Stochastic Cooling Studies in RHIC*

Submitted to the: - <.-- c-c 1 2003 Particle Accelerator Conference BNL 69610 - CP Portland, Oregon, May 12-16,2003 -.- Stochastic Cooling Studies in RHIC*

M. Blaskiewiczt, J.M. Brennan, P. Cameron, J. Wei BNL, Upton NY 11973, USA Abstract 70 Emittance growth due to Intra-Beam Scattering signifi- Au-Lola1 ~ cantly reduces the heavy ion luminosity lifetime in RHIC. 60 bunched Au - h bunched deuterons - Stochastic cooling of the stored beam could improve things 0 50 considerably by counteractingIBS and preventing particles F from escaping the rf bucket [ 11. High frequency bunched- E; 40 beam stochastic cooling is especially challenging but ob- 30 servations of Schottky signals in the 4-8 GHz band indi- vr cate that conditions are favorable in RHIC [2] . We report 3 20 here on measurements of the longitudinal beam transfer a function carried out with a pickupkicker pair on loan from 10 FNAL TEVATRON. Results imply that for ions a coasting 0 beam description is applicable and we outline some general 012345678 features of a viable momentum cooling system for RHIC. time (hours) 1 INTRODUCTION Figure 1: Evolution of the bunched and total intensity in gold (Au) and deuteron (D) beams. There are 55 bunches When colliding gold (Au) ions in RHIC, the longitudinal of each species and the bunched beam data have been emittance grows during the course of a store. The domi- smoothed to reduce noise. nant mechanism is intrabeam scattering (IBS), which is the result of small angle Coulomb collisions between the ions in a single bunch. Figure 1 shows the evolution of the total and bunched intensities. The deuteron beam remains in the RF bucket with nearly constant intensity. For the gold beam 2 both the bunched and total intensities decay with time. Fig- 1.5 ure 2 shows the evolution of the gold longitudinal profile. The traces have been scaled to a peak value of one. The 1 initial peak current was 2.4 amperes and seven hours later it is 0.4 amperes. The net RF voltage per turn is given by[4] 0.5 V(6,)= VAsin(6,) + Vs sin(76,) (1) 0 where 6, is in units of RF phase for the accelerating cavities -0.5 with h = 360, VA M 250 kV is the voltage on the acceler- -15 -10 -5 0 5 10 15 ating cavities, VS M 2.4 MV is the voltage on the storage time (ns) cavities, and the stable synchronous phase is 6, = 7r since store is above transition (7 > y~).The FNAL, pickup and Figure 2: Evolution of the longitudinal profile for an Au kicker are installed in the yellow ring. During the gold- bunch. The lowest trace was taken just after rebucketing deuterium run we worked with the gold beam. During the and each trace above is an hour later. polarized proton run we worked with protons.

2 COHERENT BEAM RESPONSE to different gain in our experimental setups. In both cases the beam was driven at fcent - A f with A f M 5 kHz. The Figure 3 compares the coherent response of gold to pro- proton beam spectrum has two narrow lines that are absent tons. The FNAL kicker [5] was driven with about 5 Watts in the gold signal. The proton beam shows a strong narrow of power at single frequencies, 5 GHz for gold, 4 GHz for band signal near the revolution line that was also observed protons. The longitudinal beam response was detected with in the Tevatron [SI. We suspect this signal is due to long the FNAL pickup. The difference in the noise floor is due lived coherent oscillations in the proton beam [SI. Since IBS rates for gold are about 10 times larger than those for *Work performed under contract numbers #DE-AC02-98CH10886 and #DELAC05-@3OR2275 with the auspices of the United States Depart- protons, we expect gold coherence to diffuse away. The ment of Energy. proton signal also shows anarrow line at fcent+Af, which t [email protected] is reminiscent of a bunched beam response. This feature was not always present in the proton spectrum. 0.008 To analyze the data considera coasting beam that has the same number of particles and the same momentum distri- 0.006 bution as the bunched beam. The rms Schottky current for 0.004 both cases satisfies 0 0.002 -=0 2 C Y-3 0 - 2P(f)Sf /I/ (2) 5 -0.002 N’ cn 9 -0.004 where I, denotes the rms Schottky current, I is the DC -0.006 beam current, Sf is the resolution bandwidth of the spec- -0.008 trum analyzer, P(f)is the normalized frequency distribu- -0.01 tion, and N is the number of particles in the beam. -20 -15 -10 -5 0 5 10 15 20 Now take the same coasting beam and apply a longitudinal voltage kick Ti cos(fl2t). Model the beam’s frequency f - fcent (kW distribution as a Lorentzian so that Figure 4: Transfer function measurements for protons at Af 1 4.8 GHz. P(f)= - r (f - fcent)’ + Af2* For drive frequencies near the center of the distribution, and neglecting collective effects, the ratio of the rms beam current at the drive frequency to the coasting beam current is qQ 1 (3) 1 f 1 = 2hrfCentT0Iq I ’ where ET = ymc2 is the total energy per particle, q is the charge per particle, TOM 12.8~sis the revolution period, and E^ = Af/lqlfcent is the fractional energy spread.

