Electrostatic instabilities excited by an energetic ion beam injected at an arbitrary angle with respect to the magnetic field in a collisionless plasma are discussed. Threshold conditions on the angle of injection and on the beam density are derived for the cross-field ion-ion mode, the modified two-stream mode and the ion-acoustic modes. The time evolution of the momentum and the thermal energy of each plasma component in the presence of the instabilities is calculated from moments of the quasi-linear equation. The background ions are significantly heated by most of the waves, exceptions being the modified two-stream mode and the resonant ion-acoustic mode. A wave with phase velocity close to the slow ion-acoustic wave has been found when the beam has a small density and a velocity greater than the acoustic speed by approximately a factor of five.

An experimental investigation of the disturbed flow field created by conducting bodies in a mesosonic, collisionless plasma stream is reported. Part 1 dealt with ion focusing by the body's plasma sheath and the subsequent filling of the near-wake void region. In part 2, the mid-wake region is investigated, where, for bodies of the order of a Debye length in size, the focused ion streams converge to form a significant current density peak on the wake axis. A parametric description is obtained of the behaviour of the amplitude, width, and position of this peak. The results also indicate that portions of the axial ion peak are created by additional mechanisms and that body geometry affects the mid-wake structure only when the sheath is sufficiently thin to conform to the shape of the body.

Strong electrostatic double layers were produced with a triple plasma configuration in the large plasma chamber (5 m long, 2·5 m diameter) at IPM in Freiburg, Federal Republic of Germany. Owing to relatively low densities (1011 1012m−3), Debye lengths of a few centimetres and layer thicknesses of the order of a metre were obtained. Layers both with and without magnetic fields were studied. Analysis of particle spectra prove that wave-particle interactions play a minor role in maintaining the strong electric field. The three-dimensional potential distribution is measured and is qualitatively discussed in terms of particle budget. For cases with a magnetic field it tends to agree with observations above the aurora. Comparisons are made with double-layer theory and computer experiments, and general agreement is found as far as the available results allow.

The general theory of ionizing shock waves in a magnetic field has been constructed. The theory takes into account precursor ionization of a neutral gas ahead of the shock wave front, caused by photo-ionization, as well as by the impact ionization with electrons accelerated by a transverse electric field induced by the shock front in the incident flow of a neutral gas. The concept of shock wave ionization stability, being basic in the theory of ionizing shock waves in a magnetic field, is introduced. An additional equation for the electric field in the shock wave is obtained. This equation, together with the investigation of the singular point in the downstream flow behind the shock wave front, provides all the information required for solving the problem. For example, this provides two additional boundary conditions for the shock waves of type 2, determining the value and direction of the electric field in the incident flow. One additional boundary condition determines a relation between the value and direction of the electric field for supersonic shock waves of type 3. There are no additional boundary conditions for supersonic shock waves of type 4. The electric field ahead of the shock front has two degrees of freedom. As well as for shocks of other types, its value is less than that of the transverse electric field at which an ionization wave could be emitted by the shock wave front (the ionization stability condition). The additional relationship for supersonic waves of type 4 determines the onset of an isomagnetic (viscous) jump in the structure of the shock wave front. The boundary conditions and ionizing shock wave structures, considered earlier by the authors of the present paper in the ‘limit of electrostatic breakdown’, as well as the structural determination of the electric field, considered earlier by Leonard, are limiting cases in the theory developed here. The ionizing shock wave structures are shown to transform from the GD regime at a low shock velocity to the MHD regime at an enhanced intensity of the shock wave. The abruptness of such a transition (e.g. the transition width on the Mach number scale) is determined by precursor photo-ionization.

The fluid equations for electrostatic wave forms propagating at small angles to a constant magnetic field are investigated. Both ion cyclotron and charge separation effects are included. Numerical results are given for initial conditions which are consistent with soliton formation. These results show a hybrid nonlinear wave form containing oscillations which are identified as short-wavelength fast ion-acoustic waves and long-wavelength slow ion-acoustic waves. An approximate analytic analysis is performed using the Bogoliubov–Krylov–Mitropolskii perturbation method.

We have derived a set of coupled mode equations which govern the nonlinear interaction of three high-frequency electrostatic surface waves through a low-frequency density perturbation produced by them. The set is compared with that obtained when a similar problem is solved for bulk waves in an infinite plasma. Some differences are shown to exist caused by the specific features of surface waves such as the amplitude attenuation normal to the interface and their hybrid nature.

