An electromagnetic particle-in-cell simulation code is used to investigate particle density effects on the nonlinear amplification of inverse-bremsstrahlung electron acceleration, according to the schemes proposed by Kawata et al. and by Hussein and Pato. It is shown that although the space-charge self-consistent field does not modify the basic results obtained with the one-particle model, the electromagnetic fields produced by the transverse particle current play a substantial role for large beam densities.

The properties of longitudinal and transverse oscillations in isotropic unmagnetized plasmas of arbitrary composition are investigated on the basis of the Maxwell equations and the relativistic Vlasov equation. We show that in such plasmas (i) superluminal longitudinal and transverse waves undergo no collisionless Landau damping; and (ii) all isotropic particle distributions functions are stable against the excitation of longitudinal and transverse waves. Specializing to the textbook example of longitudinal fluctuations in a pure-electron equilibrium plasma, we derive various analytical expressions for the longitudinal dispersion relation valid for any value of the electron plasma temperature characterized by the dimensionless parameter μ=mec2=kBTe, which allow simpler approximations for non-relativistic (μ[Gt]1) and ultrarelativistic (μ[Lt]1) temperatures. The resulting longitudinal dispersion relation for nonrelativistic temperatures μ[Gt]1 can be expressed in terms of the Fried and Conte plasma dispersion function, but does not agree with the earlier results of Landau, Jackson and others, which were calculated starting from the non-relativistic form of the Vlasov–Maxwell equations. We establish a significant difference in the argument of the plasma dispersion function. This difference only shows up because we have started from a relativistically correct formulation of the kinetic theory, and it profoundly influences the results for the real and imaginary part of the frequency also for non-relativistic plasma temperatures. We show that the non-relativistic limit of the longitudinal dispersion relation reduces to the Landau–Jackson form only if the (unphysical) limit of an infinitely large value of the speed of light c→∞ is taken.

A general class of solutions is found for the resistive hydromagnetic equation. The results are applied to the case of a prescribed stagnation point flow. It is shown that general solutions with magnetic null points exist. Scaling laws for the length and the width of the current sheet of the solutions are given for the general case. It is shown that the length of the current sheet increases with magnetic Reynolds number unless the outflow boundary conditions prevent the sheet length from growing. The latter would result in the appearance of boundary layers in the outflow region.

A new generation mechanism for electromagnetic waves near the fundamental plasma frequency is discussed. It is shown that a travelling Langmuir pump wave can nonlinearly convert into electromagnetic, Langmuir and ion-acoustic daughter waves via a hybrid stimulated modulational instability. The linear and nonlinear temporal dynamics of this modulational process involving coupling to a resonant ion-acoustic wave are studied. The wave energy conservation relations are derived. The roles of frequency mismatch, dissipation and wave dispersion in the temporal evolution of nonlinear coupling of two wave triplets are analysed.

We present a Rayleigh–Ritz variational model of the electron sheath in crossed-field devices. Using laminar layer orbits, this model predicts equilibria in agreement with the classical Brillouin model. Other predictions include the existence of existence of non-classical, stable equilibria as well as limit cycles. This variational model also predicts the existence of a stable propagating diocotron mode, which is absent from the Brillouin model but is present in the double-box model of Kaup and Thomas. Comparisons of these results with those of the cold-fluid theory are discussed.

We reconsider the problem of particle acceleration by large-amplitude electromagnetic waves. We make use of a fully relativistic Hamiltonian formalism to show that, as opposed to nonelativistic results obtained by Kuo and Lee, acceleration in unmagnetized systems is severely arrested when the phase velocity of the electromagnetic mode approaches the speed of light. For subluminal waves, however, acceleration is shown to be still effective.

Fast computer codes for evaluating non-thermal velocity distributions are needed in order to carry out routine analysis of neutron signals in plasmas heated by neutral-beam injection (NBI). By neglecting the magnetic field inhomogeneity along a field line, i.e. neglecting trapped-particle effects, calculations of the velocity distribution can be made relatively rapidly. In this paper, we investigate under which circumstances such an approximation is justified. We solve the bounce-averaged Fokker–Planck equation, which includes particle trapping, by expressing the solution in terms of a series of appropriate eigenfunctions of the pitch-angle scattering operator. The eigenfunctions, eigenvalues and time-dependent coefficient functions are calculated numerically. We use the solution for calculating the effect of particle trapping on neutron production for beam-heated deuterium plasmas.

