14 research outputs found
Bernstein modes in a weakly relativistic electron-positron plasma
The kinetic theory of weakly relativistic electron-positron plasmas, producing dispersion relations for the electrostatic Bernstein modes was addressed. The treatment presented preserves the full momentum dependence of the cyclotron frequency, albeit with a relaxation on the true relativistic form of the distribution function. The implications of this new treatment were confined largely to astrophysical plasmas, where relativistic electronpositron plasmas occur naturally
On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials
The paper concerns - convergence to equilibrium for weak solutions of
the spatially homogeneous Boltzmann Equation for soft potentials (-4\le
\gm<0), with and without angular cutoff. We prove the time-averaged
-convergence to equilibrium for all weak solutions whose initial data have
finite entropy and finite moments up to order greater than 2+|\gm|. For the
usual -convergence we prove that the convergence rate can be controlled
from below by the initial energy tails, and hence, for initial data with long
energy tails, the convergence can be arbitrarily slow. We also show that under
the integrable angular cutoff on the collision kernel with -1\le \gm<0, there
are algebraic upper and lower bounds on the rate of -convergence to
equilibrium. Our methods of proof are based on entropy inequalities and moment
estimates.Comment: This version contains a strengthened theorem 3, on rate of
convergence, considerably relaxing the hypotheses on the initial data, and
introducing a new method for avoiding use of poitwise lower bounds in
applications of entropy production to convergence problem
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Heat flux limitation for an anisotropic velocity distribution
The classical electron heat conductivity is derived analytically for a biMaxwellian electron velocity distribution function having temperature T/sub parallel to/ inwards and T/sub perpendicular to/ sideways. Magnetic fields and elctron-electron collisions are omitted and only electron-ion collisions are included presently. We normalize the heat conductivity to that for an isotropic distribution having temperature T, where T = (2T/sub perpendicular to/ + T/sub parallel to/)/3. The variation of this ratio from the case of T/sub perpendicular to much less than T/parallel to/ through T/sub perpendicular to/ = T/sub parallel to/ to T/sub perpendicular to/ much greater than T/sub parallel to/ is investigated. For T/sub perpendicular to/ much greater than T/sub parallel to/, this ratio is strongly inhibited for inward gradients, whereas for T/sub parallel to/ much greater than T/sub perpendicular to/, it is strongly inhibited for sideways gradients. In these cases when the heat flow is decreased, the region of applicability of linear gradient theory is greatly expanded to much largr ratios of the mean free path to gradient scale length
Ionization Mechanisms in Two-Temperature Air Plasmas
Investigations have been conducted to understand and experimentally validate the mechanisms of ionization in two-temperature atmospheric pressure air plasmas in which the electron temperature is elevated with respect to the gas temperature. The first part of the paper reports the results of numerical simulations performed with a new two-temperature chemical kinetic model, with reaction rate coefficients determined as weighted sums of elementary rate coefficients over the internal energy levels of atomic and molecular species. These calculations yield the surprising result that, for a given constant gas temperature, the steady-state electron number density exhibits an S-shaped dependence on the electron temperature. The middle limb of the S-shaped curve, which corresponds to electron number densities between approximately 10 13 and 10 17 e - /cm 3 , is found to be kinetically unstable. This S-shaped behavior is caused by competing ionization, charge transfer reactions, two-body dissociative recombination, and three-body electron recombination reactions, and therefore is characteristic of molecular plasmas. The numerical results are then interpreted in terms of macroscopic discharge parameters (electric field and current density) by means of Ohm's law and the electron energy equation. The resulting current density vs. electric field characteristic also exhibits an S-shaped dependence, which suggests that it may not possible to operate a stable discharge at electron number densities greater than 10 13 cm -3 by the sole use of a discharge operating at constant electric field. On the other hand, it may be possible to produce stable air plasmas by operating the electrical discharge at constant current density, as the electric field vs. current density characteristi..
On potentially negative space time covariances obtained as sum of products of marginal ones
Generalised product-sum model, Geostatistics, Nonseparability, Separability, Space–time covariance functions,