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Concept
Plasma modeling
Résumé
Plasma modeling refers to solving equations of motion that describe the state of a plasma. It is generally coupled with Maxwell's equations for electromagnetic fields or Poisson's equation for electrostatic fields. There are several main types of plasma models: single particle, kinetic, fluid, hybrid kinetic/fluid, gyrokinetic and as system of many particles.
The single particle model describes the plasma as individual electrons and ions moving in imposed (rather than self-consistent) electric and magnetic fields. The motion of each particle is thus described by the Lorentz Force Law.
In many cases of practical interest, this motion can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relatively slow drift of this point.
The kinetic model is the most fundamental way to describe a plasma, resultantly producing a distribution function
where the independent variables and are position and velocity, respectively.
A kinetic description is achieved by solving the Boltzmann equation or, when the correct description of long-range Coulomb interaction is necessary, by the Vlasov equation which contains self-consistent collective electromagnetic field, or by the Fokker–Planck equation, in which approximations have been used to derive manageable collision terms. The charges and currents produced by the distribution functions self-consistently determine the electromagnetic fields via Maxwell's equations.
To reduce the complexities in the kinetic description, the fluid model describes the plasma based on macroscopic quantities (velocity moments of the distribution such as density, mean velocity, and mean energy). The equations for macroscopic quantities, called fluid equations, are obtained by taking velocity moments of the Boltzmann equation or the Vlasov equation. The fluid equations are not closed without the determination of transport coefficients such as mobility, diffusion coefficient, averaged collision frequencies, and so on.
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