Radial equilibrium of relativistic particle bunches in plasma wakefield accelerators

TL;DR

This paper provides a detailed analysis of the radial equilibrium state of relativistic particle beams in plasma wakefield accelerators, combining analytical, numerical, and simulation methods to reveal the beam's density, radius, and momentum distribution.

Contribution

It introduces a comprehensive description of the radial equilibrium of relativistic beams in plasma wakefield accelerators, including self-consistent wakefields and particle distributions.

Findings

Beam density peaks near the axis

Beam radius remains constant along the beam

Transverse momentum distribution varies with radius

Abstract

Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principle simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum distribution of beam particles depends on the observation radius and is neither separable, nor Gaussian.