The model of a stationary medium traversed by a weak plasma stream directed along a magnetic field is investigated. The usual linear treatment is adopted, and the stream is taken to be ‘cold’, with only electron (perturbation) motions considered. The objective is to assess the plane-wave growth associated with both Cerenkov and cyclotron instabilities; in particular, the dependence of the growth on frequency and angle of phase propagation. The main discussion is of the case when the stationary medium is a cold plasma in which both electron and positive ion motions are taken into account. Various expressions for the growth are derived, and numerical calculations are presented in graphical form.

Considering the general dispersion equation for the whistler mode, the condition of critical stability is discussed and the values of k2 and the field strength for critical stability are determined. The waves grow due to resonance; the stability criterion is studied and the growth rate is also calculated. The results for a special case of simple velocity distribution with a loss cone are obtained and compared with those due to cold dispersion. In the magnetosphere the thermal electrons which can be treated as cold, should be included in the distribution and this is discussed in § 5. Finally, we have established the regions of stable and unstable plasma for the special velocity distribution function and it can be seen how these depend on the size of loss cone.

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.

Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

Periodic plane waves propagating in a homogeneous cold Vlasov plasma under the influence of an external magnetic field B0 have been studied in this paper. Non-linear coupled differential equations for the two transverse components of the local magnetic field have been obtained for any angle α between B0 and the wave vector. Starting from the previously obtained exact solution for α = 90° and the zeroth-order solution for α = 0, two perturbation methods are used to obtain first-order solutions for α = 0 and intermediate angles. A numerical example has been worked out in detail for a specific value of the field energy density; although it is not possible to match the two sets of results rigorously, they seem to converge smoothly to the same limit.

We present here a simple expression for the resonant particle growth rate of arbitrary plasma waves propagating at an arbitrary angle to a uniform magnetic field in a spatially homogeneous plasma. We then are able to see that cyclotron harmonic wave-particle resonances contribute to instability when the resonant particle pitch angle distributions are anisotropic, while the phase velocity resonances of the Landau form are unstable to beam type phenomena. A sufficient condition for resonant particle stability is that particle distributions be isotropic and monotonically decreasing with increasing energy everywhere.

We consider semi-quantitatively the cyclotron resonance instability of ion cyclotron and magnetosonic waves propagating at an angle to the magnetic field in an infinite uniform plasma. The velocity distributions of electrons and ions consist of a dense cold component and a diffuse high-energy tail. If the high-energy protons are sufficiently intense and their pitch angle distributions sufficiently anisotropic, instability occurs for those waves propagating parallel to the magnetic field. If the spectrum of resonant protons is sufficiently hard, a reasonably large cone of propagating angles about the magnetic field can be unstable. Observed fluxes of trapped protons in the magnetosphere should destabilise the ion cyclotron wave at a lower intensity threshold than for at least one class of electrostatic waves.

The loss-cone instability of plasma confined in a mirror-type trap is considered. Relaxation of the particle distribution in the trap with a length larger than the mean free path between ‘turbulent’ collisions is described by conventional quasilinear theory. A quasi-linear equation for the ion distribution is solved analytically for the case of a small loss-cone volume of particles in velocity space (it takes place, for instance, in the case of a trap with a larger mirror ratio).

The theory of Allis and Rose based on the hypotheses of congruence and proportionality is used to formulate the problem of ambipolar diffusion and drift of a plasma of added carriers in a semiconductor in the presence of a magnetic field. These hypotheses together with the linearized equations for the particle flow densities of the electrons and holes permit an expression for the particle flow density of the added carriers to be derived. In its final form this expression is composed of a drift and diffusion term in which the ambipolar group mobility and diffusion coefficient appear as tensorial quantities. These antisymmetric tensors will reduce to the scalar quantities of van Roosbroeck (1953) when the magnetic field is set equal to zero and to the proper tensorial quantities for the added minority carriers in strong extrinsic n or p type semiconductors. Finally, as an illustrative example, the ambipolar continuity equation for the particle density of added carriers is solved as an initial-value problem in an unbounded domain in order to analyze the space and time behaviour of a pulse of added carriers whose initial distribution is a Dirac delta function.

A study is made of finite amplitude, oblique, hydromagnetic waves in a cold collision-free plasma. It is shown that the equations admit steady solutions which describe flow through a front. Ahead of the front, the flow is uniform, but behind the front the magnetic field and flow variables oscillate irregularly in a random manner. The fronts are called ‘quasi-shocks’, although they have more in common with the laminar-turbulent transition of fluid mechanics than with the classical shock wave. The structure of the quasi-shocks is examined, and estimates are made for the mean values behind the front. The relevance of the quasishocks to the so-called ‘collision-free shock’ is considered, and comparison is made with the ‘bow shock’ on the solar wind near the earth. It is shown that the quasi-shock is consistent with some of the observed data.

The problem of combined Rayleigh—Taylor and Kelvin—Helmholtz instability for incompressible plasmas carrying a uniform magnetic field is investigated taking account of the Hall current. The resistivity and the finite ion Larmor radius effects are left out. It is found that the finite Larmor frequency is destabilizing in nature. The growth rate of an otherwise (without the Hall current) unstable configuration is increased, and unstable modes may be produced in otherwise stable situations for reasonably large values of the Hall current. The Hall effect also results in overstable modes.