A resistive transverse damper is often needed in particle accelerators operating with many bunches and it is usually very efficient as it can considerably reduce the necessary amount of ...nonlinearities needed to reach beam stability through Landau damping. In the CERN LHC for instance, the required current in the Landau octupoles is predicted to be reduced by an order of magnitude for zero chromaticity (for the beam and machine parameters used during the last year of Run 2, in 2018, this corresponded to∼2000Awithout damper and∼200Awith damper, knowing that the maximum current available in the Landau octupoles is∼550A ). However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called ITSR instability (for imaginary tune split and repulsion). Until now, only one type of impedance-driven transverse coherent instability has been explained for a single bunch in a circular particle accelerator, at zero chromaticity and without a multiturn wake: the transverse mode coupling instability. A transverse mode coupling instability can also be observed in the presence of Landau damping, beam-beam, electron cloud or space charge. However, the ITSR instability exhibits a different mechanism, which is not due to mode coupling. The purpose of this article is to explain in detail both this new instability mechanism and its mitigation using a simplified analytical model, which has been carefully benchmarked, using the pyheadtail macroparticle tracking code, by Oeftiger (one of the code’s developers).
Intrabunch motion Métral, E.
Physical review. Accelerators and beams,
01/2021, Letnik:
24, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Impedance-driven (but not only) coherent beam instabilities are usually studied analytically with the linearized Vlasov equation, ending up with an eigenvalue system to solve. The eigenvalues ...describe the beam oscillation mode-frequency shifts, leading in particular to intensity thresholds defined by the longitudinal mode coupling instability in the longitudinal plane and by the transverse mode coupling instability in the transverse plane in the absence of chromaticity. This can be directly compared to measurements in particular for the lowest modes and in the absence of tune spread. In the presence of nonlinearities or when higher-order modes are involved, this becomes quite difficult, if not impossible, and the coupling between the modes cannot be directly measured (or simulated) anymore. Another important observable is the intrabunch motion, which can be also accessed analytically thanks to the eigenvectors. To the author’s knowledge, until now, the intrabunch signal has only been explained theoretically for independent longitudinal or transverse beam oscillation modes, i.e., when the bunch intensity is sufficiently low compared to the mode coupling threshold. It was never explained theoretically in detail when two (or more) modes are involved. For instance, no answers were already given to these questions: is (are) there some fixed point(s) when the transverse mode coupling instability starts? If yes, where is it (are they)? And what happens in the presence of mode decoupling? Any number of modes can be treated with the general approach discussed in this paper, which is based on the galactic Vlasov solver (which was previously successfully benchmarked against the pyheadtail macroparticle tracking code as concerns the beam oscillation mode-frequency shifts). However, to be able to clearly see what happens when the bunch intensity is increased, the simple case of two modes is discussed in detail. The purpose of this paper is to describe the different regimes, below, at, above the transverse mode coupling instability and also after the mode decoupling (as it happens sometimes), using a simple analytical model (where two modes are considered together), which helps to really understand what happens at each step. Better characterizing an instability is the first step before trying to find appropriate mitigation measures and push the performance of a particle accelerator. The evolution of the intrabunch motion with intensity is a fundamental observable with high-intensity high-brightness beams.
The study of collective effects in circular accelerators can be tackled by solving numerically the Vlasov equation or by using tracking codes. The two methods are obtained with different approaches: ...Vlasov solvers consider a continuous distribution function and describe the beam with coherent oscillation modes in frequency domain (ending up usually with an eigenvalue system to solve), while tracking codes use macroparticles and wakefields in time domain. In this paper we present two Vlasov solvers for the study of collective effects (from impedances/wakefields only) which evaluate the frequency shift of coherent oscillation modes and possible mode coupling instability in the single-bunch case for both longitudinal and transverse planes. In the longitudinal plane the Vlasov solver also takes into account the potential well distortion due to the wakefields under some conditions. In parallel to this theoretical approach, tracking codes, which include collective effects, have been used as benchmark. In particular, starting from their results, we also propose a new method to study the frequency shift of coherent modes and compare it with the output of the Vlasov solvers.
A destabilizing effect of the detuning impedance has been recently observed in simulations of the CERN Proton Synchrotron (PS) at the injection energy: while without the detuning impedance the ...instability is faster in the vertical plane as expected (due to the elliptical shape of the vacuum chamber), with detuning impedance the instability appears to be faster in the horizontal plane. In order to understand the detuning impedance destabilizing effect, we study the collective behavior for the simpler case of a coasting beam with PS-like parameters and a simplified impedance model. The analysis, carried out from both numerical and theoretical points of view, highlights a new destabilizing mechanism related to the coupling of slow and fast waves.
A new model for the description of beam instabilities in synchrotrons featuring wakefields and space charge forces is proposed, using the circulant matrix approach. The predictions of this model are ...discussed in light of past ones, with a particular emphasis on the possible mitigation of the transverse mode coupling instability by space charge forces. The existence of transient amplification in spite of the absence of unstable eigenvalues in configuration featuring strong space charge forces is also addressed. It is shown that this behavior can be recovered when considering an airbag distribution. Yet when considering a more realistic Gaussian distribution, the radial modes lead to other types of mode coupling instabilities. The predictions of the new model are then compared to results of an experiment conducted at the CERN Super Proton Synchrotron, showing a reasonable agreement.
Abstract
The I.FAST CBI is an immersive challenge-based innovation program funded by the H2020 I.FAST project. The 10-day face-to-face challenge brings together students of different disciplines from ...all over Europe to work together on innovative projects using accelerator technology applied to environmental challenges. We report on the first edition of the I.FAST CBI, the proposed projects and feedback from the students.
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