Interaction between high intensity beam and structure resonances

TL;DR

This paper investigates the interaction between high intensity beams and structure resonances using numerical simulations to verify theoretical predictions, revealing different beam reactions depending on resonance conditions and highlighting phase space mixing as a key mechanism.

Contribution

It extends theoretical understanding of structure resonance by numerically validating the interaction principles and exploring the beam's response in different resonance scenarios.

Findings

Beam reaction varies for different resonance stop bands.

Phase space mixing links resonant and non-resonant effects.

Numerical simulations support theoretical predictions.

Abstract

With the help of the linearized perturbation theory, the collective beam instability due to the space charge, modelled by the Vlasov-Poisson equation, is well studied in the former research theoretically in a general sense [Chao Li and R. A. Jameson PRAB, 21, 024204 (2018)], where the related instability is depicted by the "structure resonance". As an extension of the theoretical study, this paper aims to verify the validity of the structure resonance with numerical simulations and to show the basic principles which interpret the interaction between structure resonance and beam in a general sense. It is found that the reaction of beam to the structure resonance ($n\sigma\approx 180^\circ$) differs for the cases with $n= 0$ and $n\ne 0$ stop bands. The non-resonant "plasma oscillation" is also revisited; the "phase space mixing", lying in the transient plasma oscillation, is the mechanism that ties the resonant effects, non-resonant effects and macroscopic beam phenomena together.