The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

An electron charge is suddenly switched on while drifting through a warm collisional plasma. It acts thereafter with an arbitrary time-dependence. The evolution of the plasma, initially at rest, is considered in two and three dimensions. A general solution is first established for drift-modified slow plasma modes and then employed in subthermal drift analysis. Its abrupt switch-on causes the electron charge to release, during subthermal drift, a fully symmetric thermal front Г which subsequently expands ahead of it into an undisturbed receding expanse. A transversely symmetric response develops inside Г. On switch-off, the drifting charge releases another thermal front Г0 which also precedes it but trails non-concentrically behind Г. Plasma response continues after switch-off. Response properties between Г and Г0 differ strikingly from those inside Г0. Applications are next considered, first in three dimensions, for a subthermal pulsating electron with a generally complex frequency ω. The prepermanent state response inside Г comprises an axisymmetric dominant component ø∞ plus a spherically symmetric transient component øtr. ø∞ acquires the frequency ω. øtr has amplitudes dependent on and wave crests independent of both frequency ω and drift; it suffers a fast (slow) ω–independent temporal attenuation in a collisional (collisionless) plasma. The geometrical drift wave structure of ø∞ is closely examined for real ω and a collisionless plasma. Every energy surface associated with ø∞ nucleates at the electron; from there, it evolves slower than a phase surface, which eventually ‘disappears’ past Г. The leading energy surface, which nucleated at switch-on, develops permanently inside Г; it serves as an energy front that seals off the energy sustaining ø∞ since switch-on. Finally, the two-dimensional evolving drift field of an activated antenna line is computed.

Ion-acoustic solitons in a three-component plasma which consists of electrons and positive and negative ions have been investigated experimentally. When the concentration of negative ions is smaller than a certain value, positive or compressive solitons are observed. At the critical concentration, a broad pulse of small but finite amplitude propagates without changing its shape. When the concentration is larger than this value, negative or rarefactive solitons are excited. The velocity and the width of these solitons are measured and compared with predictions of the Korteweg-de Vries equation which takes the negative ions and the ion temperature into consideration. Head-on and overtaking collisions of the rarefactive solitons have been observed to show that the solitons are not affected by these collisions.

An analytical formulation is presented for envelope-type solutions of intense polarized electromagnetic waves propagating in cold unmagnetized plasmas. Induced charge separation is fully taken into account and nonlinearities due to mass variation of both electrons and ions are included. Localized solutions are found for the case of subluminous wave phase velocity. The spectrum of solutions (dependence of wave amplitude on the free parameters in the theory, phase velocity and frequency) is discussed and compared with previous analytical and numerical results.

The process of excitation of the Alfvén wave is studied by means of the qualitative method of quantum mechanics.

External injection of magnetic helicity into a plasma may be possible through the introduction of appropriately polarized electromagnetic waves. A concept of steady-state current-drive is presented, based on the validity of conservation of helicity (appropriately defined for finite frequency processes). It is shown that such external injection of helicity can maintain a steady-state current by compensating the volt-seconds consumed through plasma resistivity. Such a mechanism, if experimentally successful, is particularly interesting at high densities because the efficiency of the process does not depend on plasma density, as opposed to other radio-frequency current-drive techniques.

With positive ambipolar potential, ion non-resonant neoclassical transport leads to increased particle confinement times. In certain regimes of filling pressure, microwave powers (ECRH and ICRH) and positive potential, new folds can now emerge from previously degenerate equilibrium surfaces allowing for distinct C, T, and M modes of operation. A comparison in the equilibrium fold structure is also made between (i) equal particle and energy confinement times, and (ii) particle confinement times enhanced over the energy confinement time. The nonlinear time evolution of these point model equations is considered and confirms the delay convention occurrences at the fold edges. It is clearly seen that the time-asymptotic equilibrium state is very sensitive, not only to the values of the control parameters (neutral density, ambipolar electrostatic potential, electron and ion cyclotron power densities) but also to the initial conditions on the plasma density, and electron and ion temperatures.

This paper calculates, on a kinetic basis, the dispersion relation and field polarization for waves propagating linearly through a homogeneous magnetoplasma when thermal velocities are far less than the phase velocity. Approximations are brought in only as necessary and their physical significance explained. The result is an improved derivation of the Sen–Wyller generalization of the Appleton–Hartree formula for velocity-dependent collision frequency. Further generalization to several charged species is made, and the dispersion relation is also considered in terms of the angle between the ambient magnetic field and the group (rather than phase) propagation direction. Special case reduction to the Appleton-Hartree formula is confirmed. Complications concerning the limit of weak spatial dispersion are discussed. The analysis is restricted to weakly ionized plasmas in which the charge to neutral particle mass ratios are small, collisions are weak, and the wave vector is predominantly real.

Amplitudes of electromagnetic waves with combination frequencies, radiating from a narrow inhomogeneous layer of the magnetoactive plasma due to interaction of the surface waves, are determined. The method used allows for discontinuity of the tangential components of the wave electric field at the combination frequencies at the plasma boundary.

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Finite Larmor radius corrections have been considered in the effects of strong magnetic fields on stimulated Raman scattering. A nonlinear dispersion relation describing the various channels of decay has been derived from the Vlasov-Maxwell equations and frequencies and growth rates determined for the decay of incident laser light in the extraordinary mode into scattered extraordinary mode radiation and electron Bernstein waves. A relativistic one-and-a-half dimensional particle code has been used to simulate the scattering process and the results from the numerical experiments have been compared with those obtained analytically, the agreement being generally good. Growth rates of the Bernstein waves are substantial when sufficiently strong magnetic fields are present in hot plasmas. Under these conditions the kinetic analysis shows that, in contrast to the predictions of fluid theory, the scattered light emitted from densities well below the quarter-critical layer can have a frequency less than ½ω0 where ω0 is the laser frequency. In an unmagnetized plasma this occurs only when the plasma has a finite temperature.