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Tentative Analysis of Proposals on SB Longitudinal Polarization

Tentative Analysis of Proposals on SB Longitudinal Polarization. S. Nikitin Budker Institute of Nuclear Physics SB RAS Visit to LNF INFN (Frascati) 14 Sept.-3 Oct. 200 9. Items. Calculation of the radiative relaxation time of longitudinal polarization and the stationary polarization degree

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Tentative Analysis of Proposals on SB Longitudinal Polarization

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  1. Tentative Analysis of Proposals on SB Longitudinal Polarization S. Nikitin Budker Institute of Nuclear Physics SB RAS Visit to LNF INFN (Frascati) 14 Sept.-3 Oct. 2009

  2. Items • Calculation of the radiative relaxation time of longitudinal polarization and the stationary polarization degree for the present variant of polarization insertion (SLAC-Frascati) with 3/2*Pi spin rotation angle in the bend magnets between the rotator and I.P.(independent approach) • Comparison with Siberian Snake • Estimate of depolarization effect due to field errors • Trying an alternative variant of the spin rotator scheme with the aim to enlarge margins affecting the depolarization time

  3. Crude estimation of the SLAC-Frascati scheme S. Nikitin/SB-NOTE-ACC- 2008- 001: S.A. Nikitin 16.09.09

  4. Calculation of the stationary longitudinal polarization degree for the 2009 SuperB project (LER E=4.18 GeV) • SLAC-Frascati variant of the spin rotator insertion • Betatron contribution account based onS. Nikitin/SB-NOTE-ACC- 2008- 001 n=9.5 n=9.5 S.A. Nikitin 21.09.09

  5. Siberian Snake estimation S.A. Nikitin 21.09.09

  6. Spin Response Function Calculation for LER arcs S.A. Nikitin 27.09.09

  7. Estimation of depolarization effects of field errors1. Radial magnetic field in arcs S.A. Nikitin 28.09.09

  8. Estimation of depolarization effects of field errors2. Tilts of focusing elements in arcs S.A. Nikitin 28.09.09

  9. Example of an alternative layout based on the use of tunable–over-energy spin rotator scheme* * S.A. Nikitin, preprint Budker INP 2009-4 - one of available energy points from a comparatively long interval near 4.2 GeV (independent coupling localization in every insertion; another energy value other values of angles) S.A. Nikitin 16.09.09

  10. Spin kinetics with the alternative spin rotator scheme • Minimal depolarization effect in a long energy interval • (possibility to vary HER and LER energies) • 80 min depolarization time at an optimal energy 4.1 GeV S.A. Nikitin 16.09.09

  11. Resume, remarks and current activity • Calculation of the radiative spin relaxation time has been done accounting betatron contribution into spin-orbital coupling from the optics at the solenoid insertions. SLAC-Frascati scheme lets to obtain 76% polarization degree in stationary conditions of the Trickle Injection mode at a beam lifetime of 3 min. • Spin-response function for transverse field imperfections has been calculated for azimuths in LER arcs. Applied approach is based on the DKS formula with taking into account a general spin phase advance of p over the section with rotators and I.P. Estimations as well as more accurate considerations of depolarization effects of field errors are available using this function. • Hxfield errors due to 100 micron uncorrelated vertical displacements of quads as well as due to tilts of the dipoles with angle spread 3*10-4 do not notably affect the polarization when neglecting the spin resonances with betatron tunes. • Estimated depolarizing effect of quad tilts with angular spread 3*10-4 matches with that from spin rotators in only narrow regine of the radial betatron tune near the spin resonance • Siberian Snake becomes preferred in the case of Fast Kicker Injection mode (Raimondi). • Proposed alternative tunable-over-energy spin rotator scheme increases depolarization time . by a factor of 4 but requires essential changes in a bend magnet configuration as well as in optics at the section with rotators. • Estimation of the Beam-Beam depolarization effect at SB LER is in a progress. For this aim the spin response function at I.P. of a specific form is under consideration.

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