The coupled mode equations which govern the nonlinear interaction of three electrostatic high-frequency surface waves and a low-frequency density perturbation are analysed considering time-dependent solutions only. We show the existence of a filamentation instability in the static limit for the low-frequency density perturbation. In the opposite case (density perturbation close to the lowfrequency surface wave resonance) we arrive at a decay instability where only surface waves take part. The parametric approximation (growth rate and threshold) as well as the nonlinear evolution of both types of instabilities are studied.

Solutions for transverse, normal and switch-off ionizing shock waves have been obtained on the basis of the general theory of ionizing shock waves in a magnetic field presented in part 1. Some details of the shock structure were considered at Pm → 0. In particular, the transition from the gasdynamic to the magnetohydrodynamic regime, while increasing the shock velocity, is traced in detail. The additional relationship, obtained in part 1, determines the value of a transverse electric field ahead of the front for the case of a transverse shock wave and for normal and switch-off shock waves, if the latter are shock waves of type 3. In the case of normal and switch-off shock waves of type 4, basic relationship obtained in part 1 is not a boundary condition, but determines the position of a viscous isomagnetic jump in the shock structure. The transition of ionizing shock waves from the GD to the MHD regime, while increasing the shock velocity, was considered. The width of such a transition on shock velocity scale depends significantly on the intensity of precursor photo-ionization. In particular, this transition occurs slowly at zero precursor photo-ionization: the electric field ahead of the front tends to zero as l/vxo when vxo increases. The problem of formation of ionizing shock waves ahead of a magnetic piston and a conducting piston with a magnetic field directed along the normal to the piston surface has been solved. We indicate the set of flow parameters, for which Chapman-Jouguet's model of ionizing front motion ahead of the piston is inapplicable. A transition from the Chapman-Jouguet regime to the MHD one is considered.

Resonant three-wave interaction in a spatially non-uniform magnetized fluid plasma is considered. We calculate the coupling coefficients Vj for wave propagation in arbitrary directions and demonstrate that new terms, which appear in Vj owing to the presence of density gradients, can dominate actual wave coupling processes.

The parametric decay of a magneto-acoustic pump wave into low-frequency waves modified by finite temperature effects is considered. The excited waves are the kinetic Alfvén wave and the ion-acoustic wave. The former wave plays an important role in linear heating schemes employing the mode conversion of magneto-acoustic waves at the Alfvén resonance. Here we calculate the parametric growth rates and pump thresholds for excitation of these waves. The main result is that finite temperature effects tend to reduce the growth rate of Alfvén waves.

The first-order Chew, Goldberger & Low (GGL) equations for electrons including the effect of finite Larmor radius are applied to the whistler wave. The zerothorder velocity distribution function for electrons in the GGL expansion is assumed to be an anisotropic Maxwellian. The effect of electron thermal motion on the propagation of whistler waves is analysed by use of a dispersion relation and properties of the refractive index surface. It is shown that the electron thermal motion intensifies the tendency of whistler waves to follow the lines of force of the earth's magnetic field at appropriate values of electron temperature anisotropy.

Analytic solutions for cylindrical, rigid-drift equilibria were searched for by checking the invariance of the second-order, nonlinear differential equations of the line density and particle density under one-parameter Lie groups. No invariance was found for the cylindrical screw-pinch for the polytrope index γ ╪ 2 of the pressure equation of state. For the Z-pinch, the differential equation for the line density for arbitrary γ is invariant under one group and reduces by Euler's method to an intractable first-order, nonlinear differential equation. In the case of a θ-pinch, the nonlinear differential equations for the particle density and line density are invariant at least under the translation group. The particle density is found as an implicit function of the radial distance r, involving incomplete beta functions of the γth power of the particle density.

The propagation of small-amplitude hydromagnetic waves in a collisionless, heat-conducting plasma is investigated using the first-order Chew-Goldberger- Low (CGL) fluid equations including the effect of finite Larmor radius of the ion. The first-order heat flux equations are derived by use of Macmahon's technique. The zeroth-order velocity distribution function of the ion in the CGL expansion is assumed to be a heat-flux-bearing distribution function. The effect of heat flux on the propagation of hydromagnetic waves is analysed by use of phase speed and refractive index surfaces and the amplitude relation between the density perturbation and the magnetic field perturbation. It is shown that the hydromagnetic wave propagation characteristics are asymmetric with respect to the direction of external magnetic field to zeroth order and first order for magneto- acoustic and Alfvén waves, respectively, and the garden hose instability criterion is modified by the heat flux anisotropy.

