The effects of lithium and heavier ions (i.e. having specific charge Zj e/mj smaller than the proton's), on the electromagnetic cyclotron instability in warm anisotropic (bi-maxwellian) proton plasmas, are analytically and numerically investigated. It is found that the occurrence of resonances for modes with ωr = Ωj (ωr, real wave frequency; Ωj, ion gyrofrequency), which produce a cut-off in the phase velocity, leads to the possible existence of two different situations. (i) If the proton thermal anisotropy is smaller than a critical value A pc (which depends on the ion specific charge), the resonance and therefore the ‘stop band’ occurs outside the unstable range. The maximum growth rate, as well as the instability range in k space, may increase with the relative ion concentration ion and warm proton particle densities, respectively. There is an optimum value of η for maximum enhancement of the instability. (ii) If Ap > Apc, the unstable spectrum in Wr space is divided by the ‘stop band’ into two distinct regions. In the higher-frequency region, the maximum growth rate, as well as the width of the unstable spectrum, decrease with increasing relative ion concentration. For η > ηc, the instability is completely suppressed. In the lower-frequency region, however, the maximum growth rate and the extension in k space may increase with η.

Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).

A theoretical and experimental investigation of the forced radial magnetoacoustic oscillations of a magnetized plasma column is presented in this paper. Forced magneto-acoustic oscillations of a magnetized argon afterglow plasma are generated continuously by passing an RF current through a solenoid wrapped around the discharge tube. The radial variation of the amplitude of the magnetic field disturbance [bz(r)] associated with these oscillations is measured at various times during the decay of the afterglow plasma. A theoretical description of these oscillations is developed in which the collision frequencies between the various plasma constituents are treated as free parameters. The values of these free parameters at any given instant during the decay of the plasma are determined by fitting computed bz{r) radial profiles to the measured ones. The electron temperature Te, and the ion-neutral cross section for momentum transfer QD are deduced from these collision frequencies. The reliability of this plasma diagnostic technique is demonstrated by its ability to yield values for Te and QD which compare favourably with the results obtained by other workers.

We show theoretically that the electron density and temperature of a plasma could be deduced from the measurements of the transfer impedance between two small dipole antennae, each much shorter than a Debye length, separated by a distance of ten or more Debye lengths. In contrast to the quadripole probe, this ‘double-dipole probe’ relies on not producing perturbations in the plasma, rather than on minimizing their effects. The plasma is assumed to be warm and isotropic, and the motion of the ions is neglected. First, it is shown that, in a Maxwellian plasma, the frequency response of a double-dipole probe is easier to interpret than that of a quadripole probe with the customary square layout. Then, in a second step, the transfer impedance of the former probe is calculated in a Cauchy plasma, and the results are compared with those previously obtained in a Maxwellian plasma. By so doing, we show that, for large distances between the dipoles, the real part of the transfer impedance is sensitive to the form of the tail of the distribution function.

Monochromatic electrostatic waves of large amplitude were excited by the interaction of an electron beam with a bounded plasma. These waves were identified as resonant beam modes, which are amplified by multiple reflexion in a cavity. Nonlinear effects, such as the generation of harmonies and sidebands, were observed.

The paper discusses the dispersion relation for longitudinal electron waves propagating in a collisionless, homogeneous isotropic plasma, which contains both Maxwellian and suprathermal electrons. It is found that the dispersion curve, known to have two separate branches for zero suprathermal energy spread, depends sensitively on this quantity. As the energy half-width of the suprathermal population increases, the branches approach each other until they touch at a connexion point, for a small critical value of that half-width. The topology of the dispersion curves is different for half-widths above and below critical; and this can affect the use of wave-propagation measurements as a diagnostic technique for the determination of the electron distribution function. Both the distance between the branches and spatial damping near the connexion frequency depend on the half-width, if below critical, and can be used to determine it. The theory is applied to experimental data.

A small-signal analysis is carried out for a geometry consisting of two parallel conducting planes, with a magnetized plasma resting on the one plane, and a vacuum gap between the plasma and the other. Each of the solutions found to fit the boundary conditions consists of a superposition of two ‘transverse’ wave-functions with one and the same longitudinal propagation constant. Numerical solution of the dispersion relations yields the following. (i) A set of slow waves, in good agreement with the well-known quasi-static approximation. (ii) Fast waves, which approximate TM waves (Hz ≐ 0) propagating only at relatively high frequencies. (iii) Fast waves propagating in the same frequency range as the TM waves, but with negligible longitudinal electric field component Ez, thus resembling TE waves. (iv) A set of waves with a dispersion which resembles that obtained from coupling between fast forward and slow backward modes of propagation. (v) A single wave, not obtainable from the slow-wave approximation which resembles the helicon wave of the one-dimensional case, with the frequency approaching the cyclotron frequency at small wavelengths, provided the magnetic field is relatively strong (ωc < ωp), the spacing between the conducting planes not too narrow and the fill-factor not too small. For relatively weak magnetic fields (ωc < ωp), this wave appears as a surface wave with frequency approaching the lower hybrid frequency at small wavelengths.

In a high-density magnetized plasma composed of two ion species of different charge-to-mass ratios, electrostatic waves propagating across the magnetic field exhibit a resonance at the Buchsbaum or ion-ion hybrid frequency, in addition to the resonances at the upper and lower hybrid frequencies. In this paper, the possibility of stimulated scattering of electromagnetic waves incident normal to the magnetic field from electrostatic waves at the ion-ion hybrid frequency is investigated. Based on the cold-plasma equations, it is found that such a process is theoretically possible. Formulas for the threshold power and growth rate are obtained, which show that the threshold power is much greater, and the growth rate much less, than those of stimulated scattering from upper and lower hybrid waves.

