We record with sadness the death of Franz Kahn, a former Associate Editor of the Journal of Plasma Physics.

Franz was born in Germany in 1926, but his family emigrated to England in 1938. He attended Oxford University, obtaining First Class Honours in Mathematics in 1947, and continuing as a research student there, eventually gaining his D.Phil. in 1950. His thesis work already involved him in plasma physics, under one of the pioneers of the subject. His supervisor was Sydney Chapman, and his topic was that of the production of plasma by solar flares, and its interaction with the Earth's atmosphere. This field had already been opened by Chapman and a previous pupil, Vincent Ferraro, in the 1930s. The idea had originally been phrased in terms of ‘corpuscles’, i.e. energetic ions and electrons, but it had gradually been realized that electrostatic forces give such a medium a coherence, so that it should be described as a fluid, notwithstanding the lack of collisions. This is of course the basic idea of plasma physics, and when the importance of magnetic fields was included, one had all the ingredients of magnetohydrodynamics.

In order to operate a plasma focus at high axial sheath velocities, the geometry of the inner electrode (anode) of a 3 kJ Mather-type device was modified. Double-stage stepped-anode configurations were tested with the speed-enhanced region sufficiently long for a significant increase in speed but not long enough to allow the development of force-field flow-field separation at the end of the axial phase. Peak axial speeds up to 15 cm μs−1 were achieved. The neutron and soft X-ray productions were found to be sheath-velocity-dependent. A new scaling law for the non-beam component of the neutron yield is proposed.

Large-amplitude, negative-potential solitary waves in a plasma containing positive and negative, cold, collisionless ions and isothermal electrons are studied computationally and analytically. When their amplitude and speed are large, both speed and width are proportional to the square root of amplitude. That is, amplitude is proportional to speed squared, while width increases directly with speed. Approximate expressions relating these quantities are derived.

The L mode in electromagnetic proton-cyclotron waves (EPCWs) propagating parallel to a uniform ambient magnetic field is studied here analytically. A generalized Lorentzian distribution function is used to model the plasma. Analytical expressions for the wavenumber and for both the temporal and convective growth rates for a multi-ion plasma are obtained within the linear theory. This analytical approach is appropiate for β∥<1, which is the ratio of plasma kinetic pressure to magnetic field pressure. The characteristics of the unstable spectrum are found to be independent of high-energy particles. For a plasma composed of electrons plus hot and cold protons, it is shown that the maximum growth rates as functions of cold-proton concentration δ can always decrease, or can increase until δ reaches a certain peak value and decrease thereafter, or can always increase, depending on the thermal anisotropy of the hot protons. This behaviour is similar to that in Maxwellian plasmas. However, for the convective growth rate, the expression for the optimum cold-proton concentration shows a significant dependence on the spectral index κ. Therefore, when cold protons are injected, it is more difficult to obtain optimum amplification in a Lorentzian plasma than in a Maxwellian plasma. It is also shown that the influence of the high-energy tail on the generation and amplification processes of the EPCWs is controlled by thermal anisotropy and cold-ion population. As a consequence of the latter, temporal and convective growth rates can be larger than, equal to or smaller than those of Maxwellian plasmas, depending on the anisotropy of the hot-proton distribution and on the cold-proton concentration.

The propagation of one and two electron beams in a plasma is considered in the case when the source is time-dependent. When the electron-plasmon interaction time is assumed to be much less than the electron flying-off time, the main gasdynamic equations are obtained on the basis of the quasilinear theory of weak turbulence. The solution for a monoenergetic beam is a beam–plasma structure moving with constant velocity. In general, two beams propagate as two beam–plasma structures with constant velocities. However, the second electron beam influences the flying-off dynamics of both beams. This peculiar interaction modifies the shapes of the structures.

The effect of a large ion Larmor radius on the Rayleigh–Taylor instability is investigated using the Vlasov fluid model. The results are compared with an ideal magnetohydrodynamic model. It is found that this effect reduces the growth rate of the Rayleigh–Taylor instability with respect to the ideal magnetohydrodynamic growth rate.

Propagation of nonlinear space-charge waves in an ion-beam–plasma system is investigated in a double-plasma device. The velocity of the beam is high enough to avoid ion–ion instability. The density ratio of the beam to the plasma is kept high ([les ]0.6), which makes the maximum amplitude of solitary waves large. The measured velocity and width of the compressional solitary waves of the fast and the slow beam mode are compared with predictions of the pseudopotential method in which the temperatures of beam and plasma ions are taken into consideration. Reasonable agreement is obtained between the experimental and theoretical results.

