Two temperature gas equilibration model with a Fokker-Planck type collision operator

2014 ◽  
Author(s):  
A. R. Méndez ◽  
G. Chacón-Acosta ◽  
A. L. García-Perciante
Keyword(s):  
Collision Operator ◽  
Two Temperature ◽  
Equilibration Model ◽  
Fokker Planck

scholarly journals Generalized collision operator for fast electrons interacting with partially ionized impurities

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
L. Hesslow ◽  
O. Embréus ◽  
M. Hoppe ◽  
T. C. DuBois ◽  
G. Papp ◽  
...  
Keyword(s):  
Growth Rate ◽  
Electric Fields ◽  
Collision Operator ◽  
Impurity Content ◽  
Fast Electrons ◽  
Generalized Operator ◽  
Partially Ionized ◽  
High Electric Fields ◽  
Bound Electrons ◽  
Fokker Planck

Accurate modelling of the interaction between fast electrons and partially ionized atoms is important for evaluating tokamak disruption mitigation schemes based on material injection. This requires accounting for the effect of screening of the impurity nuclei by the cloud of bound electrons. In this paper, we generalize the Fokker–Planck operator in a fully ionized plasma by accounting for the effect of screening. We detail the derivation of this generalized operator, and calculate the effective ion length scales, needed in the components of the collision operator, for a number of ion species commonly appearing in fusion experiments. We show that for high electric fields, the secondary runaway growth rate can be substantially larger than in a fully ionized plasma with the same effective charge, although the growth rate is significantly reduced at near-critical electric fields. Furthermore, by comparison with the Boltzmann collision operator, we show that the Fokker–Planck formalism is accurate even for large impurity content.

A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime

2012 ◽  
Vol 12 (5) ◽  
pp. 1541-1561 ◽  
Author(s):  
Jingwei Hu ◽  
Shi Jin ◽  
Bokai Yan
Keyword(s):  
Numerical Scheme ◽  
Landau Equation ◽  
Collision Operator ◽  
Collision Term ◽  
Fluid Regime ◽  
Quantum Operator ◽  
Simple Quantum ◽  
Dirac Distribution ◽  
Bose Einstein ◽  
Fokker Planck

Abstract We construct an efficient numerical scheme for the quantum Fokker-Planck- Landau (FPL) equation that works uniformly from kinetic to fluid regimes. Such a scheme inevitably needs an implicit discretization of the nonlinear collision operator, which is difficult to invert. Inspired by work [9] we seek a linear operator to penalize the quantum FPL collision term QqFPL in order to remove the stiffness induced by the small Knudsen number. However, there is no suitable simple quantum operator serving the purpose and for this kind of operators one has to solve the complicated quantum Maxwellians (Bose-Einstein or Fermi-Dirac distribution). In this paper, we propose to penalize QqFPL by the "classical" linear Fokker-Planck operator. It is based on the observation that the classical Maxwellian, with the temperature replaced by the internal energy, has the same first five moments as the quantum Maxwellian. Numerical results for Bose and Fermi gases are presented to illustrate the efficiency of the scheme in both fluid and kinetic regimes.

scholarly journals A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

2016 ◽  
Vol 315 ◽  
pp. 644-660 ◽  
Author(s):  
Robert Hager ◽  
E.S. Yoon ◽  
S. Ku ◽  
E.F. D'Azevedo ◽  
P.H. Worley ◽  
...  
Keyword(s):  
Collision Operator ◽  
Fusion Plasma ◽  
Non Linear ◽  
Fokker Planck

scholarly journals Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Planck Collision Operator

2014 ◽  
Vol 54 (4-6) ◽  
pp. 517-523 ◽  
Author(s):  
M. A. Dorf ◽  
R. H. Cohen ◽  
M. Dorr ◽  
J. Hittinger ◽  
T. D. Rognlien
Keyword(s):  
Collision Operator ◽  
Fokker Planck

Transport coefficients for a two-temperature equal-mass plasma in a uniform magnetic field

1994 ◽  
Vol 52 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. Y. Abdul-Rassak ◽  
E. W. Laing
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electric Current ◽  
Uniform Magnetic Field ◽  
Transport Coefficients ◽  
Equal Mass ◽  
Temperature Ratio ◽  
Fokker Planck Equations ◽  
Two Temperature ◽  
Fokker Planck

Transport coefficients for electric current and heat flux have been calculated for a two-temperature equal-mass plasma for several values of the temperature ratio R in the range 1 < R ≤ 100. Transport coefficients have been obtained using the linearized Fokker—Planck equations.

scholarly journals Turbulent ‘polarization’ terms and the Balescu–Lenard operator

1982 ◽  
Vol 27 (1) ◽  
pp. 83-94 ◽  
Author(s):  
John A. Krommes ◽  
Michael T. Kotschenreuther
Keyword(s):  
Dielectric Function ◽  
Collision Operator ◽  
Plasma Turbulence ◽  
Turbulence Theory ◽  
Particle Propagator ◽  
Fokker Planck

Certain unfamiliar terms in renormalized plasma turbulence theory are interpreted in terms of the familiar physics of the Balescu–Lenard collision operator. Specifically, it is argued that the so-called polarization parts of the operator which renormalizes the particle propagator are related to fluctuations of the Fokker–Planck coefficient which describes polarization drag, and to fluctuations of the effective dielectric function of the medium.

An analytical solution to the Boltzmann–Fokker–Planck equation for multi-component non-homogeneous plasmas

1989 ◽  
Vol 41 (3) ◽  
pp. 457-467 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman
Keyword(s):  
Boltzmann Equation ◽  
Energy Exchange ◽  
Collision Operator ◽  
Planck Equation ◽  
Large Temperature ◽  
Relaxation Rates ◽  
Plasma Model ◽  
Slowing Down ◽  
Component Plasma ◽  
Fokker Planck

The previously obtained analytical solution to the Boltzmann equation for nonhomogeneous plasmas with relative large temperature and density gradients is generalized in the following sense. (i) The relatively simple Bhatnagar, Gross and Krook collision operator is replaced by the Fokker-Planck operator expressed in terms of relaxation rates (slowing down, energy exchange, etc.). (ii) The simple Lorentzian plasma model is replaced by a multi-component plasma model with realistic masses and temperatures.

THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE

1992 ◽  
Vol 02 (02) ◽  
pp. 167-182 ◽  
Author(s):  
P. DEGOND ◽  
B. LUCQUIN-DESREUX
Keyword(s):  
Small Parameter ◽  
Cross Section ◽  
Collision Operator ◽  
Scattering Cross Section ◽  
Main Concern ◽  
Mathematical Framework ◽  
Coulomb Collisions ◽  
Scattering Cross ◽  
Boltzmann Collision Operator ◽  
Fokker Planck

The Fokker-Planck collision operator is usually considered as an approximation of the Boltzmann collision operator when the collisions become grazing. A mathematical framework to this approach has recently been given in Ref. 2, by assuming that the scattering cross-section is smooth and depends upon a small parameter ε which tends to zero. However, the connection between ε and the physical quantities is unclear. In the present paper, our main concern is the Boltzmann operator for Coulomb collisions and its Fokker-Planck approximation. In the case of Coulomb collisions, the scattering cross-section has a non-integrable singularity when the relative velocity of the colliding particles tends to zero and a careful analysis is required. Furthermore, by a scaling of the collision operator, the small parameter which is involved in the Fokker-Planck asymptotics is clearly identified to the plasma parameter, and an expansion which is consistent with the physical observations is derived.

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