ZGOUBI USERS' GUIDE - HEP

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126 4 DESCRIPTION OF THE AVAILABLE PROCEDURESs4ssss4ss 1 §MATRIX: Calculation of transfer coefficients, periodic parametersMATRIX causes the calculation of the transfer coefficients of the structure, at the spot where it is introduced in thestructure, or at the closest horizontal focus. In this last case the position of the focus is calculated automatically in thesame way as the position of the waist in IMAGE. Depending on option IFOC, MATRIX also delivers the Twiss functions,tune numbers, chromaticities and other perturbation parameters in the hypothesis of a periodic structure.Depending on the value of option IORD, different procedures followIf IORD = 0, MATRIX is inhibited (equivalent to FAISCEAU, whatever IFOC).If IORD = 1, the first order transfer matrix ?1 big Ais calculated, from a third order expansion of the coordinates. Forinstance4>4T4T4 w > T 4 o ‰ _o 4" ¬ w o 4o > 4 T 4 oo > 4 will yield, neglecting third order terms, o 4 ‰ w1 7$7 ¬@ 41 bhg Aand ofthe second order matrix ?If IORD = 2, fifth order Taylor expansions are used for the calculation of the first order transfer matrix ?A. Other higher order coefficients are also calculated.bhgkjAn automatic generation of an appropriate object for the use of MATRIX can be obtained by means- if IORD = 1, of the procedure OBJET(KOBJ = 5[.I, I=1,9]) (pages 39, 194), that generates sets of up to 9*11 trajectories.In this case, up to nine matrices may be calculated, each one wrt. to the reference trajectory of concern as indicated usingI in KOBJ = 5[.I, I=1,9] ;- if IORD = 2, of the procedure OBJET(KOBJ = 6) that generates a set of 61 trajectories.The next option, IFOC, acts as follows‰ ‰ref. . wIf IFOC = 0, the transfer coefficients are calculated at the location of MATRIX, and with respect to the referencetrajectory. For instance, ‰and‰above are defined for particle number as ‰ ‰, and wIf IFOC = 1, the transfer coefficients are calculated at the horizontal focus closest to MATRIX (determined automatically),while the reference direction is that of the reference particle. For ‰instance, is defined for particle number ‰ ‰as ref.)). w focus, while‰is defined as‰ ‰ wIf IFOC = 2, no change of reference frame is performed: the coordinates refer to the current frame. Namely, ‰ ‰ ,‰ ‰Periodic structures , etc.If IFOC = 10 + NPeriod, MATRIX calculates periodic parameters characteristic of the structure such as Twissfunctions and tune numbers, assuming that it is NPeriod-periodic; no change of reference is performed for thesecalculations. If IFOC = 2 additional periodic parameters are computed such as chromaticities, beta-function momentumdependence, etc.These quantities are derived from the first order perturbed and unperturbed transfer matrices as obtained in the waydescribed above, and by identification with the Twiss ?G form .1 big A ¤&` {a(.)-G -
4.5 Output Procedures 127PICKUPS: Beam centroid path; closed orbit’ed key-¨In conjunction with REBELOTE, this procedure computes by the same method the closed orbit in the periodic structure.PICKUPS computes the beam centroid path, from average value of particle coordinates as observed ¨¦´¡W¢atwords.The ¨¦´¨ list of concern follows the keyword PICKUPS.¡.¢
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CEA DSM DAPNIA-02-395 (2002)ZGOUBI
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Table of contentsPART A Description
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PART ADescription of software conte
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8¤¥ PARTICUL Particle characteris
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10ELECTROMAGNETIC ELEMENTSDecapoleD
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!!%" && 131 NUMERICAL CALCULATION
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1.2 Integration of the Lorentz Equa
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1.2 Integration of the Lorentz Equa
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4Ž ^ ˜ ¡§ ^"- ^ ˜ ¡ ^¡wTGT
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in fourth order. The coefficients
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4 ´ ´""4§> ´4 >4>1.4 Calculati
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A cylindrically symmetric field can
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Introducing also ¡The derivatives
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30 3 SYNCHROTRON RADIATION¾ÍôVT
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32 3 SYNCHROTRON RADIATIONÉ Éwher
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354 DESCRIPTION OF THE AVAILABLE PR
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4.2 Definition of an Object 37where
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4.2 Definition of an Object 39\Pqî
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4.2 Definition of an Object 41¹q
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4.3 Declaration of options 43\P4.3
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4.3 Declaration of options 45END or
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4.3 Declaration of options 47· £
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4.3 Declaration of options 49{ww{{q
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4.3 Declaration of options 51GASCAT
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4.3 Declaration of options 53·{N$
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4.3 Declaration of options 55PARTIC
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4.3 Declaration of options 57RESET:
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4.3 Declaration of options 59if qî
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4.3 Declaration of options 61P4©@4
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4.3 Declaration of options 63:£¨
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u2 >04.4 Optical Elements and relat
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4.4 Optical Elements and related nu
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Page 75 and 76: 4.4 Optical Elements and related nu
Page 123 and 124: 4.5 Output Procedures 123¨ ¢ < ¤
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Page 131 and 132: 4.5 Output Procedures 131TWISS: Cal
Page 133 and 134: 4.6 Complementary Features 133U@©@
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Page 139 and 140: Keywords and input data formatting
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Page 146 and 147: 146 Keywords and input data formatt
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176 Keywords and input data formatt
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Examples 231oÑwü¦INTRODUCTIONSev
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2331 MONTE CARLO IMAGES IN SPES 2Fi
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235********************************
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237zgoubi data file.800 MeV/c KAON
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2393 IN-FLIGHT DECAY IN SPES 3Figur
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241Excerpt of zgoubi output : histo
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243Excerpt of zgoubi output : first
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245zgoubi data file (begining and e
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247zgoubi data file.MICROBEAM LINE,
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2499 HISTO HISTOGRAHISTOGRAMME DE L
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253INTRODUCTIONThe basic zgoubi FOR
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REFERENCES 255References[1] F. Méo
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Indexacceleration, 56, 58, 74, 155,
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