Theory of spatially non-symmetric kinetic equilibria for collisionless plasmas

Abstract

The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of the Vlasov-Maxwell equations. In this paper the issue is addressed for non-relativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of single-particle dynamics. Starting point is a non-perturbative formulation of gyrokinetic theory, which allows one to construct "a posteriori" with prescribed order of accuracy an asymptotic representation for the magnetic moment. In terms of the relevant particle adiabatic invariants generalized bi-Maxwellian equilibria are proved to exist. These are shown to recover, under suitable assumptions, a Chapman-Enskog form which permits an analytical treatment of the corresponding fluid moments. In particular, the constrained posed by the Poisson and the Ampere equations are analyzed, both for quasi-neutral and non-neutral plasmas. The conditions of existence of the corresponding non-symmetric kinetic equilibria are investigated. As a notable feature, both astrophysical and laboratory plasmas are shown to exhibit, under suitable conditions, a kinetic dynamo, whereby the equilibrium magnetic field can be self-generated by the equilibrium plasma currents.

arXiv comment15 pages

References in corpus (11)

• Tangled Magnetic Fields in Solar Prominences
• The structure and radiation spectra of illuminated accretion disks in AGN. II. Flare/spot model of X-ray variability
• Hot-spot model for accretion disc variability as random process
• Hamiltonian formulation for the classical EM radiation-reaction problem: application to the kinetic theory for relativistic collisionless plasmas
• Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles
• Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations
• Kinetic axi-symmetric gravitational equilibria in collisionless accretion disc plasmas
• Kinetic description of rotating Tokamak plasmas with anisotropic temperatures in the collisionless regime
• Absolute stability of axisymmetric perturbations in strongly-magnetized collisionless axisymmetric accretion disk plasmas
• Dressed-particle approach in the nonrelativistic classical limit
• Collisionless kinetic regimes for quasi-stationary axisymmetric accretion disc plasmas

Cited by in corpus (9)

• Kinetic theory of equilibrium axisymmetric collisionless plasmas in off-equatorial tori around compact objects
• Synchronous Lagrangian variational principles in General Relativity
• Kinetic equilibria of relativistic collisionless plasmas in the presence of non-stationary electromagnetic fields
• Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas
• Carter-constant induced mechanism for generation of anisotropic kinetic equilibria in collisionless N-body systems
• Magnification effect of Kerr metric by configurations of collisionless particles in non-isotropic kinetic equilibria
• Polytropic representation of the kinetic pressure tensor of non-ideal magnetized fluids in equilibrium toroidal structures
• Polytropic representation of non-isotropic kinetic pressure tensor for non-ideal plasma fluids in relativistic jets
• Symmetric Ideal Magnetofluidostatic Equilibria with Non-Vanishing Pressure Gradients in Asymmetric Confinement Vessels