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.

Stationary flows with an ignorable coordinate are analysed and the differential equation for the only independent current function of the problem is obtained for the polytropic, incompressible and adiabatic cases. The possibility of confinement for the stationary symmetric plasma fluxes is then investigated and the confinement conditions are given. Some examples are solved for the particular case of helical symmetry; for general flows it is possible to construct magnetically confined plasma columns only with cylindrical shape; whereas if the plasma velocity has the direction of the ignorable coordinate, we show that it is possible to construct magnetically confined plasma columns with helical shape and plasma flux along the helices.

The gravitational instability of an infinite homogeneous, finitely conducting, rotating, collisionless, anisotropic-pressure plasma in the presence of a uniform magnetic field with finite-ion-Larmor-radius (FLR) corrections and generalized polytropic laws is investigated. The polytropic laws are considered for the pressure components in directions parallel and perpendicular to the magnetic field. The method of normal-mode analysis is applied to derive the dispersion relation. Wave propagation is considered for both parallel and perpendicular axes of rotation. Longitudinal and transverse modes of propagation are discussed separately. The effects of rotation, finite electrical resistivity, FLR corrections and polytropic indices on the gravitational, firehose and mirror instabilities are discussed. The stability of the system is discussed by applying the Routh–Hurwitz criterion. Extensive numerical treatment of the dispersion relation leads to several interesting results. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that rotation stabilizes the system by decreasing the critical Jeans wavenumber. It is also seen that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew–Goldberger–Low (CGL) set of equations in comparison with the magnetohydrodynamic (MHD) set of equations. It is found that the effect of FLR corrections is significant only in the low-wavelength range, and produces a stabilizing influence. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the finite electrical resistivity removes the polytropic index [nu] from the condition for instability. The inclusion of rotation alone or FLR corrections alone or both together does not affect the condition for mirror instability. The growth rate of the mirror instability is modified owing to uniform rotation or FLR corrections or both together. We note that the condition of mirror instability depends upon the polytropic indices. We also note that neither the mirror instability nor the firehose instability can be observed for the isotropic MHD set of equations.

Energy transfer from particles to low-frequency turbulent fields in the non-uniform magnetized plasma is studied. Sufficient conditions for plasma stability are derived taking account of magnetic field shear.

Shock waves in plasmas with strongly anisotropic viscosity and thermal conductivity are considered. The analysis is restricted to the case where the plasma beta is less than unity. The set of two equations that governs propagation of small-amplitude MHD waves at small angles with respect to the unperturbed magnetic field in such plasmas is derived. A qualitative analysis of this set of equations is carried out. It is shown that the shock structure is described by a solution that is a separatrix connecting two stationary points: a stable node and a saddle. This solution describes the structure of a fast quasiparallel shock wave, and it only exists when the ratio of the magnetic field component, perpendicular to the direction of shock-wave propagation after and before the shock is smaller than a critical value. This critical value is a function of the plasma beta. The structures of shock waves are calculated numerically for different values of the shock amplitude and the ratio of the coefficients of viscosity and thermal conductivity.

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.

The positive column of a gas discharge is investigated in the subcritical regime when no self-excited nonlinear ionization wave exists. We derive a model equation for the so-called wave of stratification, which is an externally excited envelope wave. The main point of this work is that, in contrast to previous papers, we take into account the radial structure of the homogeneous column. The mathematical description of the wave of stratification in the form of a complex Ginzburg–Landau equation follows by a systematic reductive perturbation method. The coefficients in the Ginzburg–Landau equation are first calculated in general and are then evaluated explicitly for a low-pressure argon discharge. The results are compared with those obtained from a frequently used simpler model that neglects any radial structure. Finally, the dynamics of the nonlinear wave of stratification is demonstrated via numerical simulations.

Plasma-wave instability caused entirely by an external large-scale electric field E0 is considered for the pure electron Bernstein mode. It is assumed for the angle α between the wave vector k and the normal n to the direction of the external magnetic field B0 that the relation α≈tanα[Lt ]1 is fulfilled. The quasistatic time variation of the field E0, which is parallel to B0, provides the possibility of realizing the direct initiation (by the large-scale field E0) mechanism for the development of instability. An expression for the growth rate is obtained for the case when the external electric field E0 together with Landau damping and pair Coulomb collisions are taken into account in a modified dispersion relation (MDR). This expression is correct in the framework of linear theory for the frequency ranges typical of electron cyclotron waves and Bernstein modes. The influence of the electric field in the MDR is taken into account through the method of Brinca and Dysthe. A numerical analysis of obtained instability is performed for specific values of the plasma parameters.

In this paper, a set of two-dimensional simulations for resistive magneto-hydrodynamical equations are performed to investigate the interaction between a solar-wind filament and the magnetosphere when the filament is obliquely oriented with respect to the direction of the magnetospheric field. Detailed pictures for the interaction are given. For typical parameters near the magnetopause, a filament with a sufficiently large excess flow velocity will penetrate into the magnetosphere, and will then be repelled back towards the magnetopause by the highly compressed and bent magnetospheric field. Finally, the filament will be smeared along the magnetospheric field near the magnetopause. When the angle is small, the filament will penetrate deeply into the magnetosphere before it is repelled back. Therefore there is a maximum depth a penetrated filament may reach into the magnetosphere. The effect of spontaneous reconnections behind a penetrating filament on the penetration appears to be negligible.

