1. RCS simulation 現状 と 今後 平成１ 8 年 4 月１４日 發知

2. Comparison with Machida’s result Machida’s result (6.72, 6.35) 181 INJ., 0.6 MW@Ext. W/O CC W/ CC W/ Mult. of BM & QM W/O Mult. of BM & QM W/ CC Beam survival turns time (sec) Present result QxQx QyQy 1200 turns

3. Comparison of Beta functions Machida’s beta Present beta Beta function for 1/3 of RCS @ (6.72, 6.35) B x (m) B y (m) s (m)

4. Comparison of painting area Machida Present Normalized phase space Matched beam, Emittance of linac beam:  Gaussian(2  ) with  =1.0  for  x n,  y n Mismatched beam, Emittance of linac beam:  Gaussian(4  ) with  =0.25  for  x n,  y n 324  216  Effective painting area: ~ 170  (x & y) mm mrad Effective painting area: ~ 170  (x), 100  (y) mm mrad x-x’ y-y’ x-x’ y-y’ ~170  ~100 

5. Improvement of painting Effective painting area: ~ 170  (x), 100  (y) mm mrad Effective painting area ~ 170  (x & y) mm mrad Twiss parameters of linac beam  x =10.740 m,  x =-1.640  y =11.334 m,  y =+0.4 Twiss parameters of linac beam  x =10.740 m,  x =-1.640  y =11.334 m,  y =  0.4 Improved x-x’ y-y’ x-x’ y-y’

6. Beam loss after “some improvements” (6.72, 6.35), 181 INJ., 0.6 MW@Ext. Chromatic cor. : ON Beam survival turns W/ Mult W/O Mult xx Paint area Linac beam profile

7. RCS simulation - Mesh transverse : 50(r) x 64(  ) for R=0.17 m longitudinal : 100 - Injection energy and beam power 181 MeV inj., 0.6 and 0.3 MW @ Ext. - Number of macro particles 200000 - Paint type Correlate - Linac beam profile  x : 0.256  (rms), 3.750  (99.5%)  y : 0.252  (rms), 3.485  (99.5%)  p/p : 0.00007(rms), 0.00013 (99.5%)  0.25  for  x,y, 0.0001 for  p/p Gaussians (4  ) with - Twiss parameter of linac beam (mismatched beam)  x =-1.640,  x =10.740 m  y =-0.4,  y =11.334 m - Tracking condition -

8. Effective painting area ~ 170  (x & y) mm mrad Twiss parameters of linac beam  x =10.740 m,  x =-1.640  y =11.334 m,  y =  0.4 Painting Mismatched beam, Correlate paint

9. RCS simulation - Errors to be included in the simulations - (1) Multipole field components of BM & QM BM : MEASURED data & TOSCA QM : TOSCA (The measurement will be performed soon.) (2) Field errors of BM & QM BM : MEASURED data, Shuffling QM : No data → Random error [ Gauss(2  ) with  =5E-4 ] (The measured data will be available soon.) (3) Alignment errors of BM & QM Random error [ Gauss(2  ) with  =0.1 mm for dx & dy,  =0.2 mrad for d  (4)Leak fields from INJ & EXT DC SEPTA TOSCA (in progress) (6)B-Q, Q-Q tracking errors (5) Magnetic interference (7) Bump field errors included in simulations The measurements of (Q-S), (Q-STR) … are planned.

10. K0K0 K 1 (m -1 ) K 2 (m -2 ) K 3 (m -3 ) K 4 (m -4 ) K 5 (m -5 ) K 6 (m -6 ) BM 0.262E+0-0.202E-1 -0.503E-1 0.363E+0-0.133E+20.234E+3-0.637E+5 QFL -0.207E+0-0.109E-1-0.245E+2- QDL --0.205E+0--0.108E-1--0.243E+2- QFM -0.214E+0-0.769E-2-0.127E+3- QFN -0.221E+0-0.888E-2-0.358E+3- QDN --0.236E+0--0.946E-2--0.382E+3- QDX --0.210E+0--0.845E-2--0.341E+3- QFX -0.161E+0-0.770E-2-0.160E+3- SDA ---0.308E+0---- SDB ---0.308E+0---- SFX --0.378E+0---- Multipole field components K n estimated at (6.68, 6.27) [ BM : Measurement & TOSCA QM : TOSCA ]

11.  mm mrad Q x -2Q y =-6 4Q x =27 Q x -4Q y =-18 2Q x -2Q y =0 3Q x +4Q y =45 Nonlinear resonances at RCS QxQx QxQx QyQy QyQy  p/p=0%  p/p=0.5% - Multipole field in the BM and QM applied : K 0 ～ K 6 - Chromatic correction : ON (SDA=  0.317, SDB=  0.276, SFX=0.417 m -2 ) - Synchrotron oscillation : ON assuming the stationary bucket - Physical aperture : set for all the BM, QM, SM - Start point of tracking : 1 st QDX - Initial condition of the beam particle:  x =  y, x=(  x /  x ) 1/2, x’=0, y=(  y /  y ) 1/2, y’=0, z=0,  p/p=0 and 0.5% - Number of turns : 5000 xx yy We looked for the maximum  x =  y for which the beam survives within the physical apertures up to 5000 turns.  x =  y

12. Field & Alignment errors of BM  BL)/(BL)  x (m)  y (m)  (rad) BM No. After shuffling

13. Field & Alignment errors of QM  GL)/(GL)  x (m)  y (m)  (rad) QM No.

14. COD &   caused by errors(1)~(3) COD dx (m) dy (m) s (m) |COD x |<~1.5 mm (before cor.) <~0.5 mm (after cor.) |COD y |<~4.5 mm (before cor.) <~0.8 mm (after cor.) Before correction After correction with STM  (6.72, 6.35) →(6.7217, 6.3492)  / ~0.025% (x), 0.013% (y)

15. Preliminary results (6.72, 6.35) 0.6 MW @ Extr. Chromatic cor. : ACC Beam survival turns W/O Mult W/ Mult W/ Mult, ERROR, COD cor. W/ Mult, ERROR

16. Survey of operating point QxQx QyQy - Chromatic correction : NCC, DCC(181MeV), ACC - Beam power : 0.3MW or 0.6MW at Extr. - 3 rd resonance correction(x-2y=-6) : ON or OFF - Several errors (field, alignment errors…) ON or OFF - COD correction with STRs ON or OFF

17. Simulation system at JAEA ■ インテル Pentium D プロセッサ 920 (2x2MB L2 キャッシュ /2.80GHz/800MHz FSB) ■ デュアルチャネル DDR2-SDRAM 1024MB PC2-4200(512MBx2) ■250GB Serial-ATA ハードディスク ■ インテル 945G Express チップセット ………………………………………… ○ Mouse computer Lm-i 913 (×1 ３台 ＋ 10 台？ ) CPU TIME (INJ~EXT ： ~15000 turns) : ~ 2.5 months Short term simulation up to ~3000 turns(15 days) (survey of operating point) ○ Parallel computer at JAEA CPU TIME (INJ~EXT ： ~15000 turns) : ~ 1 months Long term simulation (full simulation from INJ through EXT)