Basic Properties of Plasma in Fluid Model

Abstract

AbstractIf the spatial variation of plasma is longer than the particle mean free path and the time variation is sufficiently longer than the plasma Coulomb collision time, the plasma can be approximated as being in local thermal equilibrium (LTE) at any point (t, r). Then the velocity distribution functions of the particles become Maxwellian. In addition, assuming Maxwellian is also a good assumption in many cases even for collisionless plasmas such as high-temperature fusion plasmas. In the fluid model of plasmas, The plasmas can be described in terms of five variables characterizing local Maxwellian: the density n(t, r), flow velocity vector u(t,r), and temperature T(t, r). So, the mathematics used in fluid physics is widely applicable to studying plasma phenomena.Although conventional fluids are neutral, plasma fluids of electrons and ions couple with electromagnetic fields. It is, therefore, necessary to solve Maxwell’s equations simultaneously. It is also possible to approximate electrons and ions as two different fluids or as a single fluid in case-by-case. This requires an insight into what kind of physics is important in our problem.After reviewing the basic equation of fluids, several fluid models for plasmas are shown. Especially, a variety of waves appears because of charged particle fluids are derived to know why waves are fundamental to knowing the plasma dynamics. The mathematical method to obtain the wave solutions as an initial value problem is explained as well as the meaning of the resultant dispersion relations.Magneto-hydrodynamic equations (MHD) are derived to explain the effects of the Biermann battery, magnetic dynamo, etc. The relationship of magnetic field and vortex flow is studied. Resistive MHD is derived including the Nernst effect, which becomes important for the magnetic field in strong electron heat flux.Finally, electromagnetic (EM) waves in magnetized plasmas are derived to see how to use for diagnostics in the laboratory and observation of wide range of electromagnetic waves from the Universe.