To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

An investigation of the decay laws of energy and of higher moments of the Elsässer fields z±=v±b in the self-similar regime of magnetohydrodynamic (MHD) turbulence is presented, using phenomenological models as well as two-dimensional numerical simulations with periodic boundary conditions and up to 20482 grid points. The results are compared with the generalization of the parameter-free model derived by Galtier et al. [Phys. Rev. Lett.79, 2807 (1997)], which takes into account the slowing down of the dynamics due to the propagation of Alfvén waves. The new model developed here allows for a study in terms of one parameter governing the wavenumber dependence of the energy spectrum at scales of the order of (and larger than) the integral scale of the flow. The one-dimensional compressible case is also dealt with in two of its simplest configurations. Computations are performed for a standard Laplacian diffusion as well as with a hyperdiffusive algorithm. The results are sensitive to the amount of correlation between the velocity and the magnetic field, but rather insensitive to all other parameters such as the initial ratio of kinetic to magnetic energy or the presence or absence of a uniform component of the magnetic field. In all cases, the decay is significantly slower than for neutral fluids in a way that favours for MHD flows the phenomenology of Iroshnikov [Soviet Astron.7, 566 (1963)] and Kraichnan [Phys. Fluids8, 1385 (1965)] as opposed to that of Kolmogorov [Dokl. Akad. Nauk. SSSR31, 538 (1941)]. The temporal evolution of q-moments of the generalized vorticities 〈[mid ]ω±[mid ]q〉 =〈[mid ]ω±j[mid ]q〉 up to order q=10 is also given, and is compared with the prediction of the model. Less agreement obtains as q grows – a fact probably due to intermittency and the development of coherent structures in the form of eddies, and of vorticity and current sheets.

A nonlinear dispersion relation that governs the interaction between a high-frequency pump wave and the low-frequency modes in a plasma is derived. Previous results are generalized and discussed.

Waves in a magnetized electron–positron plasma, supporting a large-amplitude electric field E0 of superluminal phase speed, are considered. The case of perturbations with the same phase speed as the large-amplitude wave can be treated exactly, and we restrict our attention to this case, obtaining analytical results. The exact analytical results provide insight into the effect of the magnetic field and the large-amplitude wave on the harmonic structure of the perturbations. Three solutions are found for waves polarized perpendicular to E0. Waves are amplitude-modulated for weak magnetic fields (relative to the strength of the large-amplitude wave) and frequency-modulated for strong magnetic fields. This suggests that frequency modulation may be relevant to pulsars.

The resonant interaction of compressive and rarefactive ion acoustic solitons is studied experimentally in a multicomponent plasma containing additional negative-ion species. With increasing concentration of negative ions, the resonance amplitude increases for compressive ion acoustic solitons when the angle of collision is fixed. When the negative-ion concentration is larger than a critical value, the rarefactive ion acoustic solitons undergo resonant interaction for a lower resonance amplitude. Theoretical predictions of the Korteweg–de Vries equation agree with experimental findings.

Using a particle-in-cell code, we are able to simulate the excitation of ion acoustic solitons from a grid whose potential is suddenly increased. The numerical results are in substantial agreement with previous laboratory experiments.

The dispersion relation and boundary conditions for surface waves propagating on the plane interface between a vacuum and a drifting plasma have recently been derived by Lee and Cho [J. Plasma Phys.58, 409 (1997)]. It is the purpose of the present comment to show that the boundary conditions and dispersion relation are incorrect.

Shoucri (1999) has commented on our paper (Lee and Cho 1997) in view of his relativistic calculation, and has stated that the boundary condition and the dispersion relation obtained there are incorrect. In this response, we reaffirm that all the results contained in Lee and Cho (1997) are correct in so far as one uses the nonrelativistic equation of motion. In particular, the boundary condition that we used (equation (57) in Lee and Cho 1997) is valid in both the nonrelativistic and the relativistic theory, and is equivalent to equation (11) of Shoucri (1999). Shoucri's hasty conclusion that our boundary condition (57) is incorrect appears to be due to his neglect of the fact that a boundary condition can be put into different forms depending upon problems under consideration.

One way to derive a boundary condition for the surface-wave problem with a sharp boundary is to assume an inhomogeneous plasma having a varying density N(x) (in the notation of Lee and Cho 1997), integrate the inhomogeneous wave equation or the Maxwell equations across the infinitesimal transition layer, and specialize N(x) as a step function, as was done in Lee (1995). Starting from the Maxwell equations on p. 418 of Lee and Cho (1997) and calculating the currents relativistically, we find that the following three boundary conditions are equivalent, and any one of them is acceptable:

(i) equation (57) in Lee and Cho (1997);

(ii) equation (11) in Shoucri (1999);

(iii) formula here

(in the notation of Lee and Cho (1997), with γ as the relativistic factor).