scholarly journals The Formal Nonequilibrium Theory of Partially Ionized and/or Nonuniform Gas Mixtures

1968 ◽  
Vol 21 (5) ◽  
pp. 609 ◽  
Author(s):  
EL Bydder ◽  
BS Liley
Keyword(s):  
Spontaneous Fission ◽  
Distribution Functions ◽  
Stimulated Emission ◽  
Gas Mixture ◽  
Moment Equations ◽  
Collision Integrals ◽  
Velocity Distribution Functions ◽  
Nonequilibrium Theory ◽  
Nonuniform Gas ◽  
Natural Decay

Starting from Boltzmann�like equations, moment equations for a general gas mixture are developed. The equations are closed, and the collision integrals evaluated, by using Grad's 13�moment approximations for the velocity distribution functions. The collision integrals are determined for all possible types of binary encounters, which include recombination and attachment, spontaneous fission and natural decay, charge exchange and elastic collisions, and excitation and fission� and fusion�like processes. The derivation of transport relationships is considered, while the extension of the results to include such direct radiative phenomena as absorption, photoionization, stimulated emission, and Compton scattering is also briefly discussed.

scholarly journals Collision Integrals for Tensorial Hermite Polynomials in Mixtures of Rarefied Gases and Plasmas

1996 ◽  
Vol 49 (6) ◽  
pp. 1135 ◽  
Author(s):  
Kurt Suchy
Keyword(s):  
Velocity Distribution ◽  
Balance Equation ◽  
Hermite Polynomials ◽  
Collision Integral ◽  
Distribution Functions ◽  
Null Sequence ◽  
Rarefied Gases ◽  
Collision Integrals ◽  
Orthogonal Expansions ◽  
Velocity Distribution Functions

The collision integral of Maxwell's balance equation (equation of change) for tensorial Hermite polynomials is calculated with velocity distribution functions represented as orthogonal expansions of local Maxwellians with respect to these polynomials. Closed expressions are obtained for the tensorial coefficients in the expansion of the collision integral with respect to products of Hermitian moments, i.e. velocity averaged Hermite polynomials. The averages over the collisional kinetic energies are represented by transport collision frequencies with two superscripts, which form a/null-sequence with increasing second superscript.

Intensification of transfer processes in a nonuniform gas-mixture stream

1966 ◽  
Vol 10 (3) ◽  
pp. 208-210 ◽  
Author(s):  
I. T. El'perin ◽  
A. L. Parnas
Keyword(s):  
Gas Mixture ◽  
Transfer Processes ◽  
Nonuniform Gas

Large-Debye-distance effects in a homogeneous plasma

1989 ◽  
Vol 41 (3) ◽  
pp. 493-516 ◽  
Author(s):  
Jan Scheffel ◽  
Bo Lehnert
Keyword(s):  
Normal Mode ◽  
Numerical Solutions ◽  
Normal Mode Analysis ◽  
Distribution Functions ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Order Unity ◽  
Phase Velocities ◽  
Standard Normal ◽  
Velocity Distribution Functions

The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

scholarly journals Ion-driven Instabilities in the Inner Heliosphere. I. Statistical Trends

2021 ◽  
Vol 923 (1) ◽  
pp. 116
Author(s):  
Mihailo M. Martinović ◽  
Kristopher G. Klein ◽  
Tereza Ďurovcová ◽  
Benjamin L. Alterman
Keyword(s):  
Solar Wind ◽  
Particle Interaction ◽  
Radial Distance ◽  
Solar Wind Plasma ◽  
Distribution Functions ◽  
Nyquist Criterion ◽  
Velocity Distribution Functions ◽  
Instability Growth ◽  
Statistical Trends ◽  
The Impact

Abstract Instabilities described by linear theory characterize an important form of wave–particle interaction in the solar wind. We diagnose unstable behavior of solar wind plasma between 0.3 and 1 au via the Nyquist criterion, applying it to fits of ∼1.5M proton and α particle Velocity Distribution Functions (VDFs) observed by Helios I and II. The variation of the fraction of unstable intervals with radial distance from the Sun is linear, signaling a gradual decline in the activity of unstable modes. When calculated as functions of the solar wind velocity and Coulomb number, we obtain more extreme, exponential trends in the regions where collisions appear to have a notable influence on the VDF. Instability growth rates demonstrate similar behavior, and significantly decrease with Coulomb number. We find that for a nonnegligible fraction of observations, the proton beam or secondary component might not be detected, due to instrument resolution limitations, and demonstrate that the impact of this issue does not affect the main conclusions of this work.

scholarly journals Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012007
Author(s):  
S S Sitnikov ◽  
F G Tcheremissine ◽  
T A Sazykina
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Direct Solution ◽  
Steady State Regime ◽  
Collision Integrals ◽  
Flow Formation ◽  
Binary Gas Mixture ◽  
State Regime

Abstract Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

Formation of non-thermal electron velocity distribution functions in kinetic magnetic reconnection

2021 ◽  
Author(s):  
Xin Yao ◽  
Patricio A. Muñoz ◽  
Jörg Büchner
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Field Strength ◽  
Magnetic Reconnection ◽  
Electron Beams ◽  
Distribution Functions ◽  
Electron Velocity ◽  
Diffusion Region ◽  
Electron Velocity Distribution ◽  
Velocity Distribution Functions

<div> <div>Magnetic reconnection can convert magnetic energy into non-thermal particle energy in the form of electron beams. Those accelerated electrons can, in turn, cause radio emission in environments such as solar flares. The actual properties of those electron velocity distribution functions (EVDFs) generated by reconnection are still not well understood. In particular the properties that are relevant for the micro-instabilities responsible for radio emission. We aim thus at characterizing the electron distributions functions generated by 3D magnetic reconnection by means of fully kinetic particle-in-cell (PIC) code simulations. Our goal is to characterize the possible sources of free energy of the generated EVDFs in dependence on an external (guide) magnetic field strength. We find that: (1) electron beams with positive gradients in their parallel (to the local magnetic field direction) distribution functions are observed in both diffusion region (parallel crescent-shaped EVDFs) and separatrices (bump-on-tail EVDFs). These non-thermal EVDFs cause counterstreaming and bump-on-tail instabilities. These electrons are adiabatic and preferentially accelerated by a parallel electric field in regions where the magnetic moment is conserved. (2) electron beams with positive gradients in their perpendicular distribution functions are observed in regions with weak magnetic field strength near the current sheet midplane. The characteristic crescent-shaped EVDFs (in perpendicular velocity space) are observed in the diffusion region. These non-thermal EVDFs can cause electron cyclotron maser instabilities. These non-thermal electrons in perpendicular velocity space are mainly non-adiabatic. Their EVDFs are attributed to electrons experiencing an E×B drift and meandering motion. (3) As the guide field strength increases, the number of locations in the current sheet with distributions functions featuring a perpendicular source of free energy significantly decreases.</div> </div>

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