Theory of laser wakes in plasma channels

Abstract

Excitation of accelerating modes in transversely inhomogeneous plasma channels is considered as an initial value problem. Discrete eigenmodes are supported by plasma channels with sharp density gradients. These eigenmodes are collisionlessly damped as the gradients are smoothed. Using collisionless Landau damping as the analogy, the existence and damping of these “quasi-modes” is studied by constructing and analytically continuing the causal Green’s function of wake excitation into the lower half of the complex frequency plane. Electromagnetic nature of the plasma wakes in the channel makes their excitation nonlocal. This results in the algebraic decay of the fields with time due to phase-mixing of plasma oscillations with spatially-varying frequencies. Characteristic decay rate is given by the mixing time τm, which corresponds to the dephasing of two plasma fluid elements separated by the collisionless skin depth. For wide channels analytic expressions for the field evolution are derived. Implications for electron acceleration in plasma channels are discussed.