A generalization of the stability analysis of rippled non-neutral electron beams is presented. The treatment covers regimes ranging between those known as ‘Brillouin flow’ (ωpe = ωc/2½) and ‘immersed flow’ (ωpe≪ωc). It considers electrostatic surface waves with azimuthal symmetry (l = 0) as well as harmonic modes (l≠0). Both long-wavelength and short-wavelength domains are analysed. A general discussion of instability is given in terms of the solution of the Mathieu-Hill equation. New unstable modes are found and their growth rates are derived and compared.

Stability of doublet plasmas in the Doublet III device against resistive axisymmetric MHD modes has been studied. The real characteristics of the device were modelled as accurately as possible. Thus, for example, the actual toroidal geometry was used, the field shaping coils (F-coils) which surround the plasma were included, and the location of real limiters was incorporated for determination of the plasma surface. We have used two parameters to model the plasma current distribution and the equilibrium boundary conditions: one describes the flatness of the current profile, the other describes the fraction of the poloidal plasma flux contained within the separatrix. Thus we have determined stability as a function of these two parameters. If the fluxes at the F-coils are kept fixed, there are stable as well as unstable regimes in this two-dimensional parameter space. If the F-coil fluxes are controlled to imitate the presence of virtual F-coils with fixed fluxes located closer to the plasma, it is possible to stabilize the plasma. This stabilization is discussed in the paper and numerical examples are given. Finally, the relationship between the results of this paper and experimental observations from Doublet III is discussed.

The penetration of an externally applied rotating magnetic field into a plasma cylinder is examined. Steady-state solutions of an appropriate set of magneto-fluid equations show that, provided the amplitude and rotation frequency of the field are suitably chosen, the penetration is not limited by the usual classical skin effect. The enhanced penetration of the rotating field is accompanied by the generation of a unidirectional azimuthal electron current which is totally absent in a purely resistive plasma cylinder.

We discuss various aspects of the spontaneous generation of magnetic fields in a Langmuir plasma. We first of all show that the correct general expression for the ponderomotive force leads to the solenoidal current responsible for the magnetic-field generation. We derive the ponderomotive-force expression and also the magnetic-field generation equations from a two-time-scale two-fluid description. We also use a kinetic approach to derive the magnetic-field generation equations. We discuss the stability of monochromatic Langmuir waves and show that they are subject to both the ordinary modulational instability and to a magneto-modulational instability. We show that the coupled nonlinear equations describing the electric field strength amplitude, the plasma density, and the self-generated magnetic field can, under certain conditions, be reduced to a generalized cubic nonlinear Schrodinger equation. We finally show, by using a virial theorem, that the self-generated magnetic field does not stabilize the wave collapse.

Analytic calculations of three important effects of toroidal field ripple on suprathermal ions in tokamak plasmas are presented. In the first process, collisional ripple-trapping, ions become trapped in local magnetic wells near their banana tips owing to pitch-angle scattering as they traverse the ripple on barely unripple-trapped orbits. In the second process, collisionless ripple-trapping, ions are captured (again near a banana tip) owing to their finite orbits, which carry them out into regions of higher ripple. In the third process, banana-drift diffusion, fast-ion banana orbits fail to close precisely, due to a ripple-induced ‘variable lingering period’ near the banana tips. These three mechanisms lead to substantial radial transport of banana-trapped, neutral-beam-injected ions when the quantity α*≡ε|τ|/Nqδ is of order unity or smaller.

The generation of a steady azimuthal current in a cylindrical plasma column using a rotating magnetic field is numerically investigated. The mixed initial-boundary-value problem is solved using a finite difference method. It is shown that substantial azimuthal current can be driven provided that the amplitude of the rotating magnetic field is greater than a certain threshold value which depends on the plasma resistivity.

The existence of finite-amplitude Langnwir solitary waves in a two-electron-temperature plastia is investigated. A now type of soliton, in which the density depression and the electric field amplitude scale in the same manner, and which travels at the effective sound speed, has been found.