ZGOUBI USERS' GUIDE - HEP

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 -