Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

An introduction to the use of projection-operator methods for the derivation of classical fluid transport equations for weakly coupled, magnetised, multispecies plasmas is given. In the present work, linear response (small perturbations from an absolute Maxwellian) is addressed. In the Schrödinger representation, projection onto the hydrodynamic subspace leads to the conventional linearized Braginskii fluid equations when one restricts attention to fluxes of first order in the gradients, while the orthogonal projection leads to an alternative derivation of the Braginskii correction equations for the non-hydrodynamic part of the one-particle distribution function. The projection-operator approach provides an appealingly intuitive way of discussing the derivation of transport equations and interpreting the significance of the various parts of the perturbed distribution function; it is also technically more concise. A special case of the Weinhold metric is used to provide a covariant representation of the formalism; this allows a succinct demonstration of the Onsager symmetries for classical transport. The Heisenberg representation is used to derive a generalized Langevin system whose mean recovers the linearized Braginskii equations but that also includes fluctuating forces. Transport coefficients are simply related to the two-time correlation functions of those forces, and physical pictures of the various transport processes are naturally couched in terms of them. A number of appendices review the traditional Chapman–Enskog procedure; record some properties of the linearized Landau collision operator; discuss the covariant representation of the hydrodynamic projection; provide an example of the calculation of some transport effects; describe the decomposition of the stress tensor for magnetised plasma; introduce the linear eigenmodes of the Braginskii equations; and, with the aid of several examples, mention some caveats for the use of projection operators.

Download Full-text

Kinetic Theory Treatment for Heat Transfer in Plasma Spraying

Heat Transfer, Volume 5 ◽

10.1115/imece2002-33079 ◽

2002 ◽

Author(s):

Q. Zhang ◽

M. A. Jog

Keyword(s):

Heat Transfer ◽

Kinetic Theory ◽

Plasma Spraying ◽

Thermal Plasma ◽

Particle Surface ◽

High Plasma ◽

Transport Equations ◽

Electron Velocity ◽

Theory Approach ◽

Charged Species

In plasma spraying process thermal plasma is used as a heat source to heat and melt metallic or ceramic particles. In this paper, heat transfer from a thermal plasma to a solid spherical particle has been analyzed using a kinetic theory approach. We have considered a solid particle introduced in an ionized gas made up of electrons, ions, and neutrals. Two-sided electron velocity and temperature distributions and two-sided ion velocity distributions are used. Maxwell’s transport equations are obtained by taking moments of the Boltzmann equation. The transport equations are solved with the Poisson’s equation for the self-consistent electric field. The ion and the electron number density distributions, temperature distribution, and the electric potential variation are obtained. The charged species flux to the particle surface is evaluated. Heat transport to the surface is calculated by accounting for all the modes of energy transfer including the energy deposited during electron and ion recombination at the surface. Results indicate that contribution to heat transfer from charged species recombination is substantial at high plasma temperatures.

Download Full-text

Kinetic theory of partially ionized reactive gas mixtures

Physica A Statistical Mechanics and its Applications ◽

10.1016/s0378-4371(03)00481-3 ◽

2003 ◽

Vol 327 (3-4) ◽

pp. 313-348 ◽

Cited By ~ 21

Author(s):

Vincent Giovangigli ◽

Benjamin Graille

Keyword(s):

Kinetic Theory ◽

Gas Mixtures ◽

Partially Ionized ◽

Reactive Gas

Download Full-text

NEUTRINO CAPTURE INDUCED SUPERNOVA EXPLOSIONS

International Journal of Modern Physics D ◽

10.1142/s0218271810017895 ◽

2010 ◽

Vol 19 (08n10) ◽

pp. 1483-1490 ◽

Cited By ~ 2

Author(s):

T. STROTHER ◽

W. BAUER

Keyword(s):

Kinetic Theory ◽

Heavy Ion Collisions ◽

Supernova Explosion ◽

Heavy Ion ◽

High Energy ◽

Transport Equations ◽

Core Collapse ◽

Ion Collisions ◽

Supernova Explosions ◽

Explosion Mechanism

Motivated by the success of kinetic theory in the description of observables in intermediate and high energy heavy-ion collisions, we use kinetic theory to model the dynamics of core collapse supernovae. The specific way that we employ kinetic theory to solve the relevant transport equations allows us to explicitly model the propagation of neutrinos and a full ensemble of nuclei and treat neutrino–matter interactions in a very general way. With these abilities, our simulations have observed dynamics that may prove to be an entirely new neutrino capture induced supernova explosion mechanism.

Download Full-text

Equations of state for ions in non-LTE plasmas

Laser and Particle Beams ◽

10.1017/s0263034600006741 ◽

1992 ◽

Vol 10 (3) ◽

pp. 495-504 ◽

Cited By ~ 2

Author(s):

S. Eliezer ◽

E. Mínguez

Keyword(s):

Equations Of State ◽

Planck Equation ◽

Transport Equations ◽

Rate Equations ◽

Hydrodynamic Equations ◽

Ion Density ◽

Stochastic Force ◽

General Transport ◽

Explicit Rate ◽

Fokker Planck

For nonlocal thermodynamic equilibrium (LTE), the equations of state are not well defined and therefore the hydrodynamic equations are not applicable. In this case, the general transport equations (e.g., Boltzmann or Fokker–Planck) should be used. However, the coupling between atomic physics (rate equations) and the transport equations is extremely complicated. This article shows how the information given by the rate equations is translated into an effective potential. This “potential” theory is explicitly shown for two cases: lithium-like iron plasmas and aluminum plasmas. Moreover, it is suggested that the “collision terms,” and all other interactions that are not taken into account by the explicit rate equations, are described by a stochastic force given by a Langevin equation or equivalently by a Fokker-Planck equation in the ion density space.

Download Full-text