On long-time behavior of monocharged and neutral plasma in one and one-half dimensions

Robert Glassey; Stephen Pankavich; Jack Schaeffer

doi:10.3934/krm.2009.2.465

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2009, Volume 2, Issue 3: 465-488. Doi: 10.3934/krm.2009.2.465

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On long-time behavior of monocharged and neutral plasma in one and one-half dimensions

1.
Department of Mathematics, Indiana University, Bloomington, IN 47405
2.
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019
3.
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

Received: March 2009

Revised: June 2009

Published: September 2009

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Abstract

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle densities is assumed this formally becomes the relativistic Vlasov-Poisson system. These equations are considered in one space dimension and two momentum dimensions in both the monocharged (i.e., single species of ion) and neutral cases. The behavior of solutions to these systems is studied for large times, yielding estimates on the growth of particle momenta and a lower bound, uniform-in-time, on norms of the charge density. We also present similar results in the same dimensional settings for the classical Vlasov-Poisson system, which excludes relativistic effects.

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Mathematics Subject Classification: Primary: 35L60, 35B40; Secondary: 35Q60, 82D10.

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