Using kinetic theory, the electron-acoustic instability is investigated in a three-component plasma consisting of a hot electron beam and stationary cool electrons and ions. In the model considered here both the electrons and ions are magnetized, with the beam drift along the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is studied. In addition, the effects of anisotropies in the velocity distributions of the hot electron beam and the cool electrons on the instability growth rate are examined.

Weyl's well-known theorem describing the behaviour of the entropy on the Hugoniot for gasdynamics is extended to magnetohydrodynamics. In so doing, it is pointed out why similar thermodynamical arguments are not easily established for more complicated reacting fluids such as the gasdynamical equations with mass-loading.

The problem of nonlinear surface Alfvén waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schrödinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field.

A study is made of the induction of a direct field-aligned current due to Alfvén waves excited through an initial–boundary condition for an incompressible fluid with high conductivity in a non-uniform magnetic field. A simple but exact case is considered in which the direction of inhomogeneity of the magnetic field is perpendicular to that of the shear fluid motion at the boundary, and the fluid moves across the magnetic field. The boundary does not satisfy the frozen-flux condition, but has a large Lundquist number. The conductivity of the fluid held between the two boundaries is high, and the frozen-flux condition is approximately satisfied there. A preflare stage of the sun is investigated, and a reasonable magnetic field intensity and d.c. field-aligned current in the magnetic arcade are obtained for a given horizontal shear motion that is antisymmetric at both boundaries of the arcade foot points, taking account of the observed horizontal fluid motion.

The theory of particle aspect analysis is extended to a drift wave in the presence of an inhomogeneous magnetic field and an applied electric field parallel to the ambient magnetic field. The effect of a parallel electric field is included in the zeroth-order distribution function through modification of the particle thermal velocity in that direction. The plasma under consideration is assumed to be anisotropic and with low β. The dispersion relation and growth rate are evaluated and discussed for particular plasma parameters. The limitations of the theory are also pointed out.

Solutions of the full nonlinear Vlasov–Poisson system for a one-dimensional unmagnetized plasma that correspond to undamped travelling waves near Maxwellian equilibria are analysed numerically using the splitting scheme algorithm. The numerical results are clearly in favour of the existence of such waves and confirm that there is a critical phase velocity below which they cannot be constructed.

For relativistic amplitudes (‘intense propagation’), modulations of electromagnetic (EM) waves in a cold plasma are strongly coupled to longitudinal modes via the ponderomotive force, even if the unmodulated wave is purely transverse. The effect of longitudinal motions is comparable to that of relativistic nonlinearities. Hence a correct and proper expansion procedure requires solution of all the field equations up the appropriate order, including the longitudinal equations. (The plasma is assumed to be fully ionized and cold, with no net charge. The positive component may consist of either positrons or singularly charged ions. Quasi-neutrality is not imposed, but deviations are shown to be small for slow modulations.) We begin by deriving envelope equations (i.e. a reduced set of partial differential equations) governing modulations of intensely propagating, circularly polarized, plane EM plasma waves. (Here the envelope equations are not merely accurate to the appropriate order, but in fact exact.) We then analyse their modulational instabilities. Since the envelope equations are exact, they include the weakly relativistic case (transverse velocities ≪ c) as a limit. We first verify that, in this limit, the envelope equations yield the nonlinear Schrödinger equation (NLS) complete with the correct coefficients and thus the correct modulational instability conditions. Next, although the NLS does not hold for the general case of fully relativistic systems (transverse velocities comparable to c), we still succeed in deriving the modulational instability properties of intensely propagating EM waves in the fully relativistic case directly from the envelope equations, again, reproducing the weakly relativistic case as a test of the perturbation method used. Finally, we apply the results in special cases. For example, in the ultrarelativistic limit (transverse velocities close to c) of either an electron—positron or ion—electron plasma, waves with frequencies below twice the relativistic plasma frequency ωp, where , are unstable. The time scale for growth is comparable to the time for a wave packet to move past a fixed point. (This time scale is much shorter than in the weakly relativistic case, where the time scale for instability is that of the spreading of the wave packet due to linear dispersion.) Our results have important consequences for observations of pulsar micropulses, possible technological applications, and general implications for applications of Whitham theory.

