ZGOUBI USERS' GUIDE - HEP

244 5 MULTITURN SPIN TRACKING IN SATURNE 3 GEV SYNCHROTRONÄ‹Ô‹Œ‹Œ‹‹5 MULTITURN SPIN TRACKING IN SATURNE 3 GeV SYNCHROTRON0.00015X’ (rad) vs. X (m)1.TUNES0.00010.5E-40.0-0.5E-40.80.60.4-0.1E-30.2-.00015-.0008 -.0004 0.0 0.0004 0.0008Z’ (rad) vs. Z (m)0.58 0.62 0.66 0.7dP/Ps vs. Phase (rad)0.0020.0020.0010.00.0010.0(3) (2) (1)-.001-.001-.002-.002-.004 -.002 0.0 0.002 0.004-3 -2 -1 0 1 2 3Figure 49: Tracking over 3000 turns. These simulations exhibit the first order parameters and motions as produced by the multiturnray-tracing.(A) Horizontal phase-space: the particle has been launched near to the closed orbit (the fine structure is due ²Š³y´ to coupling inducedby bends fringe fields, also responsible of the off-centering of the local closed orbit - at ellipse center).(B) Vertical phase-space: the particle has been launched with ´Ëᵸ·ž¹ ºœ»_¼T½ž¾m, ´ á µ ½ . A least-square fit by ¿ N ´ =ÁÀ¢Âoà N ´$´ ÀẃÅ µŽÆ N N  ½aºaº = µÉ½ž¹ ¿ N’ÇoÈ ºo» m¾ Æ µÊ¼  ¾ ¹ N N µ¸½9¹  â N’ÇoÈ Ä Â¼T½ µ à ·a·œ·ý ý ÇoÈ(Ì µÎ½9¹ ÇoÈ ÏaÐÑoÒº ¼ Í µËÆ N Æ µ©½9¹ ¼D½ž¾ Ïœ½aÒ9¼ N  Íyields m, , , m.rad in agreement with matrix calculations.(C) Fractional tune numbers obtained by Fourier analysis for m.rad: , (theinteger part is 3 for both).(D) Longitudinal phase-space (DP, phase): articles with initial momentum dispersion º0¼D½ ¾ of ¼D½ ¾ (1), (2), ¼T½ ¾ 1.65 (3) (out ¹Õ¼ T/s); analytical calculations give accordingly momentum acceptance ofµof acceptance), are accelerated at 1405 eV/turn Ó (10¾ 1.65 .Figure 50: Crossing ¿­Ö¸µ¨Ñ&³*Í N of , ÓÔµ  ¹Õ¼ at T/s.Æ N Ç„È µ×¼  ¹  ¼T½ ¾(A) m.rad. The strength of the resonance ØÙÆyØ µÚО¹ Д¼D½ ¾isasymptotic polarization is about 0.44.. As expected from the Froissart-Stora formula the(B) The emittance is Æ N Ç„È µÊ¼a¹  ¼T½ž¾ now m.rad; comparison with (A) shows Ø„Æ•Ø that is proportional Û Æ N to .(C) Crossing of this resonance for a particle having a momentum dispersion ¼T½ ¾ of .