~ -70 -75 -80 & - -85

(d -90 Figure 5: Proton power spectrum when transfer function 3 -95 measurements were made. The center frequency is 4.8 -100 GHz, the horizontal scale is 5 kHddiv, and the vertical -0 scale is 5 dBm/div. There were N = 10” protons and -105 y = 107. The noise floor, denoted by the green line, is -86 -110 dBm. -115 -25-20-15-10 -5 0 5 10 15 20 25 30 to the Schottlq power agrees with the measurement within f-Lent (kH4 1 dB. With both qualitative and quantitative agreement, we Figure 3: Power Spectra of gold and Proton beams driven have confidence that a coasting beam theory, modified via bY the FNAL kicker. Theresolutionbandwidth ofthe Spec- the bunching factor of the beam, is reasonable for specify- trum analyzer was 30 Hi. ing a cooling system. Figure 4 shows the beam transfer function for protons taken with an HP8753 network analyzer using a 10 Hz in- 3 COOLING SYSTEM termediate frequency bandwidth. The curves are very sim- ilar to what one expects for coasting beams [SI. Fig 5 Consider a cooling system of bandwidth W. Let Nb be was taken during the same store with the same instrumental the number of particles per bunch and let rb be the bunch setup. When the coherent spike near the revolution line in length. The number of particles per independentsample of Fig 5 is ignored, the calculated ratio of the coherent power the cooling system is N, = Nb/2rbW [lo]. Consider the rms energy spread a, = &ap/p; the cooling time is Results for n = 1,2, with Td = 2T0/3 and R(0)constant between 4 and 8 GHz are shown in Figure 6. The horizontal (4) scale is for fractional moment shifts with Idp/pl 5 0.2%. The largest voltages available can confine particles with where M is the mixing factor. For RHIC gold parame- Idp/pl 5 0.17%, where the filter with k = 2 has good ters with a 4-8 GHz cooling system and lo9 particles per gain. bunch we get N,M = 2.8 x 10' which in turn implies M 1hour. Detailed calculations [7] have shown that TE 6 this cooling time will significantly improve the integrated luminosity. 4 Stochastic cooling for RHIC mightbetter be refered to as stochastic confinement. The main goal is to keep par- 2 ticles in the RF bucket, not to reduce the rms momentum spread. Consider a single particle with no RF voltage [SI. 0 In the absence of a cooling system the revolution frequency is constant and the beam current is given by -2

(5) -4 " where w is the particle's angular revolution frequency and -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 tJ = s/R is the machine azimuth. Suppose the cooling dph ( 1 0-3) pickup is at azimuth tJp and the kicker is at azimuth OK. We assume that the change in revolution frequency per turn Figure 6: Plot of eq (6) with Sk from eq (8) for RHIC pa- satisfies dw << wO/km, where wo = 2n/T0 and k,, is rameters. The vertical scale is in arbitrary units. For the the largest revolution harmonic for which the cooling sys- horizontal scale AW/WO= -vdp/p. For n = 2, the filter tem has a significant gain. Then, the average rate at which has good gain at the edge of the bucket. the particle gains or losses energy is given by

4 ACKNOWLEDGEMENTS Many thanks to Fritz Capers of CERN for useful conver- sations and encouragement. This work would have been impossible without Dave Mcginnis and Ralph Pasquinelli of FNAL, who helped with both the hardware, and our un- where is the transfer impedance between the pickup derstanding of how to use it. Finally, we acknowledge the ZT dedication and expertise of the BNL instrumentation and and kicker and Td is the delay. We do not plan on cutting RF groups. a chord across the RHIC ring so the kicker will be placed upstream of the pickup and Td is chosen so that OK - Bp - WoTd = -2T. Then 5 REFERENCES [13 J. Wei, A.G. Ruggiero, BNL/ADlRHIC-71(1990). (7) [Z] J.M. Brennan, M. Blaskiewicz, P. Cameron, J. Wei, 308, where Aw = w -WO. For the cooling system to be effective EPACO2 the transfer impedance must cause particles with w > wo [3] G. Jackson, Workshop on Beam Cooling, Montreux, 1993, to be accelerated, and particles with w < wo to be deceller- CERN 94-03, (1994). ated. Therefore, the real part of the transfer impedance must change sign at revolution lines. A natural candidate is [4] J.M. Brennan, Operation of the RHIC RF System, PACO3. a one turn delay notch filter [9] which has a transfer func- [5] D. McGinnis, J. Budlong, G. Jackson, J. Marriner, D. Poll, tion T(a)= 1- exp(-jaTO). This will be implemented PACO1, p1389 (1991). using a fiber optic delay line so there is no loss associated [6] M. Blaskiewicz, etd.Longitudinal Solitons in RHIC, PAC03 with the delayed signal. We apply one or two such filters [7] J. Wei, Workshop on Beam Cooling, Montreux, 1993, CERN in series. Also, we model the net transfer function of the 94-03, (1994). pickup, kicker, and any phase shifters to be T(a)= jR(Q) [8] E Sacherer CERN-ISR-THn8-11 (1978). where R(a)is real in the center of the cooling band and has small imaginary parts. Then, [9] G. Carron, L. Thorndahl CERN-ISR-RF/78-12(1978). [ 101 D. Mohl, CERN 87-03, p 453 (1987).