H. van Erkelens

Relativistic Boltzmann theory for a plasma

Abstract The linear or phenomenological laws such as Ohms law, Fouriers law and Ficks law are derived for a relativistic plasma in an electromagnetic field. It is shown that the choice of a reference frame as proposed by Landau and Lifshitz entails-in contrast to, for instance, the choice of Eckart-the validity of Onsagers reciprocity relations.

Relativistic Boltzmann theory for a plasma: I. The entropy production

Abstract An expression for the entropy production has been derived on the basis of which it is argued that the choice of reference frame as proposed by Landau and Lifshitz is to be preferred rather than any other possibility.

Relativistic Boltzmann-theory for a plasma: V. Reduction of the collision integrals

Abstract The complicated twelve-fold collision-integrals occurring in relativistic kinetic theory are reduced to sums of two-fold integrals which can easily be evaluated once the interactions of the particles of the system in question are specified.

Relativistic Boltzmann-theory for a plasma: IV. A variational method

Abstract By applying a variational method expressions are derived for the transport coefficients of a multicomponent mixture of charged particles moving with relativistic speeds.

Relativistic Boltzmann theory for a plasma: III. Viscous phenomena

Abstract The linear laws pertaining to viscous phenomena are derived for a relativistic plasma in an electromagnetic field. The results found in this microscopic context fit precisely into the general scheme obtained on a macroscopic level by Hooyman, de Groot and Mazur.

Relativistic Boltzmann theory for a plasma: VI. The relativistic Landau equation

Abstract The relativistic Landau equation is obtained as the Fokker-Planck approximation to the relativistic Boltzmann equation. It is shown that, as far as the transport coefficients are concerned, both equations yield identical results in the dominant term approximation. Special attention is given to Moller-, Bhabha- and Mott-scattering processes. In the case of relativistic electron-electron collisions a detailed determination of the Coulomb logarithm is given.

Relativistic Boltzmann theory for a plasma: X. Electrical conduction of the cosmological fluid

Abstract General expressions are derived for the transport coefficients related to the vectorial transport phenomena in a plasma. As an example, the electrical conductivity of the cosmological fluid is calculated.

Relativistic Boltzmann theory for a plasma: VII. Propagation of hydromagnetic waves

Abstract The kinetic theory of hydrodynamic modes is developed for a relativistic plasma. Using the Chapman-Enskog method in the case of plane wave disturbances a set of equations is derived describing, on a microscopic basis, the behaviour of small amplitude, low frequency waves. Diffusion and thermal modes, Alfven and magneto-sound waves are discussed.

Chapman-Enskog method for a relativistic ionized gas

Abstract A linearized transport equation is derived for a multicomponent ionized gas. The magnetic field is treated as a zeroth-order, the electric field as a first-order effect.

Relativistic Boltzmann theory for a plasma: VIII. Energy transport by hydromagnetic waves

Abstract An expression is derived for the mean energy flow of hydromagnetic waves in a relativistic plasma. It is shown that this wave energy flow satisfies a balance equation which relates the space attenuation coefficient of the waves to their entropy production.