Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the resulting nonlinear dispersion relation for the stochastic modes displays a real frequency shift and a corrected growth rate when contrasted with the classical quasi-linear dispersion equation.

Using a Van Kampen treatment, we study the longitudinal electron oscillations for a plasma with a cut-off Maxwellian velocity distribution. Having defined and computed excitation coefficients in the real w, k plane, we represent this ‘wave density’ through the greyness of this plane. This representation should be useful as a help to the experimenter. Moreover we show the appearance of a slightly damped pole with a phase velocity slightly smaller than the cut-off velocity Vc if this velocity is in the interval 2 to 4VT and a modification of the Landau mode which propagates for higher and higher frequencies when Vc decreases.

The recent Plum Brook—NASA experiments on counterstreaming plasma instabilities in which electric field emissions at frequencies [(n + ½) ±α]ωe (n = 1, 2, 3,…, 9, α < 0·5) have been observed, raised the theoretical problem of the non-symmetric two-stream instability. This is the case in which the counterstreaming beams have different velocities in the directions parallel and perpendicular to the static magnetic fields as well as different particle density.

We investigate theoretically this problem. The instability of quasi-electrostatic waves at shifted half odd integer multiples of the cyclotron frequency, due to two non-symmetric counterstreaming electron beams, is considered. The beam velocities parallel and perpendicular to the static magnetic field are represented by different double Dirac delta functions; no parameter limitation is imposed. A systematic investigation of (i) the coupling between plasma modes and cyclotron modes and (ii) the coupling between cyclotron modes (beam 1) and cyclotron modes (beam 2) resulting in shifted half odd integer multiples of the cyclotron frequency is carried out.

The results include approximate but simple analytical expressions for maximum growth rates and for marginal stability as well as exact numerical solutions for the detailed unstable spectra (1 ≤ m ≤ 20) in both ωτ- and kr-space. The relative weakening or suppression of certain modes is also predicted.

We investigate the influence of a lower hybrid pump field on the dispersion characteristics of various trapped particle modes and delineate the conditions for their excitation or suppression. Our calculations also reveal the existence of certain new instabilities driven by the pump.

In this paper we consider the resonant interaction between three modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field. We show that for the modified mode to be a normal mode we must have the unperturbed current equal to zero. Using the averaged Lagrangian method, we calculate the coupling coefficient for the resonant interaction between three of these modes. It is proportional only to the cube of the drift velocity, as expected from the vanishing of the unperturbed current.

This paper investigates the general problem of stability of Bernstein—Greene— Kruskal type waves. By investigating perturbations perpendicular to the wave, we obtain a general sufficient condition for instability. This is then extended to the case of magnetized plasmas with a uniform magnetic field in the direction of the BGK wave. New perturbed modes, having no counterpart in linear theory, are also found. Various special cases are considered and previous, more particular results confirmed.

Shock waves produced by magnetic compression are called transverse when the magnetic field contains no component in the direction of the shock wave normal. It is experimentally well known that very strong shocks of this type show classical MHD behaviour in terms of both jump conditions and structure. It is also known that relatively slow transverse shocks can be of an ionizing gasdynamic type with no jump in the imbedded transverse field. Since there are fundamental differences in both the structure and the jump relationships of these two types of shock waves, it is of interest to investigate the transition behaviour in the intermediate shock speed regime. A previously widely accepted model due to Kulikovskii & Lyubimov and Chu assumes no precursor ionization and requires significantly large values of the magnetic Prandtl number, Pm, within the shock structure. That model is shown to be physically inappropriate because experimentally observed transition speeds and corresponding post-shock temperatures imply negligibly small shock Pm values. Also in that model, MHD conditions are approached only asymptotically at large shock speeds. The present precursor ionization model assumes effectively zero Pm values throughout transition and into the low-speed MHD regime. As distinct from the previous theory, this model predicts the attainment of full MHD conditions at and above a well-defined finite shock speed. The assumption of a characteristic post-shock temperature model for the ionization mechanism allows unique jump relations to be formulated independently of other transport mechanisms. Results include computed values of various jump ratios and the electric field as functions of shock speed throughout gasdynamic, transition, and MHD regimes. The solutions form a one-parameter family depending on the relative combination of upstream magnetic field and density (e.g. the Alfvén velocity). Shock structure phase plane trajectories are computed at a number of typical shock speeds throughout transition.

The equilibrium configurations of a one-species guiding centre plasma are circularly symmetric. Unlike results obtained for systems with artificial periodicity, the profiles depend uniquely on the energy and mean square radius. The random phase approximation is shown to be invalid.

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

The marginal stability of a plasma carrying current along the static magnetic field with isotropic Maxwellian ions and isotropic Maxwellian electrons drifting relative to the ions is investigated. The complete electromagnetic dispersion relation is studied using numerical techniques; the electron sums are restricted to three terms which limits the analysis to frequencies much less than the electron gyro-frequency, but includes frequencies somewhat above the ion gyro-frequency. A ‘kink-like’ instability and an instability of the Alfvén mode are found to have the lowest threshold drift velocities in most cases. In fact the threshold drift for the kink-like instability can be significantly less than the ion thermal speed. Electrostatic and electromagnetic ion-cyclotron instabilities are also found as well as the electro-static ion-acoustic instability. No instability of the fast magnetosonic mode was found. The stability analysis provides only threshold drift velocities and gives no information about growth rates.

The sensitivity of electromagnetic ion-cyclotron wave growth rates to the details of the shape of proton velocity distribution functions is explored. For this purpose two different forms of bi-Lorentzian for the proton distribution functions were adopted. The growth rates for the two types of bi-Lorentzians and the biMaxwellians for the beam (hot) protons are compared. Although the growth rates for the three shapes depend on the velocity moments of the different velocity distributions in a similar way, their magnitudes were found to vary considerably.