In this paper, we use the hydrodynamic approach to study the stimulated scattering of high-frequency electromagnetic waves by a low-frequency electrostatic perturbation that is either an upper- or lower-hybrid wave in a two-electron-temperature plasma. Considering the four-wave interaction between a strong high-frequency pump and the low-frequency electrostatic perturbation (LHW or UHW), we obtain the dispersion relation for the scattered wave, which is then solved to obtain an explicit expression for the growth rate of the coupled modes. For a typical Q-machine plasma, results show that in both cases the growth rate increases with noh/noc. This is in contrast with the results of Guha & Asthana (1989), who predicted that, for scattering by a UHW perturbation, the growth rate should decrease with increasing noh/noc.

We investigate the parametric decay and modulational instabilities of a large-amplitude circularly polarized dispersive Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter waves at arbitrary angles to the background magnetic field, although our main concern in this paper is the exploration of new aspects of propagation parallel to the DC magnetic field. In addition to the well-known coupling of pump waves to electrostatic daughter waves, we find a new parametric channel where the pump wave couples directly to electromagnetic daughter waves. Excitation of the electromagnetic instability occurs only for modulation (k/k0 ≤ 1) and not for decay (k/k0 < 1). In contrast with the modulational instability excited by the electrostatic coupling, the electromagnetic modulational instability exists for both left-hand (K > 0) and right-hand (K < 0) polarization. For large k/k0, the electromagnetic channel dominates, while at lower values the electrostatic channel has a larger growth rate for modest values of dispersion, pump-wave amplitude and plasma β. Unlike the electrostatic modulational instability, the growth rate of the electromagnetic instability increases monotonically with increasing pump wave amplitude. This analysis confirms that, for decay, the dominant process is coupling to electrostatic daughter waves, at least for parallel propagation. For modulation, the coupling to electromagnetic daughter waves usually dominates, suggesting that the parametric modulational instability is really an electromagnetic phenomenon.

We investigate the parametric instabilities of a large-amplitude circularly polarized dispersive parallel-propagating Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter and side-band waves at arbitrary angles to the background (DC) magnetic field. We present the characteristics of the decay and modulational instabilities as functions of propagation angle. We find, in addition to the well-known decay and modulational instabilities, that at oblique and perpendicular propagation there is another parametric instability, namely the filamentation instability, which is characterized by a broad band-width in wavenumber and which satisfies the condition Re (ω) ≪ γ. A second parametric process at oblique and perpendicular angles of propagation, which has not been reported before is also investigated, namely the parametric magneto-acoustic instability. This instability is distinct from the filamentation instability in that it is characterized by density perturbations with large real frequencies that satisfy the condition Re (ω) ≫ γ. Unlike the filamentation instability, the magneto-acoustic instability extends over a broad angular range, but has a very narrow band-width in wavenumber. We report the dispersive characteristics of the filamentation and magneto-acoustic instabilities as functions of plasma β dispersion η and pump amplitude η for arbitrary propagation angles.

We study the nonlinear stability of a one-dimensional hydromagnetic cavity into which Alfvén waves are fed by harmonic shear motions of its boundaries and where they interact with slow magnetosonic waves. We use characteristic conditions for the outgoing and ingoing Alfven waves at the boundaries where the magnetosonic oscillations are required to vanish. Forcing of Alfven waves takes place at a frequency close to the eigenfrequency of the lowest-order mode of the cavity. We let the frequency detuning δω vary as a free parameter together with the amplitude of the forcing, the plasma β and the compressive Reynolds number Re0. Given these last three parameters and varying δω, we calculate the amplitude of the nonlinear equilibrium state of the cavity as the stationary solution of a simple forced, dissipative dynamical system that governs the evolution of the cavity over a slow time scale and to which we are led by multiple-scale and Galerkin analyses of the one-dimensional MHD equations. This amplitude is a multi-valued function of δω (bistability), and we discuss the possibility of nonlinear stabilization of the Alfven wave by locking it in one of the bistable states. This amplitude undergoes saddle-node bifurcations: we calculate the two values of δω at which this occurs and the lowest value of the Reynolds number (27/2) for this to happen. We show that the magnetic energy density released during a bistable transition scales as (Re0)2; it has a maximum at β = 1 - (⅔)½ and it may amount to a substantial part of the energy originally stored in the unperturbed cavity. The magnetic power density released scales as (Re0)3 and has a maximum at β = 1 ± (⅓)½5. We conclude that the cavity is a good site for plasma heating such as that of the solar corona.

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.