Wake excited in plasma by an ultra-relativistic point-like bunch

TL;DR

This paper models the wakefield generated in plasma by an ultra-relativistic point-like electron bunch, deriving simplified equations and analyzing the cavity formation behind the driver through numerical solutions.

Contribution

It introduces a simplified, scalable model for plasma wakefields driven by ultra-relativistic point charges, including numerical solutions for different charge signs.

Findings

A simplified system of equations for plasma electrons is derived.

The cavity dimensions scale with the driver charge.

Numerical solutions for positive driver charge are provided.

Abstract

A plasma flow behind a relativistic electron bunch propagating through a cold plasma is found assuming that the transverse and longitudinal dimensions of the bunch are small and the bunch can be treated as a point charge. In addition, the bunch charge is assumed small. A simplified system of equations for the plasma electrons is derived and it is shown that, through a simple rescaling of variables, the bunch charge can be eliminated from the equations. These equations have a unique solution, with an ion cavity formed behind the driver. The equations are solved numerically and the scaling of the cavity dimensions with the driver charge is obtained. A numerical solution for the case of a positively charged driver is also found.