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Possibilities for stochastic cooling at RHIC
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339 www.elsevier.com/locate/nima
Possibilities for stochastic cooling at RHIC J.M. Brennan, M. Blaskiewicz, J. Wei Brookhaven National Laboratory, Upton, New York, 11973, USA Available online 14 July 2004
Abstract Intra-Beam Scattering (IBS) is the fundamental performance limitation for RHIC. The emittance growth from IBS determines the ultimate luminosity lifetime and the only cure is cooling. Full-energy electron cooling will be installed to not only control emittance growth but also reduce emittances during a store. Before that, stochastic cooling could increase integrated luminosity by momentum cooling.Two significant benefits would follow; the average luminosity in a 10 h store would double, and the problem of coasting beam in the abort gap would be solved. Of course high-frequency bunched beam stochastic cooling is required and previous attempts at this at the TEVATRON and SPS were not successful. It appears that the conditions in the heavy ion collider are more favorable. First, the high charge state of ions gives better signal to noise ratio in the Schottky signal. Second, the anomalous coherent components in the pick up signals that caused saturation in the electronics in previous attempts are greatly reduced. Measurements of Schottky signals from gold beam in RHIC at 100 GeV and longitudinal beam transfer functions are presented to illustrate these points. r 2004 Published by Elsevier B.V. Keywords: Collider; Heavy ion; Stochastic cooling
1. Introduction Intra-Beam Scattering (IBS) is unavoidable with highly charged heavy ions and causes emittance growth during the store for collision physics. In the longitudinal plane the emittance quickly grows until the RF bucket is full and then particles diffuse across the separatrix and are lost to the bunch. This reduces the effective luminosity Corresponding author.
E-mail address: [email protected] (J.M. Brennan). 0168-9002/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.nima.2004.06.113
because these particles do not collide at the interaction points and also results in a significant amount of coasting beam that drifts into the beam abort gap. In a typical store enough beam accumulates in the abort gap to cause a magnet quench as it is lost uncontrollably in the ring on the kicker rise time. To prevent this, the abort gap is ‘‘cleaned’’ by slowly driving particles into collimators with the tune meter kicker to clear the gap before the beam is aborted at the end of a store. This procedure is time consuming, which takes time away from physics production, and the
ARTICLE IN PRESS 336
J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
procedure cannot be executed if a spontaneous abort occurs due to some hardware interlock. It has been known for some time [1,2] that stochastic cooling could, in principle, counteract IBS and keep the beam within the RF bucket during a store. However, in practice the technology of stochastic cooling for high-frequency bunched beams has proved impractical [3]. The two main challenges of stochastic cooling of bunched beam are: (1) the effective number of particles is much higher than the actual number in the ring, (2) anomalous coherent signals have polluted the Schottky signals and caused saturation in the electronics. Whereas the first effect is well understood and consistent with the goal of counteracting IBS in RHIC, the second effect is un-understood and proved to be essentially insurmountable in attempts at stochastic cooling at the TEVATRON and SPS. The aim of these studies was to examine the conditions in for heavy ion beam in RHIC to determine if a viable stochastic cooling system could be implemented to keep most of the beam bunched. If so, the integrated luminosity at RHIC could be improved by a factor of two or more. 2. Schottky signals The anomalous coherent lines were seen in signals from proton beams. One must ask whether the situation with highly charged ion beam is
equivalent to protons or not. On one hand, the Schottky signals from highly charged ion beams are intrinsically stronger. For the same charge in the ring an ion beam with charge Q will give Q time more power per Schottky band than protons. For gold, for example, Q ¼ 79 so the signal-tonoise ratio compared to protons is 19 dB greater. On the other hand, since the origin of the anomalous coherent signals is not understood one can not conclude that they would not be similarly enhanced. Observations of signals from gold and proton beams in RHIC reveal that coherent components are much smaller for gold than for protons. Fig. 1 illustrates the point. It shows spectra of signals from a 4–8 GHz pickup installed in the yellow ring of RHIC. This pickup and its matching kicker were loaned by Fermilab to Brookhaven to facilitate this study. The sum-mode (longitudinal) output of the pickup was amplified by 37 dB and transmitted to the instrumentation control center via 150 m of 12 in. foam dielectric coaxial cable. The amplifier approximately compensated the cable attenuation at 5 GHz. The key features to observe from Fig. 1 are: (1) the signal to noise ratio is in fact high,420 dB, (2) the coherent spikes at the center of the Schottky bands are discernable but not huge. In Fig. 1(a) the Schottky band at the center has a much larger spike than the others. This line is distinguished from the others because
Fig. 1. Spectra of signals from the 4–8 GHz pick-up with gold +79 ions at 100 GeV/n. Left, 1(a) shows coherent spike on bunch frequency harmonic at center and smaller spikes on revolution frequency harmonics. Center frequency is 7 GHz, span is 500 kHz. Right, 1(b) after several hours into store, narrower span, 200 kHz, at 5 GHz. No coherent spike is seen. Coasting beam gives asymmetric shape.
