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.

Experimental and theoretical studies were made of the decrease in the degree of ionization of shock-heated agron resulting from radiative emission. the studies were based on measurment of the time history of the electron density by means of optical interferometry used in conjunction with a rotating mirror camera. These measurments apply to the quasi-euilibrium region which follows the short electronic relaxation zone behind strong shocks. Loss of energy by rediation led to cooling of the gas as evidenced by the decreasing electron density. The analytical studies were based on the assumption that the dense plasma readiated throught both continuu, emission and emission from spectral lines. Comparison was made with experimental results, and theory and experiment were in good agreement, for a realistic choice of the parameters contained in the continuum theory. The analysis indicated that line radiation losses could not be disregarded. Sizeable loss resulted from lower level bound-bound transitions even though these lines experienced absorption.

The non-linear one-dimensional steady-state equations which govern the flow of an ion—electron beam emitted from a plane are solved in the phase plane, and it is shown that a perfectly neutralized beam follows for a large range of injection velocities of the electrons. When the velocity of the ions is less than the electron sound speed the transition region for the neutralization has a length of the order of a Debye length λD = (kT)½ (4πNe2)–½, which is a typical plasma sheath. The maximum velocity of injection of the electrons for which neutralization is predicted is, in this case, the sound speed of the electrons. If the electrons are injected with a supersonic speed, they cannot be decelerated continuously to the subsonic speed corresponding to the velocity of the ions. No bound is set on the electron injection velocity from below. When the velocity of the ion beam is greater than the electron sound speed, oscillations with an amplitude which depends on the velocity of injection of the electrons, and a wavelength which depends on the ratio of the ion velocity to the electron speed of sound, are found. In this case the injection speed of the electrons needed to obtain the steady-state oscillatory solution is bounded both from above and from below. Subsonic electrons cannot be accelerated continuously to the supersonic velocity required to match the velocity of the ions, and within the supersonic range there is shown to be a limit (depending on the ratio of the ion velocity to the electron speed of sound, so that faster electrons cannot be decelerated continuously to match the (supersonic) ion velocity.

The guided propagation of Alfvén waves in a cold plasma is discussed from several points of view. First the field of a line source is calculated at infinity. This calculation leads to a divergence in the radiated power in two directions forming very small angles with the magnetic field.

The divergence is removed if the line source is replaced by a strip source of finite width. It is shown that propagation from a strip source only a few kilo-metres wide is strongly guided by the magnetic field, with almost no spreading, along a field line extending up to, say, 4 earth radii for wave periods of about 100 sec.

A systematic continuum theory based on the method of matched asymptotic expansions is developed to deal with electrostatic probes in a slightly ionized gas. To the first approximation of thin space charge sheath, the sheath solution is shown to become common to the geometries considered, i.e. plane, cylindrically and spherically symmetric probe surfaces: the main interest lies in the last geometry. The second-order approximation strongly affects the last two geometries. Detailed numerical calculations are presented to illustrate the effects of a finite ratio of the Debye length to the characteristic body dimension; including a contraction of the sheath region and enhancement of the electric field from the asymptotic (first-order approximation) values.

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.

Equations are derived which may be used to describe the propagation of electromagnetic waves in non-uniform magnetized plasma when the wave frequency is near the second electron cyclotron harmonic. The method used is to expand the linearized Vlasov equation in powers of the electron Larmor radius divided by a typical scale length. The general equations are then specialized to the problem of the coupling of transverse waves to the longitudinal modes (Bernstein modes) which exist when all quantities vary only in a plane perpendicular to a straight magnetic field. The form of these equations for two simple models of the equilibrium plasma is given. Comments are made about the equations for the higher harmonics, and the question of boundary conditions is discussed. Finally, the general equations are examined in the limit Ω→0 in order to provide equations suitable for the description of high frequency waves in non-magnetized plasmas.

In a previous paper, the R.F. characteristics of a spherical probe immersed in a hot, low-density plasma using a realistic sheath model were considered, and a few results of computations presented. The remainder of these results are given in this paper. The dependences of R.F. admittance, and rectified current on probe radius, d.c. bias, and electron neutral collision frequency are exhibited and shown to be qualitatively in accord with the predictions of simple slab-sheath/dielectric models. It is shown how in principle, analysis of resonance rectification characteristics using curves included in the paper can yield values of electron density ne temperature Te, and electron-neutral collision frequency ν. Two methods of reduction are applied to some laboratory results obtained at Slough and are shown to give reasonably consistent values of ne and ν, but the values of Te, show considerable scatter. These methods could complement the Langmuir probe which gives more reliable values of Te than of ne in low density plasmas with ne ≾108 cm−3. Effects of magnetic fields are not included in this paper.

Previously reported numerical investigations of the non-linear Vlasov equation are extended to an intensive study of the two-stream instability. Strongly unstable initial conditions for the one-dimensional electron plasma are followed in time until the state of the plasma has become essentially time independent. Both the electric field and the distribution function appear to be characteristic of an inhomogeneous equilibrium, as previously conjectured (Armstrong 1966).

