On the relativistic non-linear interaction of cold plasma with electro-magnetic waves

Abstract

The behaviour of a fully ionized plasma composed of one type of atom and subjected mainly to electromagnetic forces (waves) is treated analytically. The problem is described by relativistic field equations and equations of motion. The general fundamental equations lead to a special system of equations yielding wave solutions in which all partial waves have the same space-time constant phase velocity. This system of equation provides: A strictly analytical periodic solution of the non-linear initial equations. The solution describes a transverse, circularly polarized electromagnetic wave. An analogous solution is obtained for a fully ionized plasma composed of electrons and k (= 1, 2, 3...) types of ions. The ions orbit in phase. The magnitudes of their orbital velocities depend on the charge and mass of the individual types of ions. A strictly analytical periodic solution of the non-linear initial equation obtained when the ion oscillation is neglected. The solution describes a longitudinal electric wave. The phase velocity of the wave has to be greater than the maximum absolute value of the longitudinal electron velocity caused by the electric field. This exact statement is dependant on a corresponding relation resulting from the Landau damping between the phase velocity and the mean thermal electron velocity. An approximate steady-state solution of the non-linear initial equations for the simultaneous coupling of the plasma, transverse and longitudinal waves. Purely longitudinal electric waves result in a constant plasma electron drift velocity (second-order): The plasma electrons stream toward the waves. A transverse plane polarized electromagnetic wave (first-order) is coupled with a plane polarized electromagnetic wave (third-order): the third-order wave oscillates at three times the frequency of the first-order wave and has a maximum amplitude which is directly proportional to the electron rest density of the wave-free plasma when the plasma frequency is sufficiently smaller than the first-order wave frequency.