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
its frequency is a harmonic of the bunch frequency. There are 60 revolution frequency harmonic lines between these bunch frequency lines. The fact that the coherence seen on the bunch frequency harmonics is much larger than on all the other revolution frequency lines indicates that this spike is not anomalous, but just an indication that the Fourier spectrum of the bunch shape has significant strength even at this very high frequency. In fact, by examining the bunch spectrum at low frequency (10 MHz) we see the same ratio of strength on the bunch harmonic lines to the revolution frequency lines. This ratio is a manifestation of the filling pattern of the bunches in the ring. If all the bunches were exactly equal amplitude then only bunch frequency harmonics would occur. In fact there is an abort gap of five missing bunches out of 60 and since the bunches are loaded each from a different injector cycle they fluctuate in intensity. Fig. 1(b) is from the same store but several hours later. By zooming on three revolution frequency lines one sees that the bunch shape has evolved to the point that there is no coherence spike surviving. Also clearly seen in these spectra is the asymmetric shape caused by the coasting beam that has escaped the bucket, lost energy and drifted to higher frequency (above transition). These results show a qualitatively different behavior for gold ions than was seen for protons at the TEVATRON and SPS.
337
3. Beam transfer function measurement The longitudinal Beam Transfer Function (BTF) reveals a great deal about aspects of the beam that are relevant to stochastic cooling. Specifically it gives the density distribution function in momentum and also contains information concerning the interaction of the beam with the beam pipe coupling impedance. Having the 4–8 GHz kicker installed in the ring enabled quantitative measurements of the BTF. Unfortunately a 4–8 GHz power amplifier was not available until only a few days before the end of the FY03 gold. Some proof of principle of single-frequency measurements were done with gold but swept frequency measurements with a network analyzer were only done with proton beam during the polarized proton running period. Fig. 2 shows the result of such a measurement of the BTF from protons at 100 GeV. The kicker was driven with a 200 W TWT amplifier via 100 m of coaxial cable. Because of the attenuation in the cable only 8 W were delivered to the kicker. The frequency was swept slowly so that a 10 Hz IF bandwidth could be used in the network analyzer. Even though the power in the kicker is small the beam response is clearly discernable from the Schottky noise because it is a coherent reaction of the ensemble of particles and is therefore enhanced by factor of N (] number of particles=1012). The
Fig. 2. Longitudinal BTF for protons at 100 GeV. Imaginary part is on left, real part on right. The center frequency is 5 GHz and the span is 50 kHz. Vertical scale is linear with 70.01 full scale.
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
338
BTF is given by Z BTFðoÞ ¼ jk P:V:
dc=dE dE ðo no0 nkEÞ þ jpc0 ðEðoÞÞ ;
where, k represents the kicker and pickup impedances, n is the harmonic number, 64,000, CðEÞ is the energy distribution function, o0 is the revolution frequency. The real and imaginary parts of the measured BTF are shown in Fig. 2. The real part is proportional to the derivative of the distribution function. It is characteristically anti-symmetric since CðEÞ is symmetric. Particles below the center of the distribution will absorb energy, while those above the center will give energy to the kicker. For frequencies outside the distribution, the interaction is purely reactive and so all the magnitude comes from the imaginary part. If we model the distribution function as a Lorentzian and write it in the frequency variable we have, cðf Þ ¼
Fig. 3. The beam response to a continuous driving frequency within the distribution. The beam is 2 1012 protons in 55 bunches at 100 GeV. The RF buckets are comprised by 300 kV at 28 MHz plus 100 kV at 197 MHz. The input power to the 8 W at 4.8 GHz.
Df 1 p ðf f 0 Þ2 þ Df 2
where, Df is the width of the distribution, 20 kHz. We can solve for the magnitude of the response relative to the DC beam current, I BTF eV 1 ; I ¼ E d2 2pffi½ 2pf T jZj DC
0
center
0
where, d is the fractional energy spread, V the kicker voltage, T0 is revolution period, Z the frequency slip parameter, 1.7 103. This result is compared to the value found in the measurement illustrated in Fig. 3. With a single frequency driving the kicker at a frequency within the beam frequency distribution the beam response is seen. The pickup impedance and electronic gain are calibrated by the size of the Schottky component in the spectrum. The observed response agrees with the calculated result to with a few dB. The beam response for protons was sometimes qualitatively different with non-linear behavior exhibited. An example is shown in Fig. 4.
