Multiple-fluid models for plasma wake-field phenomena

Abstract

In this paper we present various treatments of plasma wake-field phenomena which employ multiple-fiuid models. These models generalize the one-dimensional, nonlinear, relativistic singlefluid model which has been used extensively in previous plasma wake-field calculations. Using a two-fluid model, we discuss the interaction of a low-energy continuous electron beam with wakefield-generated plasma waves. The phenomena of continuous-beam modulation and wave period shortening are discussed. The relationship between these effects and the two-stream instability is also examined. Also, using a three-fluid model, effects due to plasma electron temperature in nonlinear plasma wake-fields are examined and compared to previous work. Finally, the consequences of ion motion induced by large-amplitude electron plasma waves are calculated by including the fluid behavior of the ions.

Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma

“…Note that both results are almost identical to the result obtained by Schroeder et al, 26 for this regime. Similar results can also be obtained by inserting the value of 0 derived above into the models of other authors 24,25,27,29 This is not surprising, since the differences that exist between the various models used to describe a relativistic thermal plasma are not yet significant for ␥ 2 ␤ 1.…”

“…After correcting an algebraic error in the derivation of Ref. 27, the limit was found to be E wb 2 Ϸ ␥ /3+1/ ͱ 2␤, which is much like the limit for a cold relativistic fluid 2 with a small thermal correction, even in the limit ␥ 2 ␤ 1. We conclude that this model does not provide a good description for a warm relativistic plasma, and that the wave-breaking limit it provides is not reliable.…”

“…27. In this model, the warm plasma is modeled using three cold fluids having density 1/3 each, and mean velocities v t , −v t , and 0, respectively.…”

“…Of course, this approach only works as long as there is an invertible relation between ⌿ and v or n; as soon as d⌿͑v͒ / dv =0 or d⌿͑n͒ / dn = 0, the fluid model breaks down. Unfortunately, many different warm-fluid models can be found in the literature, [22][23][24][25][26][27][28][29] leading to a range of conflicting "definitions" for wave breaking. As will be shown below, this is particularly the case for ultrarelativistic plasma waves, i.e., plasma waves obeying ␥ 2 ␤ 1, where ␥ is the Lorentz factor corresponding to the phase speed of the plasma wave, ␤ =3k B T 0 / ͑m e c 2 ͒, T 0 the initial plasma temperature, and m e the electron mass.…”

Real Spatial Shapes and Phase Space Structures of 3-D Nonlinear Electrostatic Plasma Wave

“…[45] but these two equations, as well as p and p , are both independent of transverse coordinates r and . Similar approximation in which all related physical quantities are independent of r and is also widely adopted in a few of related theories [46][47][48][49][50][51][52]. Only in few theories [53,54], transverse dynamics is really studied because the dependence of related physical quantities on the radial coordinates r is taken into account.…”