Stationary electron vortex states in a plasma bubble field

Abstract

Plasma wakefield accelerators (PWFAs) offer accelerating gradients of 10-100~GV/m and relativistically propagating plasma bubbles capable of confining charged particles. We study the stationary states of a vortex electron at the bubble center by solving the corresponding quasi-relativistic Schrödinger equation. Analytical solutions are obtained with Laguerre-Gaussian transverse modes and Hermite-Gaussian longitudinal envelopes. Comparing the resulting beam parameters with experimentally accessible vortex-electron bundles, we find that the transverse beam waist supported by the plasma bubble is comparable to that achieved by current electron-optical techniques. The longitudinal confinement further provides a favorable parameter regime for stable injection. Our results indicate the feasibility of maintaining localized vortex-electron states in a plasma-bubble wakefield and provide an analytical starting point for investigating their subsequent acceleration and stability.