Variational Principles for Reduced Plasma Physics

Abstract

Reduced equations that describe low-frequency plasma dynamics play an important role in our understanding of plasma behavior over long time scales. One of the oldest paradigms for reduced plasma dynamics involves the ponderomotive Hamiltonian formulation of the oscillation-center dynamics of charged particles (over slow space-time scales) in a weakly-nonuniform background plasma perturbed by an electromagnetic field with fast space-time scales. These reduced plasma equations are derived here by Lie-transform and variational methods for the case of a weakly-magnetized background plasma. In particular, both methods are used to derive explicit expressions for the ponderomotive polarization and magnetization, which appear in the oscillation-center Vlasov-Maxwell equations.

21 pages, to appear in the 2007 KaufmanFest Proceedings. New references added

References in corpus (4)

• Momentum of an electromagnetic wave in dielectric media
• Positive and negative effective mass of classical particles in oscillatory and static fields
• Electromagnetic energy and momentum in moving media
• Nonlinear finite-Larmor-radius effects in reduced fluid models

Cited by in corpus (14)

• Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations
• Beyond linear gyrocenter polarization in gyrokinetic theory
• Variational principles for the guiding-center Vlasov-Maxwell equations
• Adiabatic nonlinear waves with trapped particles: I. General formalism
• Ponderomotive dynamics of waves in quasiperiodically modulated media
• Exact Energy Conservation Laws for Full and Truncated Nonlinear Gyrokinetic Equations
• On the correspondence between quantum and classical variational principles
• Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• Noether derivation of exact conservation laws for dissipationless reduced-fluid models
• On the validity of quasilinear theory applied to the electron bump-on-tail instability
• Average nonlinear dynamics of particles in gravitational pulses: effective Hamiltonian, secular acceleration, and gravitational susceptibility
• Hamiltonian formulations for perturbed dissipationless plasma equations
• Perturbative variational formulation of the Vlasov-Maxwell equations