Plasma modeling

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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 model, kinetic model, fluid model, hybrid kinetic/fluid model and gyrokinetic model.

Contents 1 Single Particle Description 2 Fluid Description 3 Kinetic Description 4 Hybrid Kinetic/Fluid Description 5 Gyrokinetic Description 6 References

[edit] Single Particle Description

The single particle model describes the plasma as individual electrons and ions whose movement is subject to the Lorentz Force Law. In this analysis, single particle trajectories are built up by stages, by adding more and more levels of complexity to the electic and magnetic field. Its results are drifts of the guiding centers of the particle's Larmor orbits.

[edit] Fluid Description

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. The fluid equations are not closed without the determination of transport coefficients such as mobility, diffusion coefficient, averaged collision frequencies, and so on. To determine the transport coefficients, the velocity distribution function must be assumed/chosen. But this assumption can lead to a failure of capturing some physics.

[edit] Kinetic Description

The kinetic model is the most fundamental way to describe a plasma, resultantly producing a distribution function f(x, v), where independent variables x and v are position and velocity, respectively.

A kinetic description is achieved by solving the Boltzmann Equation or its reduced forms, the Vlasov Equation and the Fokker-Planck Equation, in which approximations have been used to derive manageable collision terms.

[edit] Hybrid Kinetic/Fluid Description

Although the kinetic model describes the physics accurately, it is generally more computationally intensive than the fluid model. The hybrid model is a combination of fluid and kinetic models to describe the physics more accurate than the fluid model with faster speed than the kinetic model.

[edit] Gyrokinetic Description

The kinetic equations are modified to describe the behavior of an ensemble of Larmor orbits that occur in a plasma confined by an externally generated, background magnetic field, such as those created in nuclear fusion experiments.

[edit] References

• Francis F. Chen (2006). Introduction to Plasma Physics and Controlled Fusion, 2nd ed. Springer. ISBN 0306413322. 

• Nicholas Krall and Alvin Trivelpiece (1986). Principles of Plasma Physics. San Francisco Press. ISBN 0911302581.