Most of this report is identical with material prepared forHandbuch der Physik, Volume XXI, 1956. AbstractThis report reviews the mathematical methods applicable to ionized gases. In Part I the motion of an individual electron or ion under a Lorentz force, including the effects of magnetic gradients, is studied. In Part II, with the introduction of collisions, this is no longer possible, but we can still follow the motion of an average particle. For high values of E/p, the behavior of a swarm of particles is remarkably close to the motion of the average particle, but for lower values of E/p other methods must be used. In Part III the Boltzmann equation is applied to a "Lorentzian gas," that is, to free electrons in a gas. In Part IV the equation is transformed to an integral form, the Boltzmann transport equation, so that it will be applicable to ions.

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The coupling between electromagnetic and electron plasma waves in a uniform plasma in the presence of a static magnetic field is studied. The transport equations are used to represent the plasma and Maxwell's equations to represent the fields. These yield a dispersion relation which is discussed here only for ions of infinite mass. Eight topologically different phase velocity surfaces suffice to represent the system of combined electromagnetic and electron waves for all values of plasma density and magnetic field strength. The plasma waves have cutoffs (phase velocity infinite) wherever the electromagnetic wave has a resonance (phase velocity zero); the coupling between the two waves is strong there and their respective velocity surfaces join smoothly one onto the other. Elsewhere the waves are distinct.