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GAMMA TRANSITION JUMP FOR PS2

This study analyzes transition jumps in PS2 for accelerator applications, comparing theoretical equations with practical data to optimize beam stability and prevent instabilities. The analysis covers various scenarios, from nTOF to LHC beam conditions, offering insights for improved beam performance.

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GAMMA TRANSITION JUMP FOR PS2

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  1. GAMMA TRANSITION JUMP FOR PS2 W. Bartmann, M. Benedikt, E. Métral and D. Möhl • Introduction with the case of the PS • Equations in the case with NO SC (or BB imp.) and NO tjump re-derived and solved analytically • Equations in the case with both SC (and/or BB imp.) and tjump re-derived and solved numerically • Application (and comparison with Dieter’s theory of 1969!  CERN-ISR/300/GS/69-62) to the cases below: • nTOF in the present PS • nTOF in (PS2, 10 MHz) • FT in (PS2, 10 MHz) and (PS2, 40 MHz) • LHC in (PS2, 10 MHz) and (PS2, 40 MHz) • Conclusion, outlook and appendices

  2. Introduction with the case of the PS (1/7) Thanks to M. Martini for the data!  t = - 1.24 in tjump = 500 s (see also next slides)

  3. Introduction with the case of the PS (2/7) Zoom Zoom

  4. Introduction with the case of the PS (3/7)  Currently, the nTOF bunch is the most critical at transition due to a TMCI which develops near transition crossing Simulation by Giovanni with HEADTAIL (ICAP06) Without space charge Measurements in 2000 With space charge  > 2.1 eVs are needed for ~ 71012 p/b (PS/RF Note 2002-198)

  5. Introduction with the case of the PS (4/7) Flat chamber HEADTAIL SIMULATION Head Tail - Constant energy - Bunch in the centre of the PU 1st trace = turn 1 Last trace = turn 130 Every turn shown

  6. Introduction with the case of the PS (5/7) Δz  120 cm  f  250 MHz Δz  40 cm  f  750 MHz HEADTAIL SIMULATION Turn 130 shown

  7.  Measurements from Rende in 2007 on the AD beam with low longitudinal emittance (no precise beam parameters) Introduction with the case of the PS (6/7)

  8. Introduction with the case of the PS (7/7) * R / Qt ** Assumption: Qt ~ t = 1 /  p = 11.47

  9. General result for the nonadiabatic transition region(with neither space charge, or BB imp., nor t jump)  The bunch is tilted near transition Transition Nonadiabatic time  Same picture as the one obtained by K.Y. Ng in his book “Physics of Intensity Dependent Beam Instabilities” (2006), p. 707

  10. Case of the nTOF bunch in the PS WITHOUT space charge (1/2) Tc 1.9 ms

  11. Case of the nTOF bunch in the PS WITHOUT space charge (2/2)

  12. Case of the nTOF bunch in the PS WITH space charge (1/5) STATIC (MATCHED) CASE

  13. Case of the nTOF bunch in the PS WITH space charge (2/5) DYNAMIC (“REAL”) CASE WHEN TRANSITION IS CROSSED

  14. Case of the nTOF bunch in the PS WITH space charge (3/5) DYNAMIC (“REAL”) CASE WHEN TRANSITION IS CROSSED

  15. Case of the nTOF bunch in the PS WITH space charge (4/5) EVOLUTION OF THE DYNAMIC CASE WHEN SPACE CHARGE IS INCREASED THROUGH INTENSITY

  16. Case of the nTOF bunch in the PS WITH space charge (5/5) EVOLUTION OF THE DYNAMIC CASE WHEN SPACE CHARGE IS DECREASED THROUGH LONGITUDINAL EMITTANCE

  17. (Asymmetric) t jump for nTOF in the PS (considering SC and TMCI) Tc 1.9 ms

  18. Summary table for PS and PS2 (considering SC and TMCI) It is the tof the present PS = -1.50 if PS2 BB imp. 6 times smaller than PS

  19. Case of the nTOF bunch in the PS with longitudinal inductive BB impedance (neglecting SC)  In this case, the asymmetry of the t jump is in the other direction

  20. Case of the nTOF bunch in the PS with both longitudinal inductive BB impedance and SC  Caution: Here the long. BB impedance cancels the SC for the bunch length matching but will lead to a more critical long. microwave instability!

  21. Case of the nTOF bunch in the PS with both longitudinal inductive BB impedance and SC and 2 times bigger transverse emittance

  22. Conclusion and outlook (1/3) • Transition crossing with a tjump looks possible in PS2 for the densities foreseen with the FT and LHC beams • It its more difficult for conditions corresponding to the present nTOF bunch. In this case a strong reduction of the BroadBand impedance is necessary to keep the required tjump  ~ - 2 * • Further improvement of the longitudinal density beyond that of nTOF seems excluded, even if only the (unavoidable!) space-charge impedance of the beam is taken into account * - It is believed that t until ~ - 2 can be performed - It should be done with Qt  0 - During the t jump the dispersion has the tendency to increase  This can lead to an increase of the horizontal beam size and subsequent beam losses

  23. Conclusion and outlook (2/3) • Future work: What about the time needed to perform the tjump in PS2?  Compute the instability rise-time for • Negative-mass instability * (and longitudinal microwave instability with BB impedance  Could be increased by reducing the BB impedance) • TMCI  Could be increased by reducing the BB impedance See Appendices * A preliminary estimate reveals that the time needed to perform the tjump of the present PS (i.e. ~ 500 s) could be enough as the negative-mass instability rise-time in the PS2 is larger than the one in the PS for the nTOF bunch

  24. Conclusion and outlook (3/3) • Proposed MDs in the PS in 2008 to check our estimates (fast analog signals are available in the CCC since the end of 2007): • Movie of the TMCI to compare with the HEADTAIL simulations (same data as the ones taken by Rende in 2007) • Remove the t jump and measure the evolution of the longitudinal, horizontal and vertical signals vs. transverse bunch emittance (to see the relative effect of the SC impedance, which is emittance-dependent, and the BB impedance, which is constant • Same measurements scanning the amplitude of the t jump • Same measurements scanning the transition timing (symmetric vs asymmetric jump…) for different transverse bunch emittances • …

  25. APPENDIX A: NEGATIVE MASS (SC) INSTABILITY RISE TIME FOR nTOF IN THE PS Keil-Schnell

  26. APPENDIX B: VERTICAL MICROWAVE INSTABILITY RISE TIME FOR nTOF IN THE PS Keil-Schnell (transverse)

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