The instability of a field-aligned electron beam of finite width streaming through a uniform magnetized plasma is investigated. An earlier paper presented an analysis of the normal modes for electromagnetic waves in a ‘top hat’ beam– plasma system. The present paper extends the analysis to higher frequencies and different system parameters. Besides discussing the nature of the normal modes, the wave field variation within the beam region is studied. In doing this it is found that an electrostatic approximation is useful in describing the general form of the dispersion relation, specifically showing how the beam width controls the range of allowed solutions. The electrostatic approximation is shown to be good for most of the range of frequencies considered. When the electron gyrofrequency is greater than the electron plasma frequency, the theory predicts that the cold plasma upper-hybrid resonance band (Z mode) is stable to negative Landau damping. A criterion for applying this result to beam-plasma systems other than the ones investigated here is developed, and it is found that the effect should be more readily observable in laboratory experiments than in space plasmas.

The microinstabilities of a high-pressure plasma moving along a magnetic field with a non-uniform velocity profile are investigated. A similar problem was studied earlier by Dobrowolny on the basis of hydromagnetic equations with an oblique viscosity tensor. The present paper, unlike Dobrowolny's work, gives a kinetic analysis. Perturbations with transverse wavelength both larger and smaller than the ion Larmor radius are considered. The analysis indicates that there is a large family of microinstabilities of the ‘drift’ type whose mechanism differs from the classical Kelvin–Helmholtz instability.

A pulsed, multi-stage, high-voltage accelerator is proposed which should be capable of producing intense ion beams of many million amperes and many million volts. Super ion beams produced by this type of accelerator can exceed the limiting Aifvén current for light ions, typically 107 A, at which beam pinching occurs. The beam pinching of these super-beams permits them to be precisely focused onto a thermonuclear target. With such an accelerator it seems to be possible to reach a beam voltage of 108 V with a beam current of 107 A. The resulting beam power of 1015 W should be more than sufficient to ignite a DT thermonuclear microexplosion. By the formation of a stable ion beam superpinch within a thermonuclear target, such a large beam power in conjunction with the strong self-magnetic field of the beam may even lead to the ignition of the DD and perhaps HB11 thermonuclear reactions.

The Kelvin–Helmholtz problem in a Hall plasma, including the effects of rotation, is studied. In contrast to previous results, it is shown that if the angular velocity is normal to the wave vector that describes perturbations of the interface, the rotation does not affect the stability of a shear plane. The special case of very small angular velocity is studied and it is shown that the rotation has either a stabilizing or a destabilizing effect, according as the gravitational speed is greater or less than the Alfvén speed.

Considering the influence of relativistic effects on the plasma motion in a HF field, we show that even small relativistic terms qualitatively change the propagation character of nonlinear longitudinal and transverse waves. We also find new regions and branches for the modulational instability.

We derive dispersion formulae for the transverse waves propagating through a collisionless magneto-active plasma in the direction of the magnetic field valid for relativistic as well as non-relativistic temperatures, and compare them with those of earlier works. Wave propagation under various limiting conditions of temperatures and magnetic field are discussed.

In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.

The energetic anti-loss-cone electrons can drive a low-frequency electrostatic instability, propagating transverse to the ambient magnetic field, in the presence of a cold plasma. The typical real frequency and growth rates associated with this instabifity are respectively, of the order of (ωp being the proton cyclotron frequency). The instability has a transverse wavelength ⋍10ρe (ρe being the Larmor radius of energetic electrons). For the parameters pertinent to auroral plasma at 1RE, the quasi-linear analysis shows that the instability can give rise to an oscillating electric field Esat ⋍0.5−25 mV/ m and an increase of 100–103 K in the temperature of cold electrons. The instability may be relevant to recent observations of low-frequency turbulence on the auroral field lines.

Any ion distribution f;i =(θ—ώit) is an exact solution of the Vlasov equation for a uniformly magnetized plasma. Here θ is the phase angle in velocity space and ώi is the Larmor frequency. Then fi rotates rigidly in velocity space with frequency ώ;i about an axis along a magnetic field line. If fi has anisotropy in the perpendicular velocity plane of the form fi(V, t) = fi(V) [1+A cos 2(θ— ώit)], then it represents a density modulation of frequency 2ώ;i which is confined to velocity space. This non-Maxwellian distribution is an oscillating source of free energy (a pump) which may stimulate certain ion Bernstein modes, their frequencies being near harmonics of Ωi. We here investigate the linear kinetic theory of the system. Linearization implies the parametric approximation of a strong constant pump. Application of the theory may be found in the earth's bow shock.