This work is concerned with the investigation of non-ideal (resistive) MHD effects on the excitation of Alfvén waves by externally launched fast-mode waves, in simulated tokamak plasmas; both continuum range, CR ({ωAlf(r)}min <ω<{ωAlf(r)}max) and discrete range, DR, where global Alfvén eigenmodes, GAEs (ω<{ωAlf(r)}min) exist, are considered. (Here, ωAlf(r)≡ωAlf[n(r), B0(r)] is an eigenfrequency of the shear Alfvén wave.) For this, a cylindrical current carrying plasma surrounded by a helical sheet-current antenna and situated inside a perfectly conducting shell is used. Toroidicity effects are simulated by adopting for the axial equilibrium magnetic field component a suitable radial profile; shear and finite relative poloidal magnetic field are properly accounted for. A dielectric tensor appropriate to the physical conditions considered in this paper is derived and presented. When the resistive wave equation is solved and the current drive by helicity injection, IHICD, is calculated, the following illustrative results are found to hold. For CR, (i) the maximum power absorption as well the maximum helicity injection current drive increase significantly with decreasing resistivity (i.e. with increasing temperature); (ii) unlike the power absorption, which is a maximum at a frequency between the lower and the upper edge of the CR, the total current drive is a maximum at the lower edge, and decreases strongly with increasing frequency; (iii) the behaviour of the efficiency closely follows that of the current drive; (iv) the smaller the resistivity, the smaller is the radial distance from the axis (x=0) of the maximum current-drive density. For DR, (i) the maximum power absorption in the discrete GAE case increases with decreasing resistivity even more strongly than in the CR case; (ii) unlike the CR case, the total helicity-injection current has, for almost all GAEs, a symmetric frequency dependence about the line centre; its maximum value as well as the efficiency increase strongly with decreasing resistivity; (iii) unlike the continuum case, the efficiency is almost constant over the entire width of the discrete-mode range; its value increases strongly with the GAE rank.

Mathematically exact solutions describing propagating waves are constructed for a cold magnetized plasma bounded by a rigid cylindrical dielectric. Possible particle sources and sinks due to chemical reactions are allowed. It is found that the volume waves can be either amplified or damped because of their density dependence, while the surface waves are unaffected by the sources and sinks.

The effects of electron-beam density on large-amplitude ion-acoustic waves areinvestigated in an electron-beam–plasma system with trapped electrons, using the pseudopotential method. The region of existence of ion-acoustic waves is examined, and it is shown that the conditions for their existence depend sensitively on parameters such as the electron-beam density, the electrostatic potential and the ion temperature. It turns out that a decrease in trapped electrons, an increase in beam density and a decrease in ion temperature increase the propagation speed of ion-acoustic waves, and the region of their existence spreads as the beam density decreases, the effect of trapped electrons decreases and the Mach numbers increases. New effects of electron-beam density on large-amplitude ion-acoustic waves in a plasma with trapped electrons are predicted.

The effects of the propagation angle of electromagnetic waves and the pitch angle of non-thermal electrons on the electron cyclotron maser instability and beam–plasma instability are compared. It is pointed out if the direction of propagation of electromagnetic waves is opposite to the direction of the injected electrons, the maser instability will be suppressed, and hence it cannot explain the radiation with narrow bandwidth excited by energetic electrons propagating downwards in solar flares, such as millisecond spikes, blips and the type III bursts with positive-frequency drift. This discrepancy may be solved by the non-resonant wave–particle interaction in the beam–plasma instability, in which the electromagnetic waves propagating in the same direction as the injected electron beam are mainly composed of the ordinary modes (left-circular polarization), while the electromagnetic waves propagating in the opposite direction to the beam are mainly composed of the extraordinary modes (right-circular polarization). This result is compared with a typical model of a magnetic tube in solar flares, in which the non-thermal electrons propagating upwards excite spikes, blips and type III bursts in the metre and decimetre bands, while the electron beams propagating downwards excite these temporal and spectral structures in the microwave bands.

It is proved that a system of three-wave coupling with weak damping and the same sign of the coupling coefficients can be completely described by the Weierstrass function. On the basis of the bifurcation theory of the Weierstrass function that we have developed, criteria are found for distinguishing three phases of the three-wave coupling, namely the stable phase and the excited explosive and auto-explosive phases. Two kinds of explosion mechanisms in the three-wave coupling are found and described. The mechanism for the excited explosive phase is normal because trigger energy is required in such a mechanism and the threshold λth is proportional to δ2 (δ is the frequency mismatch), whereas the anomalous mechanism for the auto-explosive phase does not need any trigger – only proper changes of internal parameters to make the absolute invariant J less than 27 are required. In addition, the repetition period of the explosive instability is given. Finally, the effects of weak damping on the bifurcation structure of the explosive instability in three-wave interactions are analysed.

Y. Nomura et al., Stochasticity in the Josephson map [J. Plasma Phys. 56 (3), 493–506 (1996)]

The third author's name should be A. T. Filippov. We apologise for this error.

S. Li et al., Inverse cascades of angular momentum [J. Plasma Phys. 56 (3), 615–639 (1996)]

In Fig. 4 on p. 626, the upper figure shows the modal angular momenta L(0, n) as functions of time, while the lower figure shows the (positive-definite) modal kinetic energies E(m, n) as functions of time. Also, the upper figure should be labelled ‘(a)’ and the lower one ‘(b)’, in order to agree with the figure caption.