Plasma modeling
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Plasma modeling refers to solving
equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
that describe the state of a
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...
. It is generally coupled with
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
for
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
s or
Poisson's equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with th ...
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.


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 Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboar ...
. 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 In physics, the motion of an electrically charged particle such as an electron or ion in a plasma in a magnetic field can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relati ...
and a relatively slow drift of this point.


Kinetic description

The kinetic model is the most fundamental way to describe a plasma, resultantly producing a distribution function :f(\vec,\vec,t) where the independent variables \vec and \vec are
position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...
and
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
, respectively. A kinetic description is achieved by solving the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...
or, when the correct description of long-range
Coulomb interaction Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
is necessary, by the
Vlasov equation The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulo ...
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 Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
.


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 Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...
or the
Vlasov equation The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulo ...
. The fluid equations are not closed without the determination of transport coefficients such as mobility,
diffusion coefficient Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
, 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.


Gyrokinetic description

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 The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ ...
. This model has been used extensively for simulation of
tokamak A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being d ...
plasma instabilities (for example, the
GYRO Gyro may refer to: Science and technology * GYRO, a computer program for tokamak plasma simulation * Gyro Motor Company, an American aircraft engine manufacturer * ''Gyrodactylus salaris'', a parasite in salmon * Gyroscope, an orientation-sta ...
and
Gyrokinetic ElectroMagnetic Gyrokinetic ElectroMagnetic (GEM) is a gyrokinetic plasma turbulence simulation that uses the \delta f particle-in-cell method. It is used to study waves, instabilities and nonlinear behavior of tokamak fusion plasmas. Information about GEM can b ...
codes), and more recently in astrophysical applications.


Quantum mechanical methods

Quantum methods are not yet very common in plasma modeling. They can be used to solve unique modeling problems; like situations where other methods do not apply. They involve the application of
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
to plasma. In these cases, the
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...
fields made by particles are modeled like a
field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...
; A web of forces. Particles that move, or are removed from the population push and pull on this web of forces, this field. The mathematical treatment for this involves
Lagrangian Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
mathematics.


Commercial plasma physics modeling codes


Quantemol-VTVizGlowVizSparkCFD-ACE+COMSOLLSPMagicStarfishUSimVSim


See also

*
List of plasma physics articles This is a list of plasma physics topics. A * Ablation * Abradable coating * Abraham–Lorentz force * Absorption band * Accretion disk * Active galactic nucleus * Adiabatic invariant * ADITYA (tokamak) * Aeronomy * Afterglow plasma * Air ...


References

* * * {{DEFAULTSORT:Plasma Modeling Plasma physics Computational physics