The spectral density of electrostatic fluctuations is investigated in a plasma containing an excess of suprathermal particles. As a model for the statistical distribution of the suprathermal particles, the kappa velocity distribution is used. It is found that the Debye length λD for such a plasma depends strongly on the spectral index κ of the velocity distribution, and can be much smaller than is commonly found for Maxwellian plasmas. Consequently the plasma parameter g=1/nλ3D can be larger, and plasma effects that depend on particle discreteness more important, than for a Maxwellian plasma. Consequently, levels of fluctuation are higher, and their extent in wavenumber and frequency greater, in plasmas containing suprathermals. Results for a number of different ‘concentrations’ of suprathermal particles are discussed and interpreted in terms of the normal- as well as transient-mode behaviour of the plasma. Both the cases Te[Gt ]Ti and Te=Ti, as well as κe[Lt ]κi and κe[Gt ]κi, are investigated.

This issue of the Journal of Plasma Physics is dedicated to Radu Balescu on the occasion of his 65th birthday.

Of the more than 170 articles published worldwide by Professor Balescu to date, more than 25 have been published in this journal. Readers of the Journal of Plasma Physics will thus be well acquainted with his contributions to the study of the interplay between plasma turbulence and the theory of transport phenomena in magnetically confined plasmas. A vast community of students, teachers and researchers will also have read or consulted the many monographs, five to date, written by Balescu and world-famous for their clarity. In his first monograph, Statistical Mechanics of Charged Particles (Interscience, New York), published in 1963, the whole of plasma physics, including the transport equation to which his name will remain attached, was put into the broader context of statistical physics. The monograph Equilibrium and Non-Equilibrium Statistical Mechanics (Wiley-Interscience, New York) followed in 1975, and still inspires many teachers today.

The author's previous work on the Rayleigh–Taylor instability is extended to the Kelvin–Helmholtz instability, and the maximum growth rate of a perturbation and an estimate of its upper bound is obtained for an infinite fluid layer under horizontal rotation where the density, horizontal velocity (shear) and magnetic field are continuously stratified in the direction of gravity. Conclusions are drawn about the possibility of stability for some directions of propagation of the perturbation, even in the case of unstably stratified density. It is also shown that the new terms that appear owing to the interaction of the horizontal shear flow, horizontal rotation and stratified magnetic field increase the range of values that contribute to the estimate of the maximum growth rate compared with previous work. Furthermore, a generalization of the sufficient condition for stability under horizontal rotation alone obtained by Johnson is calculated in the presence of density stratification. A new method is also given to obtain a sufficient condition for stability when a magnetic field is present in addition to rotation and density stratification.

The over-reflection of magnetoacoustic ion-cyclotron waves in a warm Hall plasma is investigated. It is shown that the effect of the Hall term is to strongly support over-reflection, thereby destabilizing the flow. Its relevance to the current-vortex sheet of the magnetosheath resulting from the interaction of the solar wind and the Earth's magnetopause is pointed out.

The guiding-centre equations of motion of a classical charged particle in a strong magnetic field and a strongly sheared electric field are derived. They can be used to analyse the dynamics of particles in electromagnetic fields whose spatial profiles are similar to those observed during the H mode in the DIII-D tokamak, for instance. The derivation of the equations of motion is performed up to second order in the drift parameter by applying a Hamiltonian pseudocanonical transformation that removes the gyrophase induced by the magnetic field. The main difference with the standard case of a slowly varying electric field relates to the variation of the new gyrophase and to the expression for the magnetic moment: mv2⊥/2B must be replaced by

formula here

The latter case is also reconsidered – mainly to reveal the consequences of the removal of a hidden divergence for small parallel velocities resulting from the usual averaging transformation.

From 1990, the boronized TEXTOR tokamak was characterized by an improved confinement (coined the ‘I mode’) at high power that was substantially better than the L mode, but densities had to be limited to n[bar]e0/nGR[lsim ]0.5–0.6, where nGR is the Greenwald density limit. With the injection of Ne, Si or Ar in order to increase the edge radiation and provided that γ=Prad/Ptot[greater, similar]0.5, PNBI-co/Ptot[greater, similar]0.25 and n[bar]e0/nGR[greater, similar]0.75, a further improved confinement called the radiative improved mode (RI mode) was discovered in 1993 on TEXTOR, a tokamak of intermediate size, and confirmed on TEXTOR-94. The radiated power fraction γ can reach 0.9, and the radiation is nearly isotropically distributed over the torus wall. The RI mode is characterized by its ability to obtain simultaneously and stationarily high densities and high confinement. It is linked to a substantial lowering of edge ne, Te and Ti, a reduction in particle transport and a peaking of the density profile. The RI-mode confinement scales on TEXTOR as τE= (n[bar]e0/nGR)τITERH93-P and values up to n[bar]e0/nGR≈1.2 are obtained. There is no detrimental concentration of the seeded impurity at the centre of the plasma. Results of three different interpretative and modelling approaches are in agreement with the improved confinement features; the preliminary indications are that ITG turbulence is strongly reduced. The Z mode observed on ISX-B has a clear resemblance to the RI mode. The very favourable features of the RI mode justify efforts in trying to establish it on larger machines to verify if the present scaling then holds.

