Nonlinear Stability and instability of relativistic Vlasov-Maxwell systems
نویسندگان
چکیده
We prove the nonlinear stability or instability of certain periodic equilibria of the 1 2 D relativistic Vlasov-Maxwell system. In particular, for a purely magnetic equilibrium with vanishing electric field, we prove its nonlinear stability under a sharp criterion by extending the usual Casimir-energy method in several new ways. For a general electromagnetic equilibrium we prove that nonlinear instability follows from linear instability. The nonlinear instability is macroscopic, involving only the L1-norms of the electromagnetic fields. c © 2000 Wiley Periodicals, Inc.
منابع مشابه
Linear Stability and instability of relativistic Vlasov-Maxwell systems
We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov-Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on the particle energy, we obtain a sharp linear stability criterion. The growing mode is proved to be purely growing and we get a sharp estimate of the maximal growth rate. In this paper we specifically treat ...
متن کاملNonlinear Instability of Vlasov-Maxwell Systems in the Classical and Quasineutral Limits
We study the instability of solutions to the relativistic Vlasov-Maxwell systems in two limiting regimes: the classical limit when the speed of light tends to infinity and the quasineutral limit when the Debye length tends to zero. First, in the classical limit ε→ 0, with ε being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a...
متن کاملDiscontinuous Galerkin Methods for Relativistic Vlasov-Maxwell System
The relativistic Vlasov-Maxwell (RVM) system is a kinetic model that describes the dynamics of plasma when the charged particles move in the relativistic regime and their collisions are not important. In this paper, we formulate and investigate discontinuous Galerkin (DG) methods to solve the RVM system. When standard piecewise polynomial functions are used to define trial and test spaces, the ...
متن کاملNonlinear relativistic gyrokinetic Vlasov-Maxwell equations
A set of self-consistent nonlinear gyrokinetic equations is derived for relativistic charged particles in a general nonuniform magnetized plasma. Full electromagnetic-field fluctuations are considered with spatial and temporal scales given by the low-frequency gyrokinetic ordering. Self-consistency is obtained by combining the nonlinear relativistic gyrokinetic Vlasov equation with the low-freq...
متن کاملStability Analysis of Collisionless Plasmas with Specularly Reflecting Boundary
Abstract In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at the boundary for the particles and with the perfectly conducting boundary condition for the electromagnetic field. Here we initiate our investigation...
متن کامل