1 / 38

Details of space charge calculations for J-PARC rings

Details of space charge calculations for J-PARC rings. KEK Portion. JAERI Portion. J-PARC accelerator complex. Phase 1 + Phase 2 = 1,890 Oku Yen (= $1.89 billions if $1 = 100 Yen). Phase 1 = 1,527 Oku Yen (= $1.5 billions) for 7 years. JAERI: 860 Oku Yen (56%), KEK: 667 Oku Yen (44%).

istas
Download Presentation

Details of space charge calculations for J-PARC rings

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Details of space charge calculations for J-PARC rings

  2. KEK Portion JAERI Portion J-PARC accelerator complex • Phase 1 + Phase 2 = 1,890 Oku Yen (= $1.89 billions if $1 = 100 Yen). • Phase 1 = 1,527 Oku Yen (= $1.5 billions) for 7 years. • JAERI: 860 Oku Yen (56%), KEK: 667 Oku Yen (44%).

  3. Repetition of 3GeV Synchrotron • injection 500μs • injection turns~350 • particles per pulse8.3e13 • acceleration20 ms • extraction<1μs extraction injection acceleration

  4. Repetition of 50 GeV Synchrotron • injection 0.17s • particles per pulse3.3e14 • acceleration1.96 s • extraction (slow)0.7s extraction acceleration injection

  5. Two approaches • A whole cycle of 3 GeV synchrotron takes 20 ms. • Full simulation with self-consistent model is possible. • Tracking parameters (# of macro particles, grid size, etc) have to be optimized. • Only injection period of 50 GeV synchrotron takes 0.6 s (or a bit less). • Not realistic to make self-consistent simulation. • Frozen space charge model might be justified because of well defined particle distribution.

  6. Examples of full tracking for 3GeV Syn. • Things are included. • Injection painting • Multipole errors • Misalignment • Acceleration • Aperture of all elements • Image in a circular pipe • Things are not included. • Scattering at foil. • RF jitter • Impedance Different colors shows results of different number of macro particles. Results within 3 months (1,000,000~200,000) 3 months (100,000) 5 weeks (50,000) 2 weeks (20,000)

  7. Other tracking parameters Number of azimuthal mode Max. mode = 4, 8, 16 Number of z grids z grids = 10, 20, 30, 40,50

  8. Detailed study results • Correlated and anti-correlated painting • COD and beam loss • Coupled with strong chromaticity correction sextupole, COD introduces nonlinearity of all harmonics. • Beam intensity dependence

  9. Correlated and anti-correlated painting correlated anti-correlated 0.5 s for injection There is particle loss even during injection period.

  10. Phase space density right after injection and at 3 ms later correlated anti-correlated horizontal vertical at 0.5 ms at 0.5 ms at 3 ms at 3 ms

  11. COD and beam loss Coupled with strong chromaticity correction sextupole, COD introduces nonlinearity of all harmonics. rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm

  12. Phase space density for different COD Ver. Hor. rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm • No difference in core density. • Tails are developed with COD.

  13. Beam intensity dependence 20mA 30mA cf. 30mA is design value which deliver 0.6 MW beam from RCS with tune spread of ~0,25.

  14. Intensity dependence 20mA 30mA 20mA 30mA • Core density is reduce with 30 mA. • (lower order resonance is involved?) • Tails are also developed.

  15. Summary of self-consistent simulation • A whole cycle of 3 GeV Syn can be simulated even though it takes a few months. • Horizontal and vertical coupling is the source which makes anti-correlated painting worse. • Increase of particle loss due to larger COD is attributed to tail development. Higher order effects are involved. • Intensity limitation may be explained with lower order resonance. That is a regime where coherence picture is applicable.

  16. Example of beam loss during injection with frozen space charge model • Model assumes • Particle distribution is Gaussian. • Emittance is constant. • dp/p is finite and there are synchrotron oscillations. • Transverse space charge force depends on longitudinal position.

  17. Tracking model • “Frozen model” of space charge is adopted. • Space charge potential is fixed throughout a tracking. • No self-consistency. • No coherent oscillations. • Gaussian charge distribution in 3D is assumed. • Lattice nonlinearities and misalignment errors are included. • Aperture of magnets and collimator are included so that we can estimate beam loss. • Macro particles (1,000) of 3D Gaussian distribution with 2 sigma cut are tracked for 0.12s (original design value for accumulation) or more.