The double sheath formed by thermal electrons and negative ions in a plasma and electrons emitted from an electrode is investigated. The ion energy at the sheath edge and the electric field at the electrode surface are calculated for several values of the ratio of negative-ion density to electron density. The maximum beam density above which a virtual cathode appears is given. The relation to the Langmuir limit is shown. The numerical results for the electric potential, the electric field and the space charge density are presented. The floating potential is calculated from the current balance of all components.

The long-wave, small-amplitude dynamics of obliquely propagating Alfvén waves is shown, using a reductive perturbative expansion, to be purely linear not only in one space dimension but also in the dispersionless limit in higher dimensions. Furthermore, in the context of multidimensional wave-train modulation, all the diffraction coefficients are found to tend to zero with the dispersion, while the non-linear terms in the envelope equation remain finite. In this ‘semiclassical’ limit, the envelope dynamics results in the formation of growing regions of finite-amplitude oscillations with a typical scale intermediate between the size of the wave packet and its wavelength.

In a nongyrotropic plasma no symmetry of the distribution function with respect to the velocity space coordinates exists, and, in particular, axial symmetry with respect to the background magnetic field is broken. The propagation of small-amplitude waves and their stability under such conditions are studied here in the framework of linearized Maxwell–Vlasov theory. Two types of nongyrotropic distributions are investigated: stationary and rotating distributions. Stationary nongyrotropy may be maintained by sources and sinks in velocity space. Gyrophase organization couples modes that are decoupled in a gyrotropic plasma, and drives unstable waves in a parallel as well as a perpendicular propagation direction with respect to the background magnetic field. In a rotating nongyrotropic plasma there is an additional coupling of waves at different frequencies that is analogous to a three-wave scattering process. The frequency difference of the coupling modes is just the gyrofrequency of the rotating distribution or its harmonics. This frequency-shifted coupling distributes the energy in a cascade fashion over an extended frequency range. It tends to stabilize the plasma and inhibits wave excitation.

It is shown that the truncation of the infinite hierarchy of fluid equations obtained as moments of the Vlasov kinetic equation leads to a system of nonlinear equations that describe finite-Larmor-radius effects with good accuracy. Inertial terms in the momentum balance, viscosity and heat-flux evolution equations are crucial for a uniform description of the plasma response with an arbitrary Larmor radius. In the low-frequency ordering, the obtained equations are simplified by an expansion in the parameter 1/B, where B is the equilibrium magnetic field. The results of the second-order [Oscr ](1/B2) and the fourth-order [Oscr ](1/B4) closures are compared. It is shown that the accuracy of the description improves for higher-order closures.

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case, the coupled amplitude equations are derived up to third-order terms. The nonlinear coefficients are singular in the limit in which the linear growth rates vanish together. These singularities are analysed using techniques developed in previous studies of a single unstable wave. In addition to the singularities familiar from the single-mode problem, there are new singularities in coefficients coupling the modes. The new singularities are most severe when the two waves have the same linear phase velocity and satisfy the spatial resonance condition k2=2k1. As a result, the short-wave mode saturates at a dramatically smaller amplitude than that predicted for the weak-growth-rate regime on the basis of single-mode theory. In contrast, the long-wave mode retains the single-mode scaling. If these resonance conditions are not satisfied then both modes retain their single-mode scaling and saturate at comparable amplitudes.

A perturbation method for the Vlasov–Poisson system is presented. It is self-consistent and entirely based on Lie transformations, which are considered as active transformations, generating the dynamics of the particle distribution function in the space of distribution functions. The main result is a set of three equations that forms a good starting point for a wide variety of problems concerning nonlinear wave propagation. Besides being efficient, the new perturbation method is systematic and therefore also suited for the use of computer algebra.

The relativistically correct solution of the dispersion relation of linear plasma waves in an isotropic unmagnetized equilibrium electron plasma leads to two new effects unknown from the nonrelativistic dispersion theory. First, the number of damped subluminal modes is limited to a few (mode-limitation effect); secondly, for relativistic plasma temperatures the few individual modes complement each other in the sense that the dispersion relations ωR=ωR(k) continuously match each other (mode-completion effect). The second effect does not occur at nonrelativistic temperatures.