The structure of a microwave gas discharge produced and sustained by a surface wave (SW) propagating along a cylindrical metal antenna with a dielectric coating is studied. The SW that produces and sustains the microwave gas discharge propagates along an external magnetic field and has an eigenfrequency in the range between the electron cyclotron and electron plasma frequencies. The presence of a dielectric (vacuum) sheath region separating the antenna from the plasma is assumed. The spatial distributions of the produced plasma density, electromagnetic fields, energy flow density, phase velocity and reverse skin depth of the SW are obtained analytically and numerically.

A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function   (r, t). The wave phase   (r, t) is implicitly determined by an equation of the form f( )=r·n( )−λ( )t, where n( ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f( ) determines whether the wave is a centred (f( )=0) or a non-centred (f( )≠0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase   plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

The well-known van Kampen–Case treatment of the Vlasov equation leads to a spectrum on the real axis. In this paper we show that, by going to a ‘rigged’ Hilbert space, we can derive a spectral representation that is complex and breaks time symmetry. This leads to a semigroup description in which the decay rates due to the Landau damping appear explicitly in the spectrum. Moreover, we can then define an entropy. In this way, the relation between Landau damping and irreversibility is made explicit. The analogy with the well-known Friedrichs model is stressed.

The nonlinear evolution of Kelvin–Helmholtz instability is examined in 2+1 dimensions in the context of magnetohydrodynamics. When the velocity difference U is less than the critical velocity Uc, the equation governing the amplitude evolves into a self-focusing singularity. The self-focusing of waves predominates at short wavelengths, is directionally dependent, and also depends sensitively on the strength of the applied magnetic field. The minimum velocity that allows the existence of self-focusing increases with increasing magnetic field strength. The explosive instability at the second-harmonic resonance is also investigated.

We investigate theoretically the aspect-ratio dependence of Alfvén-wave current drive (AWCD) in ‘simulated’ tokamaks, in the range 1.1[les ]R/a[les ]10 (where R and a are the major and minor radii, respectively). The study is carried out within the framework of resistive MHD, and is based on the consistent solution of the full-wave equation (E∥≠0); both shear and simulated toroidicity effects are taken into account. The AWCD includes components due to (wave) momentum transfer, helicity injection and plasma flow. The aspect-ratio-dependent features investigated include the radial profiles as well as the integrated power absorption, current drive and efficiency; the effects of antenna parameters (wavenumbers and frequency) are also explored. The numerical code developed and used for these computations has been benchmarked with the aid of analytical solutions obtained for the antenna–metallic-wall system in vacuum, as well as by the smooth transition from the vacuum case to the actual plasma case. Results of extensive calculations for the so-called Alfvén-continuum frequency range are presented and discussed.

The electron energy distribution function in a microwave discharge at the electron cyclotron resonance (ECR) condition is studied using a two-dimensional Fokker–Planck equation in the bounce-averaged approach. Our model takes into account the effects of linearized Coulomb collisions, electron cyclotron resonance heating in the quasilinear approximation, the effects of ionization and excitation of atoms, elastic scattering of electrons on atoms, and the self-consistent ambipolar potential. The plasma is considered to be slightly collisional, so that bounce averaging is valid. We perform a numerical investigation of the Fokker–Planck equation and obtain the dependences of the discharge characteristics on the parameters of the model, such as breakdown threshold values of neutral density, and the dependence of the electron density, temperature and ambipolar potential on the parameters of the ECR wave and gas density. Some results are compared with experimental data.

We demonstrate with numerical WKB solutions that stationary density profiles can exist in a crossed-field amplifier. These are density profiles that can exist in equilibrium with a high-frequency (RF) wave propagating in the slow-wave structure. These density profiles are very different from the usual Brillouin profiles. They have a finite and negative density gradient, and extend from the cathode to the anode. They carry a DC current proportional to the RF power in the slow-wave structure. The source of the DC current is a wave–particle resonance that occurs toward the top of the sheath. This resonance drives any Brillouin electron flow unstable. The electrons then redistribute themselves into a new flow – one that can be stationary in the presence of the wave–particle resonance. The new flow has a spoke-like structure, where the spokes carry the current to the anode. Various plots are given, including the DC voltage operating range, DC current flow, phase shifts, and density profiles of the total electron distribution, for various ambient magnetic fields and DC voltages. Numerical values agree reasonably well with the modelled experimental device.

Ion collisions in plasmas cause damping of hydromagnetic modes, but also a strong Hall effect if the collision time is of the same order as the gyroperiod. This is known to be very marked in the E region of the Earth's ionosphere, but should also occur in other partially ionized space and laboratory plasmas. In this work dynamic effects of such Hall currents are investigated theoretically. The linear modes that are obtained are, for sufficiently large scales, distinctly different from ordinary damped Alfvén modes, and similar to whistler waves even when the dynamic time scale is much longer than the ion gyroperiod. The dynamics of the coupling between planetary ionospheres and magnetospheric plasmas may be viewed as a reflection of Alfvén waves at a sharp boundary. By applying the results of the linear mode analysis, it is shown that the usually employed reflection coefficient needs to be replaced by a reflection tensor for large-scale waves due to self-induction of ionospheric Hall currents. This is similar to the magneto-optical Kerr effect, which is well-known in solid state physics. In the Earth's ionosphere, variations from incident torsional modes over periods as long as several minutes, which have been observed to occur over scales of a few thousand kilometres, are predicted to cause the generation of substantial eddy electric fields and compressional flows. Consequences for the energy exchange between ionosphere and magnetosphere and possibilities to observe the effect are discussed.

An understanding of the mechanisms leading to the symmetry breaking of the dynamical description of a large system with respect to the direction of time is necessary, but not sufficient to ensure the finding of a functional of the state of the system that would satisfy the requirements placed by the Second Law of Thermodynamics upon the non-equilibrium entropy S.

Ordered structures as well as chaotic motion of the magnetic electron drift vortex (MEDV) mode in a unmagnetized nonuniform plasma are discussed. In the collisionless limit, the nonlinear MEDV waves can self-organize into dipolar vortices or vortex chains. The latter exist in the regime where dipolar vortices are forbidden. When dissipation is included, the governing equations for the MEDV mode can be cast into the form of the Lorenz equations, so that chaotic solutions can exist.

The interaction of a powerful non-symmetric laser pulse with a plasma is studied. The non-symmetry is manifested in an abrupt cut-off of the rear edge of the laser pulse compared with its leading edge. At the same time, three qualitatively different regions are distinguished: the leading edge, the rear edge and the region behind the pulse, where it leaves a wake in the form of generated fields. An analytical solution has been found that defines the longitudinal accelerating field at the end of the rear edge. The results of numerical calculations confirm our physical point of view that the non-symmetry of the laser pulse increases the duration of the ion channel behind the front, thereby enhancing the focusing and effective acceleration of electron bunches.

The Van Kampen mode discussion of plasma oscillations is briefly reviewed alongside theories of non-equilbrium statistical mechanics and attention is drawn to illuminating connections between them.

Asymptotically matched solutions for electron and ion density, electron and ion velocity, and electric potential are obtained in the boundary region of a dense low-temperature plasma adjacent to perfectly absorbing walls – walls that absorb, without reflection, incident electrons and ions. Leading-order composite solutions, valid throughout the boundary region, are constructed from solutions in three subdomains distinguished by different physical length scales: the geometric length, the ion mean free path and the Debye length. The composite solutions are used to assess the impact of electron–ion recombination in the ionization nonequilibrium region on sheath and presheath profiles, and on quantities evaluated at the wall. While, at leading order, the velocity profiles throughout the boundary region are not influenced by recombination, the density and potential profiles are significantly altered when recombination is included. These results show that the region of rapid change in these profiles lies closer to the wall when recombination is explicitly included in the model. The influence of recombination on the presheath potential, and consequently the wall potential, is found to scale as the natural logarithm of the recombination length. The broadening of the density profile results in a larger flux of ions accelerating through the sheath and impacting on the wall. The influence of recombination on the ion power flux to the wall is found to scale with the inverse recombination length. This scaling influences the prediction of surface erosion rates in technological applications that utilize these plasmas.

The reaction of an equilibrium tokamak plasma to a sudden localized deposition of heat is investigated by means of numerical simulations of the time-dependent equations of resistive magnetohydrodynamics (MHD) in two spatial dimensions, in order to obtain a better understanding of the structure and dynamics of the hot plasma filaments that are observed in recent tokamak experiments. Simulation results show that the fast heating generates MHD waves and creates a localised hot filament. Pressure perturbations are carried away from the heated area by slow waves, even when the heating is applied on the Alfvén time scale. When a temperature-dependent resistivity is considered, a current peak is formed at the place of the temperature peak, and the order of magnitude of the current is given by the condition that ηJz is constant. Next to the wave dynamics, the simulations show another type of hot filament dynamics caused by j×B forces. These forces drive filaments to the centre of the plasma at a nearly constant velocity, which decreases for smaller resistivities. Two filaments can merge under the influence of this current–current interaction. This process happens on a very long time scale. For realistic tokamak resistivities, the coalescence of filaments may take place on time scales of the order of the experimentally reported lifetime of filaments, and may thus be the mechanism that determines the lifetime of the filamentation process.