A scalar field theory of 1+1-dimensional laser wakefield accelerators

Abstract

A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed circularly-polarised laser pulse. An upper bound on the dimensionless amplitude $a_0$ of the laser pulse is determined as a function of the phase speed $v$ of the wake. The asymptotic behaviour of the upper bound on $a_0$ as $v\rightarrow c$ is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on $a_0$ which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when $v$ is sufficiently close to $c$.