Fig. 4. The response of proton bunches showing non-linear behavior. The kicker is driven at one frequency, f center Df , but the beam responds at Df and 2Df . This suggest that this bunch is beyond the limit of stability by Landau damping.
The tendency of the proton bunch was not consistent and we were not able to definitively identify the conditions under which it occurred. These studies were done parasitically to machine operations and systematic variations of bunch intensity were not possible. However, there did appear to be a correlation with higher
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
bunch intensities and the non-linear response behavior.
4. Prospects for stochastic cooling The problem of strong coherent lines polluting the Schottky spectra seems to be much smaller for ions than protons. In fact, after some time during a store the coherent lines from gold ions are completely missing except on the harmonics of the bunch frequency. This indicates that the difficulties that were experienced at the TEVATRON and SPS would not hamper a stochastic cooling system at RHIC. Furthermore, observations of protons in RHIC show similar results to protons in the other collidiers, suggesting that the phenomenon is characteristic of the beam species more than the particulars of the ring, for example, impedance. Results from these studies encourage us to continue to pursue stochastic cooling in RHIC. The near term goal is to perform an experiment in which some longitudinal cooling is demonstrated. Clearly we are RF power limited, with one
339
amplifier and one kicker, but in a demonstration experiment there are many options to operate with reduced power. For example, reduced number of particles, less than optimum gain and longer cooling time, or cooling only some of the bunches in the ring to reduce CW power.
Acknowledgements Many thanks to Fritz Caspers of CERN for enlightening conversations and encouragement. This work would not have been possible without the contributions of Ralph Pasquinelli and Dave McGinnis of Fermilab, who contributed both hardware and expertise. References [1] J. Wei, A.G. Ruggiero, BNL/AD/RHIC-71, 1990. [2] J. Wei, Workshop on Beam Cooling, Montreux, 1993, CERN 94-03, 1994. [3] G. Jackson, Workshop on Beam Cooling, Montreux, 1993, CERN 94-03, 1994.
Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339 www.elsevier.com/locate/nima
Possibilities for stochastic cooling at RHIC J.M. Brennan, M. Blaskiewicz, J. Wei Brookhaven National Laboratory, Upton, New York, 11973, USA Available online 14 July 2004
Abstract Intra-Beam Scattering (IBS) is the fundamental performance limitation for RHIC. The emittance growth from IBS determines the ultimate luminosity lifetime and the only cure is cooling. Full-energy electron cooling will be installed to not only control emittance growth but also reduce emittances during a store. Before that, stochastic cooling could increase integrated luminosity by momentum cooling.Two significant benefits would follow; the average luminosity in a 10 h store would double, and the problem of coasting beam in the abort gap would be solved. Of course high-frequency bunched beam stochastic cooling is required and previous attempts at this at the TEVATRON and SPS were not successful. It appears that the conditions in the heavy ion collider are more favorable. First, the high charge state of ions gives better signal to noise ratio in the Schottky signal. Second, the anomalous coherent components in the pick up signals that caused saturation in the electronics in previous attempts are greatly reduced. Measurements of Schottky signals from gold beam in RHIC at 100 GeV and longitudinal beam transfer functions are presented to illustrate these points. r 2004 Published by Elsevier B.V. Keywords: Collider; Heavy ion; Stochastic cooling
1. Introduction Intra-Beam Scattering (IBS) is unavoidable with highly charged heavy ions and causes emittance growth during the store for collision physics. In the longitudinal plane the emittance quickly grows until the RF bucket is full and then particles diffuse across the separatrix and are lost to the bunch. This reduces the effective luminosity Corresponding author.
