A model is proposed to explain the observed electron heating in perpendicular collisionless shock waves. This relies on trapping of the electrons by the turbulent electric field to modify their orbits in such a way that they gain energy from the steady potential jump across the shock. With simple assumptions about the nature of this trapping, reasonable agreement with the experimentally observed heating is obtained. In addition, the model provides qualitative agreement with a number of other experimental observations.

The instability of right-handed, circularly polarized electromagnetic waves, propagating along an external magnetic field (whistler mode), is studied for electron plasmas with distribution functions peaked at some non-zero value of the transverse velocity. Based on the linearized Vlasov-Maxwell equations, the criteria for instability are given both for non-resonant instabilities arising from distribution functions with no thermal spread parallel to the magnetic field, and for resonant instabilities arising from distribution functions with Maxwellian dependence in the parallel velocities. It is found that, in general, the higher the average perpendicular energy, the more is the plasma susceptible to the whistler instability. These criteria are then applied to a sharply peaked ring distribution, and to loss-cone distributions of the Dory, Guest & Harris (1965) type.

The statistical properties of non-linearly interacting waves are considered from a physically motivated viewpoint. A Fokker-Planck wave transport equation is derived. In certain circumstances an H theorem can be proved.

This paper is concerned with existence conditions for steady hydromagnetic shock waves propagating in a collisionless plasma along an applied magnetic field. The electrostatic waves are excluded. The conditions are based on the requirement that solutions of the Vlasov-Maxwell equations deviate from a uniform state ahead of a wave. They are given as the conditions on the upstream flow velocity in the wave frame (i.e. in the form of inequalities among the upstream flow velocity and some critical velocities). The conditions crucially depend on the pressure anisotropy, and demonstrate possibilities of exacting collisionless shock waves for high β plasmas.

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.

Non-linear hydromagnetic waves in a cold collisionless plasma are investigated by numerical and analytic methods. For this problem, Saffman has already implied that there may exist a non-periodic wave different from the well-known solitary wave (or wave train). His analysis is based on the assumption that the quasi-ergodic theorem can be applied to the present problem. However, the propriety of the assumption has not been discussed.

It is seen from the computer calculations that in general the waves do not have periodicity, as Saffman pointed out. Furthermore, some concrete examples show the behaviour of these ergodic waves more clearly. The width of the waves is of the order of ion Larmor radius. These waves are here called quasi-wave trains. In some special cases, the waves reduce to wave trains (with periodicity). Some of them have a length scale of the geometric mean between the Larmor radii of the electron and of the ion.

The dispersion properties of drift waves in a low β weakly collisional plasma, in the presence of ion acoustic or Langmuir waves parallel to magnetic lines, are investigated. It is shown that the non-linear interaction with an ion acoustic wave mainly leads to a shift of the drift wave spectrum towards lower frequencies (and only under very particular conditions affects the stability of the drift wave). The interaction with a Langmuir wave, on the contrary, yields a contribution to the imaginary part of the frequency. The conditions under which this stabilizes unstable drift modes are derived and discussed.

Dispersion relations are calculated and solved for frequencies near the first two harmonics (Ω/Ω+ = 2, 3) of perpendicular magnetosonic waves in relativistic anisotropic plasmas. In this, wavelengths larger than the ion Larmor radius and large plasma frequency (Ω2p, ≫ Ω2+) are assumed. It is found that, even for Tψ ≫ T the plasma is stable. This result has application to the steady-state, spherically symmetrical, expanding, solar-wind plasma.

The transfer of mass and heat through a diatomic gas bounded by two plane parallel surfaces is investigated by a kinetic model which includes translational, rotational and vibrational degrees of freedom. A full range moment method is employed in the solution. Numerical solutions obtained for small temperature and pressure differences show the effect of inelastic collisions on the mass and heat fluxes. Approximate analytical expressions are derived for the mass and heat transfer rates, which are valid over the entire density range and yield the correct free-molecule and continuum limits. The results agree well with existing heat transfer and density measurements.

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized electrons undergoing an E x B drift. The linear dispersion relation is solved numerically for Te ΰTi. For a fixed ratio of drift velocity to electron thermal velocity, the growth rates of the E x B electron drift instability are smaller, and the waves are stabilized at much smaller values of k. B than in the Te ≫ Ti case.

