A Gould-Trivelpiece mode at significant power levels is excited in a cylindrical beam-plasma system by launching an external signal. The fundamental mode excites a second-harmonic wave in the upper-hybrid mode. When the second-harmonic frequency is close to (where is the upper-hybrid frequency), considerable enhancement in the second-harmonic power level is observed. The results are interpreted using a slab model.

A new action principle determining the dynamics of the Vlasov–Poisson system is presented (the Vlasov–Maxwell system will be considered in Part 2). The particle distribution function is explicitly a field to be varied in the action principle, in which only fundamentally Eulerian variables and fields appear. The Euler–Lagrange equations contain not only the Vlasov–Poisson system but also equations associated with a Lie perturbation calculation on the Vlasov equation. These equations greatly simplify the extensive algebra in the small-amplitude expansion. As an example, a general, manifestly Manley–Rowesymmetric, expression for resonant three-wave interaction is derived. The new action principle seems ideally suited for the derivation of action principles for reduced dynamics by the use of various averaging transformations (such as guiding-centre, oscillation-centre or gyro-centre transformations). It is also a powerful starting point for the application of field-theoretical methods. For example, the recently found Hermitian structure of the linearized equations is given a very simple and instructive derivation, and so is the well-known Hamiltonian bracket structure of the Vlasov–Poisson system.

We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency ωo, magnetic field Bo and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: freefall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: σ = ωR/c and ω = ωc/ω, where c is the speed of light and ωc the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of σ smaller than σcr = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field – in contrast with the case of plasma columns sustained by azimuthally symmetric waves – increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (Ω → ∞) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.

The transcendental dispersion equation for electromagnetic waves propagating in the slow mode in sheared non-neutral relativistic cylindrical electron beams in strong applied magnetic fields is solved exactly. Thus, rather than truncated power series for the modified Bessel functions involved, use is made of modern algorithms able to compute such functions up to 18-digit accuracy. Consequently, new and significantly more important branches of the velocity shear instability are found. When the shear-factor and/or the geometrical parameter a/b (pipe-to-beam radius ratio) are increased, the unstable branches join, and the higher-frequency, larger-wavenumber modes are significantly enhanced. Since analytical solutions of the exact dispersion relation cannot be obtained, it is suggested that in all similar cases the methods proposed and demonstrated here should be used to carry out a rigorous stability analysis.

A nonlinear emission mechanism of electromagnetic waves at the fundamental plasma frequency has been examined by Chian & Alves. This mechanism is based on the electromagnetic oscillating two-stream instability driven by two oppositely propagating Langmuir waves. The excitation of the electromagnetic oscillating two-stream instability is due to nonlinear wave–wave coupling involving Langmuir waves, low-frequency density waves and electromagnetic waves. In this paper the Chian & Alves model is improved using the generalized Zakharov equations. Attention is directed toward the influence of induced low-frequency and Langmuir waves on the properties of the electromagnetic oscillating two-stream instability. Presumably, the properties derived in the present context may be relevant to both space and laboratory plasmas.

The equations of high- and low-