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 Kelvin–Helmholtz (K–H) instability of two fluids of plasma streaming in opposite directions with the same velocity and in the presence of an external magnetic field is investigated. The usual magnetohydrodynamic equations with anisotropic pressure are considered. In the present problem, the two pressures parallel and perpendicular to the direction of the magnetic field are defined by polytropic pressure laws. The generalized pressure relations are used, and two equations of state for two pressures are assumed. The equations are linearized, and initially two different flow velocities are taken for the system. The flow is assumed to be in the direction perpendicular to the magnetic field. The problem is solved and a dispersion relation is obtained. From the dispersion relation, the K–H instability condition is obtained. It is found that the instability condition depends upon the polytropic indices of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low systems. It is also found that the growth rate of the instability depends upon various polytropic indices.

The nonlinear mechanism for kinetic-Alfvén-wave (KAW) excitation by upper-hybrid waves (UHWs) is discussed. Taking into account perpendicular dispersion of KAWs, caused by effects of finite ion Larmor radius and electron inertia, we examine a new channel for UHW decay, in which a pump UHW decays into another UHW and an ultralow-frequency wave, KAW: UHW→KAW+UHW. A nonlinear dispersion relation is derived, and the growth rate of the parametric decay instability is calculated for a pump UHW propagating at an arbitrary angle to the background magnetic field. We find that the resulting KAWs often have a two-peaked spectrum with different perpendicular dispersions. Using satellite observations, the analytical results are applied to show that the considered process represents an effective mechanism for KAW generation and the consequent spreading of the UHW spectrum in the Earth's magnetosphere and solar corona.

The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfvén waves (KAWs) are derived by use of plasma kinetic theory. Linear and nonlinear effects of finite ion Larmor radius are kept for arbitrary value of the ‘kinetic variable’ κ=k⊥ρi. The parametric decay KAW→KAW+KAWis investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k2⊥ in both limits κ2[Lt ]1 and κ2[Gt ]1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes Bk/B0[lsim ]10−3. Two applications concerning KAW dynamics in the magnetosphere and in the solar corona show that three-wave resonant interaction among KAWs may be responsible for the turbulent character of their behaviour, often observed in space plasmas.

We derive the dielectric tensor for multicomponent magnetized dusty plasmas, including the effect of capture of plasma electrons and ions by the dust particles. For propagation perpendicular to the external magnetic field and Maxwellian distributions of electrons and ions, we obtain compact expressions for the components of the dielectric tensor, which can be used to analyse wave propagation. An application to the magnetosonic wave is presented.

The effect of neutral-gas friction on Alfvén surface waves propagating along an infinitely conducting viscous plasma–vacuum interface has been investigated. A dispersion relation is obtained for such waves. For different values of the neutral-gas friction parameter S=νc/ω (where νc is the collisional frequency between two components of the composite plasma), the variations of the real and imaginary parts kr and ki of the wavenumber k with the viscosity parameter vp= μlω/ρ01v2A1 (where μl and ρ01 are the coefficient of viscosity and the density of plasma media 1) are shown graphically. It is concluded that a three-mode structure of Alfvén surface waves results flowing to neutral-gas friction. It is suggested that our results are useful for both laboratory and astrophysical plasmas (e.g. photospheres, chromospheres and cool interstellar clouds).

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.

Propagation characteristics of dust acoustic solitons are studied in a magnetized dusty plasma consisting of ions, electrons and negatively charged dust grains. It is found that rarefactive solitons (solitons associated with negative potentials) are possible in such a plasma. The effects on the soliton characteristics of magnetic field strength, wave propagation angle, and densities and temperatures of the plasma particles are analysed.

The recent high core gains of 29% in laser fusion experiments at the LLE Rochester are evaluated and compared with related earlier measurements where surprisingly the self-similarity model for volume compression provides a common description. This is a proof that the isentropic conditions of stagnation-free compression were mostly fulfilled at the optimized experimental gains, in contrast to highly entropy-producing shock and central spark conditions. Some projections are given of how these results may be generalized to volume ignition for the parameters of the NIF (National Ignition Facility). The proof of stagnation-free volume compression for the best laser fusion gains indicates the advantages of volume ignition, which not only is ‘robust’ and simply follows the natural adiabatic compression, but also is much less sensitive to instabilities and mixing. However, its essential advantage is that it is free from symmetry problems – in contrast to spark ignition, with its spherical detonation front.

The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain ks⊥>ρ−1i and an inverse cascade in the domain ks⊥<ρ−1i, resulting in Kolmogorov-type spectra, Wk∼(kz) −1/2(k⊥)−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k⊥ range and p=2 (at k⊥<ρ−1i) and p=3.5 (for k⊥>ρ−1i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.