Efficient numerical solution of the model kinetic equations

2012 ◽  
pp. 293-300
Author(s):  
Vladimir Titarev
Keyword(s):  
Numerical Solution ◽  
Kinetic Equations ◽  
Model Kinetic Equations

A numerical solution of the kinetic equations for a spectrum of Langmuir turbulence

1984 ◽  
Vol 31 (2) ◽  
pp. 253-261
Author(s):  
Denis Hayward
Keyword(s):  
Numerical Solution ◽  
Relativistic Electron Beam ◽  
Final Section ◽  
Plasma Heating ◽  
Kinetic Equations ◽  
Langmuir Turbulence ◽  
Quick Method ◽  
Isothermal Plasma ◽  
Principal Contributor ◽  
Made In

The main properties of a kinetic wave equation in an isothermal plasma, Te ≈ Ti, are discussed and a quick method of numerical solution based on factorization of the kernel of an integral equation is outlined. As an illustration the method is applied to the problem of plasma heating with a relativistic electron beam and it is shown how the evolution of a spectrum of Langmuir turbulence is the principal contributor to the heating of the plasma. The technique allows an estimate of the error which is present in the stationary solution, and this is made in the final section.

Spectral functions for gases: Test of approximations employing model kinetic equations

1976 ◽  
Vol 54 (2) ◽  
pp. 137-141
Author(s):  
Norbert Müller ◽  
Siegfried Hess
Keyword(s):  
Kinetic Equation ◽  
Kinetic Equations ◽  
Spectral Functions ◽  
Model Kinetic Equations ◽  
Effective Collision

Approximations to spectral functions obtained from model kinetic equations with two effective collision frequencies are tested for a special kinetic equation which can be solved exactly.

scholarly journals Model Kinetic Equations for Multiply Ionized Gas Mixtures

2021 ◽  
Vol 8 ◽  
Author(s):  
Maria A. Rydalevskaya ◽  
Yulia N. Voroshilova
Keyword(s):  
Equilibrium Distribution ◽  
Local Equilibrium ◽  
Kinetic Equations ◽  
Gas Mixtures ◽  
Distribution Functions ◽  
Transport Processes ◽  
Ionized Gas ◽  
Model Kinetic Equations ◽  
Ideal Gases ◽  
Model Equations

Model kinetic equations are proposed for the description of ionized monoatomic gas mixture flows. The mixtures are assumed enough rarefied to be treated as ideal gases after multiple ionization steps. The model equations contain the equilibrium distribution functions for the components of the gas mixtures under consideration like it was done in BGK equations and their well-known generalizations. However, in this paper the new forms of the equilibrium distribution functions are used which correspond to the entropy maximum under the constraints of momentum, total energy, nuclei and electrons (both bound and free) conservation. It is shown that the derived model equations allow us to study the local equilibrium flows of the ionized gases and the transport processes of energy, nuclei and electrons in the non-equilibrium conditions.

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