  18. Some numbers • Emittance(2sigma) 54 pi mm-mrad (36pi, 45pi, 64pi) • Acceptance at collimator 71 pi mm-mrad for H and V • Acceptance at magnets > 81 pi mm-mrad • Circulating current 10 A (3.3E14 ppp) • Incoherent tune shift -0.16 • Bare tune (22.42, 20.80)

  19. COD • Chromaticity sextupoles coupled with COD introduce beta modulation and higher harmonics of nonlinearity. • Survival at 0.12s after injection. • COD shows a rms value. Maximum is about 3 times. • Collimator aperture is adjusted taking a local COD into account. • We expect COD(rms) is less than 0.5mm after correction. • The loss is not linear as COD. survival at 0.12s (%) 80 85 90 95 100 0 0.5 1.0 1.5 2.0 COD (rms) (mm)

  20. Different lattices • Although rms COD is almost same, different lattices (seeds) give different results. • Previous example is the worst case among three. survival (%) 96 97 98 99 100 0 0.05 0.1 time (s)

  21. Beam current Blue: COD=0.5mm Red: COD=1.0mm • The pattern of COD is the same for both. Magnitude is different. • The design current is 10A. survival at 0.12s (%) 80 85 90 95 100 0 5.0 10 15 beam current (A)

  22. Initial emittance • Acceptance at collimator is fixed at 71 pi mm-mrad. • Space charge force is fixed according to the initial emittance. • We expect 54 pi mm-mrad emittance shaped at the 3-50BT collimator. • Collimator acceptance should be optimized to have the maximum survival. survival at 0.12s (%) 80 85 90 95 100 30 40 50 60 70 80 initial emittance (pi mm-mrad)

  23. Location of loss

  24. Beam loss at collimator (h=18)total 0.72 MW COD (rms) = Red: 0mm Yellow: 0.2mm Green: 0.5mm All the particles hit collimator first.

  25. Beam loss at collimator (h=18)total 0.58 MW COD (rms) = Red: 0mm Yellow: 0.2mm Green: 0.5mm All the particles hit collimator first.

  26. Frozen model with acceleration phis dp/p bunch length

  27. 99% emittance and beam loss Acceleration starts right after injection. Acceleration starts at 0.16 s after injection.

  28. Acceleration starts at 0.6 s after injection and h=18.

  29. Single particle behavior Timing of hitting collimator • Tracking without aperture limit to see single particle behavior. • Slow growth of amplitude. • Not obvious correlation with synchrotron oscillations. Trapping? horizontal position (m) -0.1 -0.05 0 0.50 0.1 0 0.01 0.02 0.03 0.04 0.05 time (s)

  30. Single particle behavior • Track a single particle which is lost in 0.6 s. • Look at betatron oscillation amplitude and transverse tune as a function of turn until a particle is lost. • For example, there are • 38 lost particles (out of 1000) when rms COD is 0mm. • 40 lost particles (out of 1000) when rms COD is 0.2 mm. • 52 lost particles (out of 1000) when rms COD is 0.5 mm.

  31. #1 #3 #2 H V H V #4 #5 #6 amplitude turn number (~ 10,000 turns) rms COD is 0.5 mm

  32. #7 #8 #9 H V H V #10 #11 #12 amplitude turn number (~ 10,000 turns) rms COD is 0.5 mm

  33. H V #13 #14 #15 • Horizontal amplitude always • increases and gets to the aperture • limit. • Vertical amplitude always decreases. • Coupling between H and V is manifest. H V amplitude #16 rms COD is 0.5 mm turn number (~ 10,000 turns)

  34. In tune space 2nx-ny=24 ny-20 ny-20 bare tune nx-2ny=-19 nx-22 nx-22 Blue points are intermediate tune of lost particles. Red points are tune just before particles are lost. Tune before particle loss are same with and without COD.

  35. Coupling between H and V is manifest, but • Tune space plot does not show resonance driving term. • 2nx-ny=24 is skew and cannot be excited even with finite dp/p and dispersion in a lattice. • If there is any way to reduce a driving term. • Since the source is not identified, it is difficult.

  36. Summary of frozen space charge simulation • Particle loss occurs because horizontal amplitude increases and hits the collimator aperture. The source of the increase is a coupling between H and V. • With finite COD, particle loss occurs with less turns. However, transverse tune when a particle loss occurs does not depend on COD magnitude. • Loss is very slow process: the order of 104 turns. Time scale of horizontal and vertical coupling is also same order.

  37. Basic loop of calculation Advance particle coordinates do ip=1,np (200,000) Simpsons uses Fourier expansion in azimuthal direction. Make parallel processing of Fourier modes. Calculate space charge potential based on particle positions. do imode=1,nmode (16) Apply space charge kicks to all particles do ip=1,np (200,000)

  38. Distribution of workload (4 CPUs) with MPI Add up all E-fields 4 CPU works in the same way imode =0,1,2 imode =3,4,5,6 imode =7~11 imode =12~16

More Related