Current driven, ‘helical’ (non-axisymmetric) modes of a tokamak with arbitrary cross-section are considered in the straight (cylindrical) geometry approximation. The plasma is considered surrounded by a resistive wall. The plasma may be unstable on a fast time-scale, namely the MHD or tearing mode time-scale, on a slow time-scale given by the wall properties or it may be stable. The formalism given in this paper allows determination of stability by relatively simple numerical means. In the case of instability on the slow time-scale, the formalism allows determination of growth rates and mode structures. Since the formalism is an eigenvalue formalism with orthogonal eigenfunctions, it is well suited for calculation of the effects on a stable plasma of slow error fields caused by externally driven error currents flowing predominantly in the direction of the ignorable co-ordinate.

A large-scale potential field with an embedded smaller-scale force-free structure (∇ × B = αB) is studied in cylindrical geometry. We consider cases in which α goes continuously from a constant value α0 on the axis to zero at large r. Such a choice of α(r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of º space are calculated, showing time-scales much shorter than the resistive decay time.

A three-dimensional nonlinear Schrüdinger equation for an electrostatic ion cyclotron wave coupled to an ion-acoustic wave in a collision-free plasma consisting of cold ions and two-temperature electrons is derived using the reductive perturbation method. It is shown that a range of wavenumbers corresponding to the instability of a plane electrostatic ion cyclotron wave against a two-dimensional modulation depends on the ratio of temperature of hot and cold electron components.

Propagation of longitudinal electron modes in Maxwellian plasma is discussed using both the Vlasov equation and the 13-moment equations. Both methods are shown to be consistent and in addition both methods are shown to predict a second (heavily damped) mode which propagates below as well as above the plasma frequency. The results are in excellent agreement with earlier experiments for near-equilibrium plasmas.

In this paper, nonlinear interaction of five monochromatic waves in a hot nonuniform streaming electron plasma has been presented. The method of formulation of the problem is based on the coupled mode theory. The wave–wave interaction phenomena have been analysed in the case of three longitudinal and two transverse waves. Furthermore, the presence of a stream velocity and its uniform gradient offers a generalization of the nonlinear interaction of an earlier work.

The equations of MHD equilibrium are solved by including plasma pressure and current in a large aspect-ratio ordering scheme for the calculation of toroidal, l = 3 stellarator vacuum fields. The extended ordering unifies the low-beta equilibrium theory for tokamaks and l = 3 stellarators, and allows solutions to be obtained simply for arbitrarily prescribed pressure and current density profiles. Expressions are given for the equilibrium magnetic field and the equation for the flux surfaces is calculated, including the effects of l = 3 shaping and toroidal displacement. These results are used to calculate equilibria for the parameters of CLEO stellarator, and we examine the role of an externally applied vertical field in reducing pressure-induced flux surface distortion and destruction.

This paper reports on the use of forced magneto-acoustic oscillations to investigate the effect of a torsional hydromagnetic (Alfvén) wave pulse of moderate amplitude on the properties of a partially ionized afterglow helium plasma. Observations of the magnetic flux associated with the oscillations, measured at a number of frequencies, are used to determine radial density proffles and to provide estimates of plasma temperature. The torsional wave is shown to cause significant re-ionization of the plasma with no corresponding increase in the plasma temperature. The torsional wave is shown to cause significant re-ionization of the plasma with no corresponding increase in the plasma temperature. However, the presence of a number of energetic particles is evidenced by the production of a significant number of doubly charged helium ions.

A Liapunov functional is constructed for the plane parallel flow of a multicomponent plasma in an external gravitational field. Sufficient conditions for stability to electrostatic perturbations are obtained. The L2-norms of certain system variables are shown to be bounded uniformly in time.

Convective instability of a plasma slab (contained between two metal walls) subject to a longitudinal external magnetic field is studied. The results show that (i) increase in the ionization rate Z causes a reduction in the stability of the plasma; (ii) the instability persists in the limit k ⇒ 0.

The electromagnetic instability of a relativistic electron beam penetrating an infinite plasma is analyzed. The purpose of this paper is to determine the effect of collisions within the plasma upon the growth rate of the Weibel-type electromagnetic instability. The dispersion relation including the effect of collisions is solved analytically and numerically. It is found that collisions can enhance the growth rate of the electromagnetic instability in the case of low plasma temperature.

A relativistic generalization of the Fokker–Planck formalism has been constructed. This is applied to the study of energy loss of high-energy electrons in plasma. Both the electron–electron and electron–ion scattering have been considered in a relativistic way. The expression obtained for the stopping power differs from that derived with the help of thermodynamic Green's function technique.