We consider two non-parallel beams, each of width a, that interact in a plasma and excite a wave that travels across their region of intersection. We determine the dependence of the amplitude of the excited wave on a for the limiting cases of large and small values of the ratio of the initial beam intensities.

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.

Dispersion relations are obtained for surface waves propagating along plasma—vacuum and plasma—plasma interfaces in a direction perpendicular to a uniform magneto-static field (that lying parallel to the interface), by setting to zero reflexion coefficient for an incident plane wave. Complete solutions to the dispersion relations are presented for both cases and the results are displayed diagrammatically. Comparisons are made with the work of other authors.

The standard model for fast magnetic-field reconnexion (Petschek 1964) is qualitatively valid, despite numerous criticisms of its quantitative details. It contains four slow magnetohydrodynamic shock waves, which radiate from a central diffusion region. On the basis of Petschek's rough analysis, it is generally stated that, for large values of the magnetic Reynolds number Rm, reconnexion can occur at a rate no faster than a fraction π/(4 log Rm) of the Alfvén speed. Alternative models of the region outside that of diffusion have been put forward by Yeh & Axford (1970), whose general solutions Vasyliusnas (1975) proved invalid, and by Sonnerup (1970), whose model is mathematically useful, but of limited practical applicability. But their results suggest that reconnexion can occur at any rate whatsoever, with the diffusion-region dimensions responding accordingly. The present paper analyses the external region for Petschek's mechanism in greater detail than hitherto, with the object of deciding whether or not there is a maximum rate. The inclinations of the shock waves are calculated as a function of the fluid speed ve at large distances, which is taken as a measure of the reconnexion rate. It is found that, in agreement with Petschek's rough analysis, there is indeed an upper limit on the allowable rate of magnetic-field reconnexion. Its variation with Rm is calculated, and it is shown, for log10 Rm ≫1, to be approximately 20% of Petschek's value. Typical values are 0·10vAe for Rm = 10·2 and 0·02vAe for Rm = 106. (vAe is the Alfvén speed at large distances from the diffusion region.)

Some comments are made about how to determine the speed with which magnetic flux is carried towards an X-type neutral point and reconnected. Conditions in the diffusion region near the neutral point are also investigated, with the conclusion that the streamlines and magnetic field lines cannot both be locally hyperbolic. Instead, two distinct modes may be possible. In the first, the magnetic field lines are straight, and the diffusion region does not differ greatly from that described by Parker (1963). In the second, the fluid velocity components increase cubically away from the neutral point with the result that, for a given reconnection rate, the diffusion region is typically five times greater than in the Parker model.

In the presence of a sufficiently strong magnetic field, the shielding of a test particle in a two-dimensional Vlasov plasma disappears. An intermediate regime is investigated, for both a stationary and a moving test particle, in which the plasma frequency ωp and the cyclotron frequency ωc are of the same order of magnitude. In the case of a stationary test particle, this intermediate regime is approximately in the range ½ ≤ a ≤ 2, where a = ωp/ωc. For a < ½, only partial shielding occurs, the potential retaining its vacuum logarithmic dependence. For a < 2, the potential approximates to the field-free case, and falls off exponentially. For a test particle moving at electron thermal speed, the typical bow wave and wake phenomenon, associated with an unmagnetized plasma, is no longer present. We find, instead, that the potential possesses upstream—downstream symmetry.

This paper considers the steady two-dimensional problem of regular reflexion and symmetric intersection of oblique magnetogasdynamic shock waves. It is assumed that the fluid medium is a non-viscous, non-heat-conducting, ideal gas of infinite electrical conductivity, and that the applied magnetic field is parallel to the velocity of the approaching stream. In view of the complexity of the shock relations, a graphical method is presented for determining the orientation and strength of the reflected shock wave in terms of the Laval number M*1 (flow speed divided by critical sound speed), the Alfvén number A1 (flow speed divided by Alfvén speed), and the shock angle ϑ 1 ahead of the incident shock. Moreover, the possible ranges of M*1, A1, and ϑ 1, for which regular reflexion may occur, are calculated and illustrated graphically for the case of a monatomic gas.

We investigate second-harmonic resonance for weakly nonlinear hydromagnetic waves travelling in a cold collisionless plasma by the method of multiple scales. We find that the second-harmonic resonance can occur between the magneto-acoustic modes; but it can occur neither between the magneto-acoustic and the Alfvé n modes, nor between the Alfvé n modes. The resonant frequency of the magneto-acoustic modes is characterized by the geometric mean of the ion and electron Larmor frequencies. We obtain steady-state solutions to the dynamical equations governing the second-harmonic resonance. The result of analysis shows that the envelopes of the two resonant waves are composed of two periodic wave- trains, two solitary pulses or a solitary pulse and a phase jump. We also extend the problem to more general dispersive wave systems.

A family of exact solutions to the MHD equations is presented for steady incompressible two- and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams. The magnetic field in each plasma is strictly parallel to the current sheet, but can have different magnitudes and directions. Resistive and viscous effects are accounted for. These flows are of considerable interest in connexion with the magnetic field merging process. They represent the limit of resistive field annihilation with zero reconnexion.

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

This paper reports calculations of the collision-free expansion of a semi-infinite plasma. It is shown that the ion front is accelerated to velocities comparable with the thermal velocity of the electrons.

A solution of the Mhd equations is presented, which describes field-line reconnexion by stagnant diffusion in the middle of a piecewise-uniform convective hydromagnetic flow. This composite solution demonstrates that the diffusion region adjusts its shape and size in accommodation to the incident merging fluids.