E-mail address: [email protected] (J.M. Brennan). 0168-9002/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.nima.2004.06.113
because these particles do not collide at the interaction points and also results in a significant amount of coasting beam that drifts into the beam abort gap. In a typical store enough beam accumulates in the abort gap to cause a magnet quench as it is lost uncontrollably in the ring on the kicker rise time. To prevent this, the abort gap is ‘‘cleaned’’ by slowly driving particles into collimators with the tune meter kicker to clear the gap before the beam is aborted at the end of a store. This procedure is time consuming, which takes time away from physics production, and the
ARTICLE IN PRESS 336
J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
procedure cannot be executed if a spontaneous abort occurs due to some hardware interlock. It has been known for some time [1,2] that stochastic cooling could, in principle, counteract IBS and keep the beam within the RF bucket during a store. However, in practice the technology of stochastic cooling for high-frequency bunched beams has proved impractical [3]. The two main challenges of stochastic cooling of bunched beam are: (1) the effective number of particles is much higher than the actual number in the ring, (2) anomalous coherent signals have polluted the Schottky signals and caused saturation in the electronics. Whereas the first effect is well understood and consistent with the goal of counteracting IBS in RHIC, the second effect is un-understood and proved to be essentially insurmountable in attempts at stochastic cooling at the TEVATRON and SPS. The aim of these studies was to examine the conditions in for heavy ion beam in RHIC to determine if a viable stochastic cooling system could be implemented to keep most of the beam bunched. If so, the integrated luminosity at RHIC could be improved by a factor of two or more. 2. Schottky signals The anomalous coherent lines were seen in signals from proton beams. One must ask whether the situation with highly charged ion beam is
equivalent to protons or not. On one hand, the Schottky signals from highly charged ion beams are intrinsically stronger. For the same charge in the ring an ion beam with charge Q will give Q time more power per Schottky band than protons. For gold, for example, Q ¼ 79 so the signal-tonoise ratio compared to protons is 19 dB greater. On the other hand, since the origin of the anomalous coherent signals is not understood one can not conclude that they would not be similarly enhanced. Observations of signals from gold and proton beams in RHIC reveal that coherent components are much smaller for gold than for protons. Fig. 1 illustrates the point. It shows spectra of signals from a 4–8 GHz pickup installed in the yellow ring of RHIC. This pickup and its matching kicker were loaned by Fermilab to Brookhaven to facilitate this study. The sum-mode (longitudinal) output of the pickup was amplified by 37 dB and transmitted to the instrumentation control center via 150 m of 12 in. foam dielectric coaxial cable. The amplifier approximately compensated the cable attenuation at 5 GHz. The key features to observe from Fig. 1 are: (1) the signal to noise ratio is in fact high,420 dB, (2) the coherent spikes at the center of the Schottky bands are discernable but not huge. In Fig. 1(a) the Schottky band at the center has a much larger spike than the others. This line is distinguished from the others because
Fig. 1. Spectra of signals from the 4–8 GHz pick-up with gold +79 ions at 100 GeV/n. Left, 1(a) shows coherent spike on bunch frequency harmonic at center and smaller spikes on revolution frequency harmonics. Center frequency is 7 GHz, span is 500 kHz. Right, 1(b) after several hours into store, narrower span, 200 kHz, at 5 GHz. No coherent spike is seen. Coasting beam gives asymmetric shape.
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
its frequency is a harmonic of the bunch frequency. There are 60 revolution frequency harmonic lines between these bunch frequency lines. The fact that the coherence seen on the bunch frequency harmonics is much larger than on all the other revolution frequency lines indicates that this spike is not anomalous, but just an indication that the Fourier spectrum of the bunch shape has significant strength even at this very high frequency. In fact, by examining the bunch spectrum at low frequency (10 MHz) we see the same ratio of strength on the bunch harmonic lines to the revolution frequency lines. This ratio is a manifestation of the filling pattern of the bunches in the ring. If all the bunches were exactly equal amplitude then only bunch frequency harmonics would occur. In fact there is an abort gap of five missing bunches out of 60 and since the bunches are loaded each from a different injector cycle they fluctuate in intensity. Fig. 1(b) is from the same store but several hours later. By zooming on three revolution frequency lines one sees that the bunch shape has evolved to the point that there is no coherence spike surviving. Also clearly seen in these spectra is the asymmetric shape caused by the coasting beam that has escaped the bucket, lost energy and drifted to higher frequency (above transition). These results show a qualitatively different behavior for gold ions than was seen for protons at the TEVATRON and SPS.
337
3. Beam transfer function measurement The longitudinal Beam Transfer Function (BTF) reveals a great deal about aspects of the beam that are relevant to stochastic cooling. Specifically it gives the density distribution function in momentum and also contains information concerning the interaction of the beam with the beam pipe coupling impedance. Having the 4–8 GHz kicker installed in the ring enabled quantitative measurements of the BTF. Unfortunately a 4–8 GHz power amplifier was not available until only a few days before the end of the FY03 gold. Some proof of principle of single-frequency measurements were done with gold but swept frequency measurements with a network analyzer were only done with proton beam during the polarized proton running period. Fig. 2 shows the result of such a measurement of the BTF from protons at 100 GeV. The kicker was driven with a 200 W TWT amplifier via 100 m of coaxial cable. Because of the attenuation in the cable only 8 W were delivered to the kicker. The frequency was swept slowly so that a 10 Hz IF bandwidth could be used in the network analyzer. Even though the power in the kicker is small the beam response is clearly discernable from the Schottky noise because it is a coherent reaction of the ensemble of particles and is therefore enhanced by factor of N (] number of particles=1012). The
Fig. 2. Longitudinal BTF for protons at 100 GeV. Imaginary part is on left, real part on right. The center frequency is 5 GHz and the span is 50 kHz. Vertical scale is linear with 70.01 full scale.
