Kinetic and Related Models (KRM)

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

Pages: 465 - 488, Volume 2, Issue 3, September 2009      doi:10.3934/krm.2009.2.465

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Robert Glassey - Department of Mathematics, Indiana University, Bloomington, IN 47405, United States (email)
Stephen Pankavich - Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United States (email)
Jack Schaeffer - Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, United States (email)

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.

Keywords:  kinetic theory, plasma, Vlasov-Poisson, monocharged, neutral, asymptotic behavior.
Mathematics Subject Classification:  Primary: 35L60, 35B40; Secondary: 35Q60, 82D10.

Received: March 2009;      Revised: June 2009;      Available Online: July 2009.