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Averaged Lorentz Dynamics and an application in Plasma Dynamics

Ricardo Gallego Torrome

Abstract

Using a geometric averaging procedure applied to a non-affine linear connection, we prove that for a narrow one particle distribution function and in the ultra-relativistic limit, a bunch of point charged particles can be described by a Charged Cold Fluid Model, without additional hypothesis on the moments.

Averaged Lorentz Dynamics and an application in Plasma Dynamics

Abstract

Using a geometric averaging procedure applied to a non-affine linear connection, we prove that for a narrow one particle distribution function and in the ultra-relativistic limit, a bunch of point charged particles can be described by a Charged Cold Fluid Model, without additional hypothesis on the moments.

Paper Structure

This paper contains 5 sections, 6 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. The Lorentz Connection
  3. The averaged Lorentz dynamics
  4. Comparison between $^L\nabla$ and $<\,^L\nabla>$
  5. Results on Kinetic Theory and Fluid Models

Key Result

Proposition 3.1

Let ${\bf M}$ and $^L\nabla$ be as before. Assume that the support of the distribution $f:{\bf \Sigma}\longrightarrow {\bf R}$ is compact and denote by $<\,^L\nabla>$ the averaged Lorentz connection. Then:

Theorems & Definitions (6)

  • Proposition 3.1
  • Theorem 4.1
  • Theorem 4.2
  • Proposition 5.1
  • Proposition 5.2
  • Theorem 5.3