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 and gyrokinetic.
Single Particle Description
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
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
. 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.
Hybrid Kinetic/Fluid Description
Although the kinetic model describes the physics accurately, it is more complex (and in the case of numerical simulations, more computationally intensive) than the fluid model. The hybrid model is a combination of fluid and kinetic models, treating some components of the system as a fluid, and others kinetically.
In the gyrokinetic model, which is appropriate to systems with a strong background magnetic field, the kinetic equations are averaged over the fast circular motion of the gyroradius
. This model has been used extensively for simulation of tokamak
plasma instabilities (for example, the GYRO
and Gyrokinetic ElectroMagnetic
codes), and more recently in astrophysical applications.