J.Y. Li, T. Hu, J. Yang, B.Q. Zeng
HUST, Wuhan, People’s Republic of China
H.G. Xu
SINR, Jiading, Shanghai, People’s Republic of China
Funding:This work was supported by National Natural Science Foundation of China (NSFC) under Project Numbers 11905074. Electron linear accelerators with an energy of ~MeV are widely required in industrial applications. Whereas miniaturized accelerators, especially those working at X-band, attract more and more attention due to their compact structures and high gradients. Since the performance of a traveling wave (TW) accelerator is determined by its structures, considerable efforts must be made for structure optimization involving numerous and complex parameters. In this context, functional key parameters are obtained through deep analysis for structure and particle motion characteristics of the TW accelerator, then a multi-objective genetic algorithm (MOGA) is successfully applied to acquire an optimized phase velocity distribution which can contribute to achieving a high capture ratio and a low energy spread. Finally, a low-energy X-band TW tube used for rubber vulcanization is taken as an example to verify the reliability of the algorithm under a single-particle model. The capture ratio is 91.2%, while the energy spread is 5.19%, and the average energy is 3.1MeV.
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N. Mounet, E. Dadiani, E. Métral, C. Zannini
CERN, Geneva, Switzerland
A. Rahemtulla
EPFL, Lausanne, Switzerland
Indirect space charge contributes significantly to the impedance of non ultrarelativistic machines such as the LEIR, PSB and PS, at CERN. While general expressions exist in frequency domain for the beam coupling impedance, the time domain wake function is typically obtained numerically, thanks to an inverse Fourier transform. An analytical expression for the indirect space charge wake function, including the time dependence as a function of particle velocity, is nevertheless highly desirable to improve the accuracy of time domain beam dynamics simulations of coherent instabilities. In this work, a general formula for the indirect space charge wake function is derived from the residue theorem. Moreover, simple approximated expressions reproducing the time and velocity dependence are also provided, which can even be corrected to recover an exact formula, thanks to a numerical factor computed once for all. The expressions obtained are successfully benchmarked with a purely numerical approach based on the Fourier transform.
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C. Zannini, H. Bartosik, M. Carlà, K.S.B. Li, E. Métral, G. Rumolo, B. Salvant
CERN, Geneva, Switzerland
L.R. Carver
ESRF, Grenoble, France
M. Schenk
EPFL, Lausanne, Switzerland
At the end of 2018, an instability with multiple bunches has been consistently observed during high intensity studies at the CERN-SPS. This instability could be a significant limitation to achieve the bunch intensity expected after the LHC Injector Upgrade (LIU). Therefore, a deep understanding of the phenomena is essential to identify the best mitigation strategy. Extensive simulation studies have been performed to explore the consistency of the current SPS model, give a possible interpretation of the instability mechanism and outline some possible cures.
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A.J. Laut, A. Lasheen
CERN, Geneva 23, Switzerland
Particles in an intense bunch experience longitudinal self-fields due to space~charge. This effect, conveniently described by geometric factors dependent on a particle¿s transverse position, beam size, and beam pipe aperture, is usually incorporated into longitudinal particle tracking on a per-turn basis. The influence of transverse betatron motion on longitudinal space~charge forces is, however, usually neglected in pure longitudinal tracking codes. A dedicated tracking code was developed to characterize the CERN PS such that an effective geometric factor of a given particle could be derived from its transverse emittance, betatron phase~advance, and momentum~spread. The effective geometry factor is then estimated per particle by interpolation without the need for full transverse tracking and incorporated into the longitudinal tracker BLonD. The paper evaluates this effect under conditions representative of the PS, where space~charge is dominant at low energy and progressively becomes negligible along the acceleration ramp. The synchrotron frequency distribution is modified and the filamentation rate is moreover increased, which could suggest a stabilizing space~charge phenomenon.
L. Intelisano, H. Damerau, I. Karpov
CERN, Meyrin, Switzerland
Landau damping is a natural stabilization mechanism to mitigate coherent beam instabilities in the longitudinal phase space plane. In a single RF system, binominal particle distributions with a constant inductive impedance above transition (or capacitive below) would lead to a vanishing threshold for the loss of Landau damping, which can be avoided by introducing an upper cut-off frequency to the impedance. This work aims at expanding the recent loss of Landau damping studies to the common case of double harmonic RF systems. Special attention has been paid to the configuration in the SPS with a higher harmonic RF system at four times the fundamental RF frequency, and with both RF systems in counter-phase (bunch shortening mode). Refined analytical estimates for the synchrotron frequency distribution allowed to extend the analytical expression for the loss of Landau damping threshold. The results are compared with semi-analytical calculations using the MELODY code, as well as with macroparticle simulations in BLonD.
I. Karpov, T. Argyropoulos, E.N. Shaposhnikova
CERN, Meyrin, Switzerland
S. Nese
University of Bergen, Bergen, Norway
Landau damping is a very important stabilization mechanism of beams in circular hadron accelerators. In the longitudinal plane, Landau damping is lost when the coherent mode is outside of the incoherent synchrotron frequency spread. In this paper, the threshold for loss of Landau damping (LLD) for constant inductive impedance ImZ/k is derived using the Lebedev matrix equation (1968). The results are confirmed by direct numerical solutions of the Lebedev equation and using the Oide-Yokoya method (1990). For more realistic impedance models of the ring, new definitions of an effective impedance and the corresponding cutoff frequency are introduced which allow using the same analytic expression for the LLD threshold. We also demonstrate that this threshold is significantly overestimated by the Sacherer formalism based on the previous definition of an effective impedance using the eigenfunctions of the coherent modes.
A. Lasheen, H. Damerau, K. Iliakis
CERN, Meyrin, Switzerland
In the context of the LHC Injector Upgrade (LIU) project, the main longitudinal limitations in the CERN PS are coupled bunch instabilities and uncontrolled emittance blow-up leading to losses at injection into the downstream accelerator, the SPS. To complement beam measurements, particle tracking simulations are an important tool to study these limitations. However, to avoid excessive runtime, simulations are usually targeting only a fraction of the cycle assuming that bunches are initially matched to the RF bucket. This ignores all initial perturbations that could seed an instability. Simulations were therefore performed along the full PS cycle by using the BLonD tracking code optimized with advanced parallelization schemes. They include beam manipulations with several RF harmonics (batch compression, merging, splittings), controlled emittance blow-up, a model of the beam coupling impedance covering a wide frequency range, as well as beam and cavity feedbacks. A large number of macroparticles is required as well as arrays to store beam induced voltage spanning several revolutions to account for long range wakefields.