The circumstances under which certain plasma dispersion equations may be used in electrostatic ray tracing problems connected with studies of ionospheric topside plasma resonances are investigated. Three plasma ‘models’ of increasing complexity are compared with each other. The models are based on the assumption of: (i) an adiabatic process with a scalar pressure, (ii) a fully adiabatic process (Buneman 1961), and (iii) an electrostatic kinetic description. It is found that near fN, and within 10° of the static magnetic field, all three models may be used with good accuracy, and collisionless damping is very small. Near fT, and for propagation nearly across the field, only the second model (ii) gives tolerably accurate results as judged by the kinetic equation. For frequencies within 10 kc s-1 of fT such as are encountered in ray tracing, collisionless damping may be neglected within a cone of ∽ 10° about the perpendicular to the field for fT < 2fH, and within ∽ 20° whenfT ≫ 2fH Model (iii) may be used to examine the dispersion equation near the electron gyroharmonics: this topic is discussed in Andrews & Fang (1971).

The dispersion relation for electrostatic plasma waves propagating at frequencies near the electron cyclotron harmonics has been evaluated, and used to determine the refractive index curves for varying values of the angle θ between the k vector and the ambient magnetic field B0 in a warm magnetoplasma. It is shown that, under certain circumstances (which are defined), the (@, θ) curves have the characteristic ‘nose’ shapes that are necessary to provide a reflexion in the ambient plasma. Thus, the oblique echo reflexion mechanism (McAfee 1968, 1969a, b), which accounts for the appearance of the resonance signals or ‘spikes’ at the plasma and upper hybrid frequencies fN and fT on topside ionograms, may also be applied to the plasma waves propagating at frequencies near the electron gyro-harmonics. The relatively high damping that occurs for θ # 90° severely restricts the ranges of θ and wave-number k over which the reflexion mechanism applies. The restriction is such that the damping is severe for all values of θ when k is large, and for all values of θ outside a cone of ∽ 2° centred on θ = 90° when k is small.

A general description of cyclotron harmonic resonant pitch-angle scattering is presented. Quasi-linear diffusion coefficients are prescribed in terms of the wave normal distribution of plasma wave energy. Numerical computations are performed for the specific case of relativistic electrons interacting with a band of low frequency whistler-mode turbulence. A parametric treatment of the wave energy distribution permits normalized diffusion coefficients to be presented graphically solely as a function of the electron pitch-angle.

The diffusion coefficients generally decrease with increasing cyclotron harmonic number. Higher harmonic diffusion is insignificant at very small electron pitch-angles, but becomes increasingly important as the pitch-angle increases. One thus expected the rate of pitch-angle scattering to decrease with increasing electron energy, since the resonant value of the latter varies proportionately with harmonic number. This indicates that, in mirror-type magnet field geometrics, such as the Earth's radiation belts, the diffusion losses of high energy electrons are likely to be appreciably slower than those at low energy. Integration of the diffusion rates along a complete bounce orbit will be required to clarify this point, however, since the high-energy particles will be subject to more rapid first harmonic diffusion near their mirror points.

The forced radial magneto-acoustic oscillations in a plasma column with nonuniform mass density and temperature are investigated. It turns out that the oscillations have a resonant character similar to that of the magneto-acoustic oscillations in a uniform plasma column. The properties of the axial and azimuthal components of the oscillating magnetic field are discussed in detail.

Stability of MGD shock waves can be investigated either by disturbing the shock discontinuity by incident waves and then considering whether the response of the shock is unique and determinate or not, or by studying the behaviour of the dissipative shock structure with variations in the magnitudes of the dissipations. Both approaches yield the same results, which appears at first sight to be a coincidence. In this paper we show, from a single treatment that includes each as special cases, why the two methods yield the same conclusions.

Also, by including the Hall term on Ohm's law, we are able to resolve the uncertainty about the stability of switch-on and switch-off shocks that occurs in the usual MHD treatment of the problem. Finally, it is shown that the Hall term also introduces the possibility of electric field layers in the unsteady shock and thereby reduces the number of shock boundary conditions. This throws some doubt on the value of the wave-interaction theory for shocks in real plasmas.