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
338
BTF is given by Z BTFðoÞ ¼ jk P:V:
dc=dE dE ðo no0 nkEÞ þ jpc0 ðEðoÞÞ ;
where, k represents the kicker and pickup impedances, n is the harmonic number, 64,000, CðEÞ is the energy distribution function, o0 is the revolution frequency. The real and imaginary parts of the measured BTF are shown in Fig. 2. The real part is proportional to the derivative of the distribution function. It is characteristically anti-symmetric since CðEÞ is symmetric. Particles below the center of the distribution will absorb energy, while those above the center will give energy to the kicker. For frequencies outside the distribution, the interaction is purely reactive and so all the magnitude comes from the imaginary part. If we model the distribution function as a Lorentzian and write it in the frequency variable we have, cðf Þ ¼
Fig. 3. The beam response to a continuous driving frequency within the distribution. The beam is 2 1012 protons in 55 bunches at 100 GeV. The RF buckets are comprised by 300 kV at 28 MHz plus 100 kV at 197 MHz. The input power to the 8 W at 4.8 GHz.
Df 1 p ðf f 0 Þ2 þ Df 2
where, Df is the width of the distribution, 20 kHz. We can solve for the magnitude of the response relative to the DC beam current, I BTF eV 1 ; I ¼ E d2 2pffi½ 2pf T jZj DC
0
center
0
where, d is the fractional energy spread, V the kicker voltage, T0 is revolution period, Z the frequency slip parameter, 1.7 103. This result is compared to the value found in the measurement illustrated in Fig. 3. With a single frequency driving the kicker at a frequency within the beam frequency distribution the beam response is seen. The pickup impedance and electronic gain are calibrated by the size of the Schottky component in the spectrum. The observed response agrees with the calculated result to with a few dB. The beam response for protons was sometimes qualitatively different with non-linear behavior exhibited. An example is shown in Fig. 4.
Fig. 4. The response of proton bunches showing non-linear behavior. The kicker is driven at one frequency, f center Df , but the beam responds at Df and 2Df . This suggest that this bunch is beyond the limit of stability by Landau damping.
The tendency of the proton bunch was not consistent and we were not able to definitively identify the conditions under which it occurred. These studies were done parasitically to machine operations and systematic variations of bunch intensity were not possible. However, there did appear to be a correlation with higher
ARTICLE IN PRESS J.M. Brennan et al. / Nuclear Instruments and Methods in Physics Research A 532 (2004) 335–339
bunch intensities and the non-linear response behavior.
4. Prospects for stochastic cooling The problem of strong coherent lines polluting the Schottky spectra seems to be much smaller for ions than protons. In fact, after some time during a store the coherent lines from gold ions are completely missing except on the harmonics of the bunch frequency. This indicates that the difficulties that were experienced at the TEVATRON and SPS would not hamper a stochastic cooling system at RHIC. Furthermore, observations of protons in RHIC show similar results to protons in the other collidiers, suggesting that the phenomenon is characteristic of the beam species more than the particulars of the ring, for example, impedance. Results from these studies encourage us to continue to pursue stochastic cooling in RHIC. The near term goal is to perform an experiment in which some longitudinal cooling is demonstrated. Clearly we are RF power limited, with one
339
amplifier and one kicker, but in a demonstration experiment there are many options to operate with reduced power. For example, reduced number of particles, less than optimum gain and longer cooling time, or cooling only some of the bunches in the ring to reduce CW power.
Acknowledgements Many thanks to Fritz Caspers of CERN for enlightening conversations and encouragement. This work would not have been possible without the contributions of Ralph Pasquinelli and Dave McGinnis of Fermilab, who contributed both hardware and expertise. References [1] J. Wei, A.G. Ruggiero, BNL/AD/RHIC-71, 1990. [2] J. Wei, Workshop on Beam Cooling, Montreux, 1993, CERN 94-03, 1994. [3] G. Jackson, Workshop on Beam Cooling, Montreux, 1993, CERN 94-03, 1994.