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Title: Double and triple-harmonic RF buckets and their use for bunch squeezing in AGS

Abstract

For the past several years we have merged bunches in AGS in order to achieve the desired intensity per bunch prior to injection into RHIC. The merging is done on a flat porch at or above AGS injection energy. Because the merges involve the reduction of the RF harmonic number by a factor of 2 (for a 2 to 1 merge) and then a factor of 3 (for a 3 to 1 merge), one requires RF frequencies 6hf s, 3hf s, 2hf s and hf s, where f s is the revolution frequency on the porch and h = 4 is the fundamental harmonic number. The standard AGS RF cavities cannot operate at the lowest frequencies 2hf s and hf s; these are provided by two modified cavities. Upon completion of the merges, the bunches are sitting in harmonic h buckets. In order to be accelerated they need to be squeezed into harmonic 3h buckets. This is accomplished by producing a double-harmonic bucket in which harmonics h and 2h act in concert, and then a triple-harmonic bucket in which harmonics h, 2h, and 3h act in concert. Simulations have shown that the squeeze presents an acceptance bottleneck which limits themore » longitudinal emittance that can be put into the harmonic 3h bucket. In this note the areas of the double and triple-harmonic buckets are calculated explicitly, and it is shown that these go through a minimum as the RF voltages are raised to the desired values. Several RF voltage ranges are examined, and the acceptance bottleneck is determined for each of these. Finally, the acceptance bottleneck for Au77+ bunches in AGS is calculated for several RF voltage ranges. The main result is that the RF voltages for the low-frequency harmonic h and 2h cavities both must be at least 22 kV in order to achieve an acceptance of 0:6 eV s per nucleon. If the harmonic h and 2h voltages are 15 and 22 kV, respectively, then the acceptance is reduced to 0:548 eV s per nucleon.« less

Authors:
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States). Alternating Gradient Synchrotron
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1336134
Report Number(s):
BNL-112605-2016-IR
R&D Project: KBCH139; KB0202011; TRN: US1701396
DOE Contract Number:
SC00112704
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BROOKHAVEN AGS; HARMONICS; CAVITY RESONATORS; BEAM BUNCHING; BEAM DYNAMICS; SIMULATION; BEAM EMITTANCE; ELECTRIC POTENTIAL; RF SYSTEMS; Alternating Gradient Synchrotron

Citation Formats

Gardner, C. J.. Double and triple-harmonic RF buckets and their use for bunch squeezing in AGS. United States: N. p., 2016. Web. doi:10.2172/1336134.
Gardner, C. J.. Double and triple-harmonic RF buckets and their use for bunch squeezing in AGS. United States. doi:10.2172/1336134.
Gardner, C. J.. 2016. "Double and triple-harmonic RF buckets and their use for bunch squeezing in AGS". United States. doi:10.2172/1336134. https://www.osti.gov/servlets/purl/1336134.
@article{osti_1336134,
title = {Double and triple-harmonic RF buckets and their use for bunch squeezing in AGS},
author = {Gardner, C. J.},
abstractNote = {For the past several years we have merged bunches in AGS in order to achieve the desired intensity per bunch prior to injection into RHIC. The merging is done on a flat porch at or above AGS injection energy. Because the merges involve the reduction of the RF harmonic number by a factor of 2 (for a 2 to 1 merge) and then a factor of 3 (for a 3 to 1 merge), one requires RF frequencies 6hfs, 3hfs, 2hfs and hfs, where fs is the revolution frequency on the porch and h = 4 is the fundamental harmonic number. The standard AGS RF cavities cannot operate at the lowest frequencies 2hfs and hfs; these are provided by two modified cavities. Upon completion of the merges, the bunches are sitting in harmonic h buckets. In order to be accelerated they need to be squeezed into harmonic 3h buckets. This is accomplished by producing a double-harmonic bucket in which harmonics h and 2h act in concert, and then a triple-harmonic bucket in which harmonics h, 2h, and 3h act in concert. Simulations have shown that the squeeze presents an acceptance bottleneck which limits the longitudinal emittance that can be put into the harmonic 3h bucket. In this note the areas of the double and triple-harmonic buckets are calculated explicitly, and it is shown that these go through a minimum as the RF voltages are raised to the desired values. Several RF voltage ranges are examined, and the acceptance bottleneck is determined for each of these. Finally, the acceptance bottleneck for Au77+ bunches in AGS is calculated for several RF voltage ranges. The main result is that the RF voltages for the low-frequency harmonic h and 2h cavities both must be at least 22 kV in order to achieve an acceptance of 0:6 eV s per nucleon. If the harmonic h and 2h voltages are 15 and 22 kV, respectively, then the acceptance is reduced to 0:548 eV s per nucleon.},
doi = {10.2172/1336134},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 8
}

Technical Report:

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  • Cottingham proposed a scheme to populate 114, instead of 57, rf buckets at the RHIC injection, which employs a low-Q rf system of maximum 40 kV in addition to the original rf system to shift the particle bunches azimuthally along the ring. The first part of this report studies the adiabatic condition required by this scheme. It is shown that the entire process can be accomplished during a time shorter than the cycling period of the AGS. Results of computer simulation, which are presented in the second part, indicate that particle loss is negligible during the manipulation of the 0.3more » eV∙s/u 197Au 79+ bunches.« less
  • Cottingham proposed a scheme to populate 114, instead of 57, rf buckets at the RHIC injection, which employes a low-Q rf system of maximum 40 kV in addition to the original rf system to shift the particle bunches azimuthally along the ring. The first part of this report studies the adiabatic condition required by this scheme. It is shown that the entire process can be accomplished during a time shorter than the cycling period of the AGS. Results of computer simulation, which are presented in the second part, indicate that particle loss is negligible during the manipulation of the 0.3more » eV{center dot}s/u {sup 197}Au{sup 79+} bunches. 5 refs.« less
  • An X-band 4th harmonic RF section is used to linearize the bunch compression process in the Linac Coherent Light Source [1]. The optimum voltage is calculated to compensate both for the second-order RF time-curvature, and for the second-order momentum compaction terms. This compensated compression retains, to a much higher degree, the initial temporal distribution of the bunch, reducing the effects of coherent synchrotron radiation [2], and also reduces the sensitivity of the final compression to bunch arrival time variations.
  • It has been suggested that the phase of the beam excited voltage in the harmonic cavity can be controlled by detuning its resonant frequency from the beam current harmonic. Unfortunately the detuning needed to flatten the acceleration waveform also corresponds to the region of Robinson instability for the harmonic cavity. Therefore, lengthening the bunch may be followed by large amplitude synchrotron oscillation of the bunch center of mass. Bunch lengthening is discussed in this note from several points of view. There follows a simple review of single electron oscillations in a quartic potential. Then equations are developed for the coupledmore » oscillations of a cavity and a rigid bunch as a fully nonlinear, time dependent initial value problem. Next, a computer program that solves these equations for one, two or more cavities, with and without externally driven fields, is described and some simulations of the harmonic cavity interaction are shown. Finally, the fully nonlinear equations are linearized to derive a dispersion relation for the case of beam excitation in the harmonic cavity. 6 refs., 5 figs.« less