The distribution function of the minority ions during ion-cyclotron heating is calculated from a kinetic equation composed of a Landau collision term and a surface-averaged quasi-linear heating term. The kinetic equation is solved by a moment method in which the minority-ion distribution function is expanded in irreducible tensorial Hermite polynomials. The coefficients of the expansion are shown to be solutions of a system of coupled algebraic equations, and the effective minority-ion temperature is deduced from a compatibility constraint. The latter equation is in general too complicated to be solved analytically. The distribution function obtained here is therefore a semi-analytical result.

Recently Mace et at. studied electron-acoustic solitary waves in a plasma using a pseudopotential approach. To find the finite ion-temperature Sagdeev potential, they used a numerical technique developed by Baboolal, Bharuthram & Hellberg. In this paper we show that the exact pseudopotential can be obtained in this case in an analytical form. The numerical results obtained by Mace et at. are compared with our result, and complete agreement is found. We also discuss the conditions for the existence of solitary-wave solutions, and obtain the soliton solutions in some cases when these conditions are satisfied.

In classical kinetic and transport theory for a fully ionized plasma in a magnetic field, collision integrals from a uniform theory without fields are used. When the magnetic field is so strong that electrons may gyrate during electron—electron and electron—ion interactions, the form of the collision integrals will be modified. Another modification will stem from strong non-uniformities transverse to the magnetic field B. Using collision terms that explicitly incorporate these effects, we derive in particular the temperature relaxation between electrons and ions and the particle transport transverse to the magnetic field. In both cases collisions between gyrating electrons, which move along the magnetic field, and non-gyrating ions, which move in arbitrary directions at a distance transverse to B from the electrons larger than the electron Larmor radius but smaller than the Debye length, give rise to enhancement factors in the corresponding classical expressions of order In (mion/mel).

A solution of dissipative nonlinear MHD taking account of the balance between viscous drag, the Lorentz force, resistive diffusion and inertia in a boundary- layer approximation is presented. It is a steady solution corresponding to a jet in a conducting fluid with viscosity. The problem is solved using a self-similar variable. An exact analytical solution is possible. The integrals of motion are obtained and their physical meaning is explained. The behaviour of the solutions is described. The entrainment of the jet is observed in some examples after an initial stage dominated by magnetic fields. These solutions are an extension of Bickley's jet for a case with magnetic field and resistivity.

By determining to first order the growth rate of a small, long-wavelength, perturbation to a Zakharov–Kuznetsov plane soliton moving at an angle α to the magnetic field, it has been found that such solitons are unstable for α α0( ∼ 38 °). To determine the stability for angles greater than α0, one needs the growth rate to higher order. The conventional approach generates a second-order growth rate that is singular at α = α0. We rigorously obtain an expression that is bounded at this point, by developing a method in which exponentially secular terms that arise are regrouped before their subsequent elimination. We then show that these solitons are unstable for all α, although the growth rate is small for α>α and goes to zero as α→½π. The relevant linearized equation is solved numerically, and excellent agreement between analytical and numerical results is obtained.

A systematic procedure is given for generating analytic approximations to the wave–particle energy transfer in magnetized transit-time interactions. The procedure can be applied to any wave-packet field structure, and yields especially simple results in the physically important limits of (i) small and large Larmor radius and (ii) small and large values of the ratio of the wave frequency to the cyclotron frequency. In many applications, the approximations developed here are the only viable means of calculating the wave—particle energy transfer, because the exact analytic theory and numerical test-particle calculations are too demanding computationally.

Large-amplitude magnetic field fluctuations often accompanied by density variations are frequently observed in front of the earth's bow shock and in the vicinity of comets by extraterrestrial in situ measurements. They are identified as a manifestation of magnetohydrodynainic (MHD) waves in space plasmas. Because of their large amplitudes (i.e. because the magnetic field amplitude is of the order of the ambient magnetic field, for instance), these fluctuations cannot be satisfactorily described by linear wave theory. In this paper the properties of one-dimensional MHD waves of arbitrary amplitude, i.e. so-called simple MHD waves, are investigated, and a relationship is derived between the enhancement of the magnetic field and the density as well as the propagation velocity. Fast large-amplitude magnetosonic waves exhibit wave steepening. Here the dependence of the steepening time on the wave amplitude is derived and illustrated numerically.