A variational sheath model for gyrokinetic Vlasov-Poisson equations (original) (raw)

Vlasov-Poisson equations for a two-component plasma in a homogeneous magnetic field

Russian Mathematical Surveys, 2014

The Vlasov-Poisson equations for a two-component high-temperature plasma with an external magnetic field in a half-space are considered. The electric field potential satisfies the Dirichlet condition on the boundary, and the initial density distributions of charged particles satisfy the Cauchy conditions. Sufficient conditions for the induction of the external magnetic field and the initial charged-particle density distributions are obtained that guarantee the existence of a classical solution for which the supports of the charged-particle density distributions are located at some distance from the boundary.

Variational principles for reduced plasma physics

Journal of Physics: Conference Series, 2009

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.

Vlasov Equation for Magnetized Plasma Particles in the Arbitrary Magnetic Field

The linearized Vlasov equation is rewritten for charged particles in the two-dimensional axisymmetric plasma models using the cylindrical coordinates. There is described a method of its solution by the Fourier expansions of the perturbed distribution functions over the gyrophase angle in velocity space, conservation integrals of particle motion in the curvilinear magnetic field and smallness of the magnetization parameters. Such an approach allows us to evaluate the main contributions of untrapped and trapped particles to the transverse and longitudinal dielectric tensor components for electromagnetic waves in tokamaks, straight mirror-traps, laboratoty dipole magnetospheric plasmas and inner part of the Earth's magnetosphere. KEY WORDS: Vlasov equation, kinetic wave theory, tokamaks, mirror traps, magnitospheric plasmas. ... ... , 4,

The solution of Vlasov's equation for complicated plasma geometry. I. Spherical type

Computer Physics Communications, 1995

The asymptotic solution of Vlasov's equation for complicated plasma geometry (spherical type) using the computer algebra system Maple is presented. The approximation of small ion and electron Larmor radii (drift approximation) for a dipole magnetic field configuration modeling the earth's plasmasphere was used. The method of solution introduces elliptic integrals as variables, which makes it possible to obtain results in a relatively simple manner. A bounce resonance factor (connected with trapped particles) different from the one appearing in the Landau damping case is found.

A general way to confined stationary Vlasov-Poisson plasma configurations

Kinetic & Related Models, 2021

We address the existence of stationary solutions of the Vlasov-Poisson system on a domain Ω ⊂ R 3 describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of Ω. In a first part we provide such an existence result for a generalized system of Vlasov-Poisson type and investigate the relation between the strength of the external magnetic field, the sharpness of the confinement and the amount of plasma that is confined measured in terms of the total charges. The key tools here are the method of sub-/supersolutions and the use of first integrals in combination with cutoff functions. In a second part we apply these general results to the usual Vlasov-Poisson equation in three different settings: the infinite and finite cylinder, as well as domains with toroidal symmetry. This way we prove the existence of stationary solutions corresponding to a two-component plasma confined in a Mirror trap, as well as a Tokamak.

The energy of perturbations for Vlasov plasmas∗,a)

Physics of Plasmas, 1994

The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called, the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that solves the linear Vlasov-Poisson equation. This solution, together with the Kruskal-Oberman energy [Phys. Fluids 1, 275 ( 1958)], is used to obtain an energy expression in terms of the electric field [Phys. Fluids B 4, 3038 (1992)]. It is described how the integral transform amounts to a change to normal coordinates in an infinite-dimensional Hamiltonian system.

New Variational Principle for the Vlasov-Maxwell Equations

Physical Review Letters, 2000

A new Eulerian variational principle is presented for the Vlasov-Maxwell equations. This principle uses constrained variations for the Vlasov distribution in eight-dimensional extended phase space. The standard energy-momentum conservation law is then derived explicitly by the Noether method. This new variational principle can be applied to various reduced Vlasov-Maxwell equations in which fast time scales have been asymptotically eliminated (e.g., low-frequency gyrokinetic theory).

A Gyrokinetic simulation model for low frequency electromagnetic fluctuations in magnetized plasmas

Science China Physics, Mechanics & Astronomy, 2021

We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of potentials. As a benchmark, we perform linear as well as nonlinear simulations of the kinetic Alfvén wave; demonstrating physics in agreement with the analytical theories.