Cooling force on ions in a magnetized electron plasma

TL;DR

This paper presents a comprehensive calculation of the cooling force on ions in a magnetized electron plasma, accounting for anisotropic velocity distributions and magnetic field effects, using an improved binary collision theory.

Contribution

It introduces a second-order perturbation approach to calculate the cooling force in magnetized plasmas, valid for any magnetic field strength and using a regularized interaction potential.

Findings

Explicit formulas for the cooling force with monochromatic electron beams.

Evaluation of the cooling force for anisotropic Maxwellian velocity distributions.

Theoretical framework applicable across different magnetic field regimes.

Abstract

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. In the common rest frame of the ion and the electron beam the ion is subjected to a drag force and it experiences a loss or a gain of energy which eventually reduces the energy spread of the ion beam. A calculation of this process is complicated as the electron velocity distribution is anisotropic and the cooling process takes place in a magnetic field which guides the electrons. In this paper the cooling force is calculated in a model of binary collisions (BC) between ions and magnetized electrons, in which the Coulomb interaction is treated up to second-order as a perturbation to the helical motion of the electrons. The calculations are done with the help of an improved BC theory which is uniformly valid for any strength of the magnetic field and where the second-order two-body forces are treated in the interaction in Fourier space without specifying the interaction potential. The cooling force is explicitly calculated for a regularized and screened potential which is both of finite range and less singular than the Coulomb interaction at the origin. Closed expressions are derived for monochromatic electron beams, which are folded with the velocity distributions of the electrons and ions. The resulting cooling force is evaluated for anisotropic Maxwell velocity distributions of the electrons and ions.