The evolution of solitary waves is studied using the KP equations derived by employing the reductive perturbation technique. It is revealed that the relativistic effect plays a role in the formation of double layers in multi-temperature electron plasmas. Because of the singularity in soliton propagation introduced by the zeros in the nonlinear coefficients of the KP wave equations. Owing to the appearance of zeros in the nonlinearity, there might be a continuous modification of the KP equation. The relevant properties of compressive and rarefactive solitons as well as shock-like soliton are considered. It is possible that the layers of various solitary waves might be observed in plasmas.

This paper reviews some of the conditions for electron MHD, and shows how this leads to anomalous resistivity, which plays an important role in the behaviour of plasma opening switches (POS are switches, based on the modification of the global resistance of a plasma flow, used to shorten the characteristic time of pulse power machines and increase their performances). Anomalous resistivity is build up from a transfer of momentum between the electrons and ion acoustic waves, which in turn modify the momentum of ions. One of the main consequences of EMHD is the diffusion of B in the plasma. A rough model envisions this diffusion as a propagation of nonlinear waves that may compete with convective transport.

A theory of current and energy modulations in an electron beam propagating through a grounded drift tube is developed. The theoretical analysis is based on the assumption that each beam segment has a prescribed current profile at the drift-tube entrance. It is shown that the current modulation amplitude decreases, reaches its minimum value and increases as the beam propagates downstream. The current modulation in the linear regime is described by a sum of the forward and backward density waves. On the other hand, the energy modulation in the linear regime is described by the difference between the forward and backward density waves.

It is shown here that the marginally mirror-trapped fraction of newly born fusion alpha particles in deuterium–tritium (DT) reaction-dominated tokamak plasmas can induce a two-stream cyclotron radiative instability for fast Alfvén waves propagating near the harmonics of the alpha-particle cyclotron frequency ωcα. This can explain both the experimentally observed temporal behaviour and spatially localized origin of the fusion-product ion cyclotron emission (ICE) in TFTR at frequencies ω≈mωcα.

The role of magnetic fields during the initial stages of protostellar cloud collapse is investigated, in particular with respect to the scenario where the magnetic force can be an effective compressor due to diamagnetic effects. A multifluid approach involving electrons, ions of different atomic masses and neutrals is adopted, where each species is treated separately. The electron fluid is compressed by the magnetic pressure force, and the other ion species are pulled by the collective electric field developed by the space charge separation. The neutrals are also dragged owing to collisions with the ions. The difference in charge-to-mass ratio ensures that each ion species is accelerated differently, resulting in a distribution following their atomic masses. This model explores the scenario where the electromagnetic forces can achieve a supercritical mass-to-flux ratio in a magnetized cloud before dynamical collapse due to gravity takes over.

A large-orbit gyrotron may operate at higher beam currents if one introduces a plasma in its interaction region. The plasma, however, is unstable to an upper-hybrid electrostatic perturbation driven via cyclotron interaction by the rotating relativistic electron beam. The growth rate of the instability is comparable to the growth rate of the cyclotron maser instability when the plasma frequency is of the order of the electron cyclotron frequency.

It is found that the admixture of weak higher short-wavelength modes (several percent of the coupled power) in the spatial power spectrum of the lower-hybrid waves radiated from the waveguide grill into an inhomogeneous scrape-off-layer plasma in tokamaks has a profound influence on the ponderomotive effects of these waves. Using the barometric formula with the ponderomotive force potential for the electron density, we solve the coupling problem self-consistently for four modes using the shooting and matching method to fulfil surface impedance boundary conditions determined by infinite-grill theory. For the symmetric spectrum, below threshold, the total reflection coefficient is independent of the coupled power. Also, at these power levels, isolated density depressions (cavitons) are formed in the spatial locations where there is constructive superposition of short- and long-wavelength modes. Intense mutual mode conversion of these waves occurs at these sites. For power levels above threshold, the reflection coefficient increases until it saturates at higher powers. Numerical results are given for the 24-waveguide grill mounted on the ASDEX tokamak.

The linear and nonlinear response tensors describe the response of a plasma to an electromagnetic field disturbance. A novel construction of the linear and quadratic response tensors for an unmagnetized collisionless plasma is presented here using a convenient 4-tensor notation. The construction uses the equations of charge continuity and gauge invariance, together with symmetry properties and dimensional arguments, to constrain the coefficients of an arbitrary linear combination of tensors. A new interpretation of the response tensors follows as expressions uniquely determined by fundamental physical constraints, and not simply as coefficients in a perturbation expansion of induced plasma response.