A simple single-fluid model is presented which accounts for the behaviour of MHD shock producing devices in which the shock and the driving current sheet are unseparated. By means of both characteristic and similarity solutions, it is shown that unusual plasma behaviour is a simple consequence of the fluid equations of motion. The important parameters in determining the performance of MilD shock tubes are the width of the current sheet at breakdown (related to the magnetic Reynolds number) and the current sheet Mach number with respect to the gas at rest. It is shown that, under many conditions, separation is more likely to be achieved with a decrease, rather than an increase, in current sheet speed. Lowering the Mach number is more influential in causing the shock to form at the front of the current sheet than raising the magnetic Reynolds number.

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.

We present here a simple and direct derivation of the equations governing the motion of a charged particle in space- and time-dependent fields in the guiding centre approximation in lowest order. The method of attack is based initially on the expansion scheme of Bogolyubov & Zubarev (1955) combined with Northrop's averaging process over one gyration period. Thus, we first resolve the instantaneous velocity of the particle into three components, r = ê1u + UE + Tw, where u is the parallel component, UE is the familiar E × B drift, and Tw is the instantaneous perpendicular component as measured in a frame moving with the UE drift. Substituting this expression into the particle's (non-relativistic) vector equation of motion, resolving it into parallel and perpendicular components, and applying Northrop's averaging process, we obtain the averaged equations of motion, in lowest order, for the components u and w. From the latter equation we prove immediately that the magnetic moment of the particle is an adiabatic invariant to lowest order. Next, we resolve the instantaneous velocity of the guiding centre into two components, R = r — p, where p is a rapidly rotating vector directed from the guiding centre to the instantaneous position of the particle. Upon applying Northrop's averaging process we obtain at once the averaged velocity of the guiding centre including the complete set of first-order drifts. From this equation we readily deduce the energy gain equation to lowest order. It is then shown that the simple averaging prescription applied here is mathematically rigorous and yields correctly all lowest order results in an expansion in reciprocal powers of the cyclotron frequency.

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.

A model kinetic equation for a plasma containing many species is set up. It is an approximation to the correct kinetic equation but is considerably simpler in form. The collision operator has the property that particles, momentum and energy are conserved, and it gives to good approximation the correct rates of transfer of momentum and energy between all pairs of species. It is also shown that the equation leads to an H-theorem.

The propagation, along the magnetic field, of a point disturbance in a cold two fluid linear plasma is solved asymptotically in various space-time régimes. The main disturbance is a pulse front travelling at approximately the Alfvén speed divided by the electron to ion mass ratio. Its proffle envelope is an Airy function. It oscillates at the mean of the gyro-frequencies and is effiptically polarized. The disturbances remaining behind this front are of two kinds: an oscillation at the sum of the gyro-frequencies which is circularly polarized and represents the ‘extraordinary’ wave, and an oscillation at the ion gyro-frequency which is elliptically polarized with changing eccentricity and orientation of axis.

The thermal conductances in a collisionless gas between coaxial cylinders and concentric spheres have been obtained for arbitrary thermal accommodation coefficients. This exact theory is based on the general theory of thermal conduction of collisionless gas developed recently by Wu which has been established according to his revised theory of thermal transpiration. The classical theory of thermal conductance between coaxial cylinders by Knudsen and Von Smoluchowski is only accurate to the first power of the temperature difference in which the velocity distribution in the system is assumed to be nearly Maxwellian. However, in the present paper, it is unnecessary to make this usual assumption and the exact theory has been established according to the revised theory of thermal transpiration.

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.

The Chapman—Enskog expansion is applied to the model Fokker—Planck equation for a plasma, derived in part 2. It is shown that the complete set of transport coefficients can be calculated without further approximations. Results are derived first in the absence of any external magnetic field. The transport coefficients are also derived when there is a strong magnetic field, in which case they become anisotropic.

The rectified electron current to a non-magnetic and to a magnetic spherical plasma probe has been investigated as a function of the frequency of the applied alternating potential, the discharge current in the plasma source and the magnitude of the magnetic field produced by a Helmholtz coil pair. The frequency at the main peak in the rectified current was found to be always greater than the gyro- frequency and to lie within a range of frequency predicted by Crawford from an analysis of a simplified model. The results of this laboratory work have been applied to a rocket-borne experiment on resonance rectification previously carried out by R.S.R.S.

A simple model of an ionizing detonation wave is studied in which the electrical conductivity jumps from zero to infinity across the wave at which a net release of exothermal energy occurs and which propagates with magnetoacoustic speed relative to the products of combustion. The upstream electric and magnetic fields are mutually orthogonal and transverse to the direction of propagation. The ratios of downstream flow parameters to those upstream and the detonation speed are presented for a range of values of the upstream electromagnetic field. It is surmised that, for a specified upstream magnetic field, physically realistic detonation waves exist only for a limited range of values of the electric field strength of invariant sign.