22
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