Thermal effects in plasma-based accelerators

Abstract

Finite plasma temperature can modify the structure of the wakefield, reduce the wavebreaking field, and lead to self-trapped electrons, which can degrade the electron bunch quality in a plasmabased accelerator. The plasma temperature evolution is described using a relativistic warm fluid theory. Alterations to the maximum amplitude of a nonlinear periodic wave exited in a plasma with nonrelativistic temperatures are presented. The trapping threshold for a plasma electron and the fraction of electrons trapped from a thermal distribution are examined using on a single-particle model. Numerical artifacts in particle-in-cell models which can mimic the physics associated with finite momentum spread are discussed.

Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves

“…As the field amplitude approaches and exceeds the maximum amplitude of a traveling wave (wavebreaking limit), particles in the tail of the plasma distribution may becomes trapped in the plasma wave [30,31]. Specifically, for laser-driven plasma waves (γ 2 ϕ τ ≪ 1 and γ 2 ϕ ≫ 1), the results of the warm fluid theory imply that the maximum longitudinal fluid velocity w max satisfies w max + √ 3β th ≃ β ϕ , where β th is the thermal velocity spread (variance) of the electron distribution.…”

“…Hence, at the maximum amplitude, β ϕ − w max ≃ √ 3β th . As the amplitude of the wave approachesÊ max , electrons in the tail of a typical plasma distribution may be trapped [30,31]. Although the peak value of the mean fluid velocity is less than the phase velocity, w max < β ϕ (and u z,max < γ ϕ β ϕ ), electrons on the tail of a thermal distribution with velocities in excess of the phase velocity will be trapped.…”

“…Specifically, thermal electrons with velocities in excess of √ 3β th . Assuming an initially Gaussian thermal distribution, this corresponds to approximately 4% of the electron population are continuously being trapped by the plasma wave with amplitudeÊ max [31]. Once a significant number of electrons become trapped in the plasma wave, the plasma wave amplitude becomes time dependent (no longer a function of only z − β ϕ ct), owing to beam loading and damping of the plasma wave, and a purely traveling wave solution is no longer possible.…”

Vlasov simulations of thermal plasma waves with relativistic phase velocity in a Lorentz boosted frame

“…Consideration of thermal effects are important in plasma-based accelerators [6] and an Eulerian-Vlasov method may be preferable to particle-based methods due to decreased noise. However, the former are very computationally intensive due to inefficient representation of the particle distribution.…”

“…Low-noise Eulerian-Vlasov simulations may be of interest for understanding the effect of the initial thermal distribution on particle trapping and wave amplitude [6]. Simulations of relativistic phase velocity waves in thermal laboratory plasmas, such as those relating to laser or beam driven plasma wakefield accelerator experiments [7][8][9], are, however, constrained by the fact that the maximum and minimum momenta that need to be resolved, in the direction of propagation, have a large difference in magnitude.…”