The nonlinear transient evolution of a suddenly applied monochromatic wave in a homogeneous plasma is considered, with particular emphasis on the magnetized case, where ordinary and extraordinary electromagnetic waves travelling normal to B are treated. Two important features are described. First, the penetration of the wave front is shown to be accompanied by ‘radiation’ of low-frequency waves, of which ion cyclotron and lower-hybrid waves are considered here. Next, the presence of a nonlinear, second-harmonic precursor is predicted, containing two natural modes of oscillation, one with exactly twice the frequency of the fundamental, and the other a slightly frequency-shifted contribution. The analysis is readily generalized to waves other than those considered here.

An extension of the method of characteristics for parabolic equations is proposed that allows the integration of the energy equation for a static, heated and radiating, heat-conducting, optically thin plasma in a magnetic field. The invariance of all physical quantities is assumed, throughout the work, to occur along an arbitrary curvilinear direction. Finally, an example is presented to illustrate how the algorithm actually works.

The results of recent experimental measurements of the differential cross-section for elastic scattering of electrons on sodium atoms were used to evaluate the electron steady-state distribution function in a weakly ionized, uniform and non-magnetized sodium plasma placed in a d.c. electric field. The field was assumed to be of moderate intensity, so that the thermal motion of the neutrals had to be taken into account in the evaluation of the distribution function. The resulting ‘modified Druyvesteinian function’ was applied to study the non-potential instabilities arising from the presence of the field in this particular plasma. Threshold drifts for both very slow and slow modes were obtained and the conditions for the onset of instabilities were discussed. It is shown that the thermal motion of the neutrals affects both critical drifts and the angles of propagation.

Ohm's law for homogeneous warm plasmas not varying with time is generalized for plasmas with parameters slowly varying in space and time. The corresponding integral constitutive relation is derived.