1. Crossing transition at RHIC V.Ptitsyn, N.Abreu, M. Brennan, M.Blaskiewicz, W. Fischer, C. Montag, R. Lee, S.Tepikian

2. RHIC transition crossing parameters Unfortunately the RHIC lattice design could not avoid the transition crossing. Making the transition energy less that the injection energy would require too long dipole magnets and too large dispersion function. Except protons, all RHIC species has to cross the transition during the acceleration ramp. Low acceleration rate of superconducting RHIC makes the transition crossing more challenging. Transition gamma  t 22.91Harmonic number h360 Acceleration rate d  t /dt, s -1 0.4Long. bunch area (95%) A, eV-s/u0.4 Ions per bunch, 1e91.1 Nonlinear compaction  1 (  *=5m) -0.3 Peak RF voltage V, kV150 Max momentum spread  max, 1e-3 5.2 Stable phase  s, rad 0.08Nonadiabatic time T c, ms73 RF frequency f rf, MHz28.124Nonlinear time T nl, ms355 Here the parameters relevant for the transition crossing of gold ions in Run-7:

3. Choice of  1 Importance of nonlinear chromatic effect at RHIC transition is stressed by the large value of nonlinear time. During that time there are particles in the beam which undergo the unstable motion because the time of the transition crossing depends on the particle momentum. J.Wei studies on the RHIC design stage showed that (without  t –jump) 70% of the beam will be lost and more than 60% emittance increase is expected.  1 depends both on the linear lattice and on the chromaticity. In order to eliminate this chromatic effect one needs:  1 = -1.5. Unfortunately,  *=3m lattice brings the dynamic aperture problem. Presently,  *=5m lattice is used at the transition with  1 ~ -0.3 Measurements of  1 showed a good agreement with predicted design value (M.Blaskiewicz et al) Calculated  1 dependence on lattice choice (different  *) and chromaticities

4.  t -jump at RHIC What jump amplitude is needed? To overcome nonlinear chromatic effect, the jump has to be at least Larger jump amplitude provides more safety margin. For the jump time the shorter is the better. Present  t -jump at RHIC changes  t by about 1 unit in 40 ms. Enhancement of the transition crossing rate by factor 60. tt   t -jump is applied to minimize the time the beam spends in nonlinear and nonadiabatic areas of synchrotron motion, thus minimizing the beam losses and longitudinal bunch area increase. Gamma Time after accramp, s 70 90 80

5.  t -jump realization First order matched  t jump scheme. Used in each RHIC sextant. Family of jump quadrupoles (gt) placed in the dispersive section (arc). At 90 o betatron phase advance between the quads, the dispersion and beta-function perturbations remain local. Betatron tune compensation family (qt) is set at the area of small dispersion. Design and realization of the  t -jump has been done by J.Kewisch, C.Montag, S.Peggs, S.Tepikian, and D.Trbojevic

6.  t jump optics distortion In RHIC the phase advance between gt-quads is 82 o Thus  -function and dispersion distortions leak to the rest of the ring. Nevertheless at optimal settings the optics distortion is acceptable. The betatron tune excursions during the jump are within 0.003. Chromaticity Time,s 708090 -2 2 1 Chromaticities also experience jump because of changes in the optics. A scheme, involving different sextupole families is under development which should allow to adjust and control this jump (C.Montag) Important for the transverse instability control.

7. As result of the  t jump application and fine tuning of betatron tunes and chromaticities the beam losses through the transition region may be done to less than 1% In Run-8 the transition in Blue and Yellow rings happened in different time, since in Yellow ring IBS-suppression lattice, with higher  t was used. transition

8. Quadrupole oscillations after transition Even with optimally timed  t jump just after transition a bunch length starts oscillations. This leads to a bunch area increase which causes the rebucketing (at the storage energy) to be less effective. Possible reasons for those oscillations:  Beam self-induced field  Remaining chromatic non-linearity (  1 ) Both those effects can cause a mismatch of the bunch area right after the transition crossing The decision was made to develop a damper to address this problem.

9. Results : successful commissioning during the 2008 d-Au run Amplitude of the 4th RF harmonic of wall current monitor signal is shown as a function of the time (left plot). Longitudinal bunch area over the energy ramp (right plot). The longitudinal bunch area at the end of the energy ramp is 10% smaller when the feedback system in on. Quadrupole feedback application N.Abreu et al

10. Remaining issues of longitudinal dynamics at the transition  Recent simulations showed possible bunch area increase due to interactions with HOM of RF cavities.  Above ~1.2e9 Au ion/bunch the clear indication of the quadrupole coupled bunch instability was seen as bunches oscillates at different phases after crossing the transition. These observed Coupled Bunch Modes can not be damped with the feedback as it is. For those modes the development of new feedback system will be required.

11. Beam radius control at the transition area  Different types of RF loops dominate the RF controls in different RHIC rings in the transition area. In Blue ring a constant mean radial orbit is maintained by the radial loop. In Yellow ring the ring-to-ring synchro loop maintains the same longitudinal phase between Blue and Yellow beams.  In the transition region, tiny difference in the bending field between Blue and Yellow rings can lead to considerable radial orbit excursion. Ramp to ramp variation of Yellow beam radial orbit excursion: 0.1-1mm Corresponding bending field error: dB/B = 2.6e-5 Bending field feedback is under development and will be tested next run. transition Mean radial orbit, mm

12.  Presently limits the ion beam intensity that can be accelerated in RHIC at ~1.1e9 Au/bunch.  The instability is very fast. Growth time (ten(s) of ms) is considerably smaller than synchrotron period (>130 ms). Should be similar to the beam break-up in linacs.  Most probably, the instability correlates in time with the chromaticity crossing 0.  The instability was first observed with small number of bunches in early RHIC runs and was cured by the application of octupoles (amplitude dependent betatron tune spread).  The instability reappeared at high number of bunches (>90) and at higher bunch intensity. In this case it shows clear dependence on the bunch position in the train. o Bunch losses vary along the bunch train o Transverse emittance blowup varies along the bunch train  Current explanation of these effects: the electron cloud, accumalted in the beam with large number of bunches, lowers the instability threshold and introduce the dependence of instability strength on bunch train position. Transverse instabilty at the transition region

13. Instability, as seen by the button BPM, affects tails of bunch mini-trains 103 bunch pattern with two mini-gaps. Time, when the instability happens also depends on the bunch position in the train. Closer to the beginning of the train -> later instability development

14. Bunch intensity transmission through the transition for 103 bunches with two gaps. gap Beam losses increase towards the end of bunch mini-trains

15. ~6.4ms (500 turns) between traces Distinctive feature: Instability arises at ~300 MHz, then the instability power moves continuously to higher frequencies as the instability develops Evolution of instability frequency content

16. Snapshots of vertical bunch centroid versus longitudinal coordinate Bunch 111 (last bunch in the train); 4ms between traces

17. What can be done against the instability?  Better chromaticity control through transition region (tools for better chromaticity measurements; chromaticity jump control)  RF counter-phasing (suggested by V. Litvinenko). Aimed to keep longer bunch throughout the transition region, reducing both electron cloud formation and bunch charge density.  Development of the high-bandwidth feedback system.  Beam scrubbing

18. Summary  Almost completely beam loss free transition crossing is done at RHIC with the  t -jump.  Longitudinal quadrupole oscillations after the transition have been successfully addressed by the feedback, minimizing the longitudinal bunch area growth.  Transverse instability at the transition, which presently limits the RHIC ion beam intensity, is under detailed exploration.