Coherent States for Particle Beams in the Thermal Wave Model

TL;DR

This paper introduces the concept of coherent states for charged particle beams within the Thermal Wave Model, using quantum mechanics analogies to analyze beam evolution in optical and accelerator contexts.

Contribution

It extends the concept of coherent states to particle beams in the Thermal Wave Model, providing a physical interpretation and analytical tools for beam dynamics in accelerators.

Findings

Gaussian-like coherent structures are identified in beam distributions.

Analytical and numerical analysis of beam evolution in quadrupole-like devices.

Coherent states provide a natural description of beam behavior in accelerators.

Abstract

In this paper, by using an analogy among {\it quantum mechanics}, {\it electromagnetic beam optics in optical fibers}, and {\it charge particle beam dynamics}, we introduce the concept of {\it coherent states} for charged particle beams in the framework of the {\it Thermal Wave Model} (TWM). We give a physical meaning of the Gaussian-like coherent structures of charged particle distribution that are both naturally and artificially produced in an accelerating machine in terms of the concept of coherent states widely used in quantum mechanics and in quantum optics. According to TWM, this can be done by using a Schr\"{o}dinger-like equation for a complex function, the so-called {\it beam wave function} (BWF), whose squared modulus is proportional to the transverse beam density profile, where Planck's constant and the time are replaced by the transverse beam emittance and by the propagation coordinate, respectively. The evolution of the particle beam, whose initial BWF is assumed to be the simplest coherent state (ground-like state) associated with the beam, in an infinite 1-D quadrupole-like device with small sextupole and octupole aberrations, is analytically and numerically investigated.