Description of longitudinal space charge effects in beams and plasma through dielectric permittivity

TL;DR

This paper introduces a universal framework using dielectric permittivity to analyze longitudinal space charge effects in beams and plasmas, enabling quick stability assessments for various geometries and distributions.

Contribution

The authors develop a novel dielectric permittivity approach that generalizes plasma response to complex beam and plasma geometries, including multiple particle species.

Findings

Derivation of a transverse geometry-dependent plasma frequency.

Unified dielectric permittivity expression for beams and plasmas.

Framework for analyzing stability of collective instabilities.

Abstract

We develop a universal framework which allows quickly solve a wide class of problems for longitudinal space charge effects in beams and plasmas in cylindrical geometry. We introduce the longitudinal dielectric permittivity for the beam of charged particles, which describes its collective space charge response. The analyis yields an effective plasma frequency, which depends on the transverse geometry of the system. This dielectric permittivity mirrors the dielectric permittivity of plasma and matches the one dimensional (1D) expression once the transverse size of the beam is large. Several particle species can be included as additive terms describing susceptibility of each specie. The developed approach allows to study stability criteria for collective beam-beam and beam-plasma instabilities for arbitrary transverse distributions in particle densities.