Analytical Solution to Electron Beam Envelope Evolution in a Plasma Wakefield

TL;DR

This paper derives an analytical solution for the evolution of an electron beam's envelope in a plasma wakefield, aiding in controlled injection processes for plasma accelerators.

Contribution

It introduces a harmonic motion-based ansatz to analytically model beam-slice envelope oscillations in nonlinear regimes, matching numerical results.

Findings

Analytical expressions agree with numerical simulations.

Pinch size determined via energy conservation.

Provides insights into beam control in plasma wakefield accelerators.

Abstract

Beam-induced ionization injection (B-III) is currently being explored as a method for injecting an electron beam with a controlled density profile into a plasma wakefield accelerator (PWFA). This process is initiated by the fields of an unmatched drive beam where the slice envelope reaches its minimum value, the 'pinch'. To control the injected beam's qualities, it is crucial to study the beam-slice envelope oscillations, especially size and the location of the pinch. In this proceeding, an ansatz based on the harmonic motion is proposed to find the analytical solution to beam-slice envelope evolution in the nonlinear regime. The size of the pinch is then found through the application of energy conservation in the transverse direction. The resulting analytical expressions are shown to be in good agreement with numerical solutions.