ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 77¥> >> ¥77 O ¨& O¨¥¥7 >>7 ALE >>>>7 ALE >7777CHANGREF: Transformation to a new reference frameCHANGREF it transports the particles to a new reference frame. It can be used anywhere in a structure. The newcoordinates of the particles , , ¥ and , , ¥ , and· 7by where, § ² ¢and ² ¢and the path length are deduced from the old ones are shifts in the horizontal plane along,respectively, · - and > -axis, and ALE is a rotation §7 wALE> 77 w § ² ¢ (*) 7> ² ¢ O¨ ² ¢w§ ² ¢aw> & > (*)Ñ· > · 7Figure 16: Scheme of the CHANGREF procedure.around the O ¨ -axis. is given the sign § ² ¢awof ALE .This keyword may for instance be used for positioning optical elements, or for setting a reference frame at the entrance orexit of field maps, or to simulate misalignements (see also KPOS).Effects of CHANGREF on spin tracking, particle decay and gas-scattering are taken into account (but not on synchrotronradiation).> (.).The example below shows the use of CHANGREF for the symmetric positioning of a dipole+quadrupole magnet in adrift-bend-drift geometry with 12.691 degrees deviation (obtained upon combined effect of a dipole component and ofquadrupole axis shifted 1 cm off optical axis).Zgoubi data file :Using CHANGREF’OBJET’51.71103865921708 Electron, Ekin=15MeV.21 1 One particle, with2. 0. 0.0 0.0 0.0 1. ’R’ Y_0=2 cm, other coordinates zero.1 1 1 1 1 1 1’MARKER’ BEG .plt -> list into zgoubi.plt.’DRIFT’10 cm drift.10.’CHANGREF’0. 0. -6.34165 First half z-rotate.’CHANGREF’0. 1. 0. Next Y-shift.’MULTIPOL’ Combined function multipole, dipole + quadrupole.2 -> list into zgoubi.plt.5 10. 2.064995867082342 2. 0. 0. 0. 0. 0. 0. 0. 0.0 0 5. 1.1 1.00 1.00 1.00 1.00 1.00 1. 1. 1. 1.4 .1455 2.2670 -.6395 1.1558 0. 0. 0.0 0 5. 1.1 1.00 1.00 1.00 1.00 1.00 1. 1. 1. 1.4 .1455 2.2670 -.6395 1.1558 0. 0. 0.0 0 0 0 0 0 0 0 0 0.1 step size1 0. 0. 0.’CHANGREF’0. -1. -6.34165 First Y-shift back, next half z-rotate.’DRIFT’10 cm drift.10.’MARKER’ END .plt -> list into zgoubi.plt.’FAISCEAU’’END’Zgoubi|Zpop0.10.050.0-.05-.1TrajectoryY_Lab (m) vs. X_Lab (m)Opticala x i s0.0 0.05 0.1 0.15 0.2 0.25Note: The square markers scheme the stepwise integrationin case of o 5 cm additional fringe field extent upstream anddownstream of the 5 cm long multipole.