Collision Integrals and the Generalized Kinetic Equation for Charged Particle Beams

TL;DR

This paper derives collision integrals for high-energy charged particle beams considering space charge effects, leading to a generalized kinetic equation that describes beam evolution.

Contribution

It introduces a derivation of collision integrals in Balescu-Lenard and Landau forms specific to charged particle beams with space charge interactions.

Findings

Derived collision integrals for charged beams

Formulated a generalized kinetic equation

Simplified the equations for practical use

Abstract

In the present paper we study the role of particle interactions on the evolution of a high energy beam. The interparticle forces taken into account are due to space charge alone. We derive the collision integral for a charged particle beam in the form of Balescu-Lenard and Landau and consider its further simplifications. Finally, the transition to the generalized kinetic equation has been accomplished by using the method of adiabatic elimination of fast variables.