The description of oscillations in inhomogeneous magnetohydrodynamic plasmas in terms of spatial Fourier modes is extended beyond the previous analyses of the incompressible case to a fully compressible plasma in a rigid box. Attention is focused upon the cusp and Alfvén continua and the discrete fast-mode spectrum. As well as providing a convenient method of numerical solution, the modal approach yields novel insights; in particular, the energy ultimately ‘absorbed’ resonantly is just that initially (and always) residing in the continua, and is readily calculated.

A systematic study of non-inductive current drive via helicity injection by global Alfvén eigenmode (GAE) waves is carried out. For illustration, the first radial mode of the discrete resonant GAE spectrum is considered. The following aspects are given special attention: spectral analysis, radial dependence and efficiency – all of these as functions of the characteristics of the waves launched by an external, concentric antenna (i.e. wave frequency and poloidal and toroidal wavenumbers). The tokamak plasma is simulated by a current-carrying cylindrical plasma column surrounded by a helical sheet current and situated inside a perfectly conducting shell, with incorporation of equilibrium (simulated) toroidal field, magnetic shear and a relatively large poloidal magnetic field component. Within the framework of low-β MHD model equations and for typical tokamak physical parameters, the following basic results are obtained: (1) in the range of poloidal wavenumbers −3[les ]m[les ]3 and toroidal wavenumbers −20[les ]n[les ]20, resonant GAE peaks below the Alfvén continuum are found; (2) the power absorption (P), current drive (I) and corresponding frequency of the GAE modes depend strongly on the sets of (m, n) values considered; (3) the ‘net’ current drive is positive (i.e. flows in the direction of the equilibrium current j0z) for m=−1, −2, −3 and −20[les ]n[les ]−1 as well as for m=+1, +2, +3 and n>10; (4) in the cases m=−1, −2, −3, the efficiency of current drive, I/P, increases with [mid ]m[mid ] and 1/[mid ]n[mid ]; (5) the radial localization of the current drive in each of the cases considered is determined and tabulated.

Multiple–scales perturbation methods are used to derive equations describing wave–wave interactions in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension. Two problems are considered: (a) the interaction between short-wavelength waves in a non-uniform large-scale background flow, and (b) wave interactions between long-wavelength waves propagating through a uniform background medium. The short-wavelength wave equations describe the interaction between the backward and forward thermal gas sound waves and the contact discontinuity eigenmode via ‘wave mixing’, in which the waves are reflected by gradients in the large scale background flow. The equations also contain quadratic wave interaction terms describing (i) the Burgers self-wave interaction term, (ii) mean–wave-field interaction terms in which a specific wave interacts with the mean field of the other waves, and (iii) three-wave resonant interactions that describe how a sound wave resonantly interacts with the contact discontinuity to generate a reverse sound wave. In the limit of no interaction between the cosmic rays and thermal gas, and for a uniform background state, the equations reduce to two coupled, integro-differential Burgers equations derived by Majda and Rosales for resonantly interacting waves in adiabatic gasdynamics. The short-wavelength equations also contain squeezing instability terms associated with the large-scale cosmic-ray pressure gradient, which were first investigated by Drury and Dorfi. A generalized wave-action equation, or canonical wave-energy equation, variational principles, and WKB analyses of the linearized equations are used to investigate the modification of the cosmic-ray squeezing instability by wave mixing. Coupled Burgers equations are also derived in the long-wavelength regime that describe resonant wave interactions for weak, diffusively smoothed cosmic-ray-modified shocks. In the latter equations, the cosmic-ray-modified sound waves can resonantly interact with either the contact discontinuity or the cosmic-ray pressure-balance mode to generate a reverse sound wave.

A two-fluid model is established to study the effect of injection on the structure of cosmic-ray-modified shocks. The model comprises a thermal plasma and cosmic rays. The cosmic rays are considered to be a massless fluid with significant pressure. Its behaviour is governed by the cosmic-ray energy equation, which can be derived from the transport equation. A term in the equation responsible for injection is proportional to the negative divergence of the plasma velocity. The rest of the dependence has to be introduced phenomenologically. It is expected that the injection of cosmic rays increases if the thermal plasma energy density increases. To fix ideas, we assume that the injection is linear in the thermal pressure. By suitable redefinition of some quantities, this model can formally be recast into a model without injection, i.e. the injection is ‘transformed’ away mathematically. Hence the results are similar to those for the modified shocks without injection. Nonetheless, there are differences. The system with injection prefers a smooth shock transition. The reason is that the injection softens the equation of state of the plasma, and induces an extra cosmic-ray partial pressure. The dependence of the effficiency of shock acceleration on the injection is also discussed.