Parameter estimation of the model of a one–dimensional infinite plasma described by the collisional Vlasov equation (original) (raw)

Fokker-Planck modeling for particle slowing down and thermalization in a Maxwellian plasma

The European Physical Journal D - Atomic, Molecular and Optical Physics, 2004

In this paper the Fokker-Planck equation, which takes into account the medium absorption and the Maxwellian behavior of the field particles at low energy for Coulomb interactions is obtained. The analytical solution of the stationary distribution function is obtained in both angle and velocity variables. In particular the electron distribution for electron-ion collisions has been obtained using this diffusion approximation for beam and isotropic sources. If the absorption is neglected the solution recovers the classical stationary Maxwell distribution. For low absorption rates the solution shows a typical slowing down spectrum for high energy and a Maxwellian-like distribution at thermal energy. For moderate and high absorption rates the test particles do not reach the thermal equilibrium and the Maxwell distribution at low energies does not appear.

Dielectric function of a collisional plasma for arbitrary ionic charge

Physical Review E, 2014

A simple model for the dielectric function of a completely ionized plasma with an arbitrary ionic charge, that is valid for long-wavelength high-frequency perturbations is derived using an approximate solution of a linearized Fokker-Planck kinetic equation for electrons with a Landau collision integral. The model accounts for both the electron-ion collisions and the collisions of the subthermal (cold) electrons with thermal ones. The relative contribution of the latter collisions to the dielectric function is treated phenomenologically, introducing some parameter κ that is chosen in such a way as to get a well-known expression for stationary electric conductivity in the low-frequency region and fulfill the requirement of a vanishing contribution of electron-electron collisions in the high-frequency region. This procedure ensures the applicability of our model in a wide range of plasma parameters as well as the frequency of the electromagnetic radiation. Unlike the interpolation formula proposed earlier by Brantov et al. [Brantov et al., JETP 106, 983 (2008)], our model fulfills the Kramers-Kronig relations and permits a generalization for the cases of degenerate and strongly coupled plasmas. With this in mind, a generalization of the well-known Lee-More model [Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984)] for stationary conductivity and its extension to dynamical conductivity [O. F. Kostenko and N. E. Andreev, GSI Annual Report No. GSI-2008-2, 2008 (unpublished), p. 44] is proposed for the case of plasmas with arbitrary ionic charge.

Field dependence of the collision integral and the Debye-Onsager relaxation effect in plasma systems

Physics Letters A, 1993

An applied strong electric field leads to a field-dependent collision integral of the Boltzmann equation. The electric field contributes to the collision integral by the collisional broadening and the intra-collisional field effect and produces a nonlinear behaviour of the conductivity. Using a linear approximation of the collisional integral with respect to the electric field, there follows an additional term to the electrical conductivity of the plasma. This additional contribution can be considered as an analogue to the well-known Debye-Onsager relaxation effect of electrolyte theory. It is found that only the GKB ansatz of Lipavsky et al. reproduces the classical limit of this effect well known from Kadomtsev's result. The quantum effects result in a remarkable behaviour in the dependence of the mass ratio of scattering particles, i.e., in a maximum of the relaxation effect at special mass ratio numbers of interacting charged particles.

A self-consistent kinetic modeling of a 1-D, bounded, plasma in equilibrium

Pramana, 2000

A self-consistent kinetic treatment is presented here, where the Boltzmann equation is solved for a particle conserving Krook collision operator. The resulting equations have been implemented numerically. The treatment solves for the entire quasineutral column, making no assumptions about λmfp/L, where λmfp is the ion-neutral collision mean free path and L the size of the device. Coulomb collisions are neglected in favour of collisions with neutrals, and the particle source is modeled as a uniform Maxwellian. Electrons are treated as an inertialess but collisional fluid. The ion distribution function for the trapped and the transiting orbits is obtained. Interesting findings include the anomalous heating of ions as they approach the presheath, the development of strongly non-maxwellian features near the last λmfp, and strong modifications of the sheath criterion.

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.