# Amplification of coupled nonlinear oscillations of charged particle beam in crossed magnetic fields

## TL;DR

This paper studies how coupled nonlinear oscillations in a charged particle beam within crossed magnetic fields can be resonantly amplified, leading to increased beam density and potential applications in accelerators and light sources.

## Contribution

It identifies conditions for resonant amplification of beam oscillations using a cold-fluid model, revealing how external magnetic fields can enhance beam acceleration and stability.

## Key findings

- Resonant conditions for oscillation amplification are established.
- Beam density increases with velocity amplitudes, reducing beam radius.
- External magnetic fields can effectively accelerate and focus the beam.

## Abstract

A non-relativistic, charged-particle beam is placed into a crossed magnetic field. For such a system, the nonlinear electrostatic oscillations generation in the different degrees of the beam freedom may be triggered by the energy/momentum exchange between the beam's particles and these external fields. The influence of oscillation dynamics of these fields and beam have been studied based on the cold-fluid hydrodynamic description. As a result, the necessary conditions under resonant amplification of the beam's natural oscillations are identified. Present results demonstrate that the beam density increases when the amplitude of radial and axial velocities increase. This process decreases the radius of the beam over the course of time. The technical application of the process applies in real accelerators such as a gyrotrons, FELs, and cyclotrons, where transverse size is limited by the size of the vacuum chamber. Thus redistribution of energy between the external field and the kinetic energy of the beam can effectively accelerate the beam by using an external magnetic field. These fields with both axial and radial directions use further this beam as an effective light source by identifying the resonance frequency to improve stability, focus particles, and wave propagation.