1. SIMPSONS: Convergence of the Space Charge simulations for RCS Noda Hotchi

2. Simulation conditions Operation tune 6.72,6.35 (D-set) Output beam power :0.2MW Macro particle number :200000 With painting process (correlated painting) With multi-pole components (bend,Quad) No chromatic correction, 3rd resonance correction No alignment error and field error(K0,K1) ----------------------------------------------------------------- macroparticle, numpart=200000, & pc=0.6129113, & ldistrib=lunigaus, distribu=gaussian, & dssig=0.1, dppsig=0.0001, & exn=0.25E-06, eyn=0.25E-06, & betax=10.73958590, alphax=-1.639643595, & betay=11.33428017, alphay=0.4, & driftspace=0., sigmacut=4.0, xinjoff=0., & injectrn=235, painttra, constnum, & iseedlon=9236487, iseedtra=4857679, &

3. Free parameters of code and estimated parameters Free parameters of SIMPSONS –r :30,50,100 –θ :32,64,128 –z :30,50,100,150,200 –time step:4.7e-9, 9.4e-9, 18.7e-9, 4.7e-8 [sec] Estimated parameters –Beam loss Realistic physical aperture and primary collimator are set Aperture of primary collimator is 324 .mm.mrad –Emittance 38,68,90 and 95% emittance

4. r mesh number(nrg) dependence Beam loss curve38,68,90 and 95% emittance at 750turn

5.  mesh number(nthg) dependence Beam loss38,68,90 and 95% emittance at 750turn

6. Conclusion(1) The current mesh sizes of r and θ (nrg=50,nthg=64) are good values for both qualitative and quantitative estimation.

7. Lngitudinal mesh number (nzg) dependence Beam loss38,68,90 and 95% emittance at 750turn

8. Conclusion(2) Mesh size of z is also good value for qualitative estimation. However, it may be insufficient for quantitative estimation of 95% emittance, as Sasha-san says. –We have chosen nzg = 100 for next stage of systematic studies. By this change, CPU time is increased about 12%(660s/turn→740s/turn), but it is acceptable…. –For the more detail estimations which selected carefully, we will use nzg=150 (CPU time30%up) or 200 (CPU time50~60%up).

9. tstep

10. And more … –We have to discuss the confidence of simulation result for a beam halo. Comparison of simulation results of different codes. Comparison of simulation result and experimental data. –It is very difficult to monitor a beam halo….