Frank Zimmermann, ILC DR teleconference fast ion effects analytical estimates of  trapping condition  exponential FBII rise time  incoherent tune shift at end of train compare three rings: OTW (3.2 km), OCS (6.1 km), TESLA (17 km) assume partial CO pressure of 0.01 nTorr use excel file provided by Tor Raubenheimer; add beam sizes from A. Wolski, & parameters for OCS

Frank Zimmermann, ILC DR teleconference straightwigglerarc length [km] energy [GeV]5 #bunches2820 bunch population2x10 10 bunch sep. [m]5.994  x [mm] 5 (2.5)55  y [mm] (2.5)0.014 average  x [m] average  y [m] ave.  x [mm] (0.19) ave.  y [mm] (0.19) parameters TESLA ring w/o (w) coupling bumps

Frank Zimmermann, ILC DR teleconference parameters OCS (assume single train, and 5 GeV) straightwigglerarc length [km] energy [GeV]5 #bunches2820 bunch population2x10 10 bunch sep. [m]1.844  x [mm] 5.5  y [mm] 0.02 average  x [m] average  y [m] ave.  x [mm] ave.  y [mm]

Frank Zimmermann, ILC DR teleconference parameters OTW straightwigglerarc length [km] energy [GeV]5 #bunches2559 bunch population2.2x10 10 bunch sep. [m]1.259  x [mm] 4  y [mm] 0.02 average  x [m] average  y [m] ave.  x [mm] ave.  y [mm]

Frank Zimmermann, ILC DR teleconference straightwigglerarc critical mass [m p ]24 (1)28544  y,exp (e-f. time) [  s] 76 (1364)67350 incoh. tune shift  Q y (0.010) results for TESLA damping ring w/o (w) coupling bumps rise-time & tune-shift estimate assumes trapping of CO, 0.01 nTorr CO pressure all around the ring, and 0.3 relative ion-frequency spread; even if ions not trapped for final conditions, certainly they are trapped during the damping process net rise time  y,exp ~83  s (162  s) total tune shift  Q y ~0.188 (0.025)

Frank Zimmermann, ILC DR teleconference straightwigglerarc critical mass [m p ]24696  y,exp (e-folding time) [  s] incoherent tune shift  Q y results for OCS damping ring rise-time & tune-shift estimate assumes trapping of CO, single train, 0.01 nTorr CO pressure all around the ring, and 0.3 relative ion-frequency spread; even if ions not trapped for final conditions, certainly they are trapped during the damping process net rise time  y,exp ~210  s total tune shift  Q y ~0.04 rise time larger & tune shift smaller than for 17-km ring

Frank Zimmermann, ILC DR teleconference straightwigglerarc critical mass [m p ]81518  y,exp (e-folding time) [  s] incoherent tune shift  Q y results for OTW damping ring rise-time & tune-shift estimate assumes trapping of CO, single train, 0.01 nTorr CO pressure all around the ring, and 0.3 relative ion-frequency spread; even if ions not trapped for final conditions, certainly they are trapped during the damping process net rise time  y,exp ~199  s total tune shift  Q y ~0.022 rise time similar to & tune shift smaller than for 6.1-km ring

Frank Zimmermann, ILC DR teleconference conclusion from comparison:  ions like CO are trapped over most of the circumference for all three designs  the 3.2-km ring (OTW) yields smallest tune shifts (~0.022)  smallest growth rates are obtained for both 3.2-km (OTW) and 6.1-km ring (OCS)  exponential rise time is about 200  s for an average CO pressure of 0.01 nTorr  with coupling bumps the tune shift and rise time for the TESLA ring assume comparable values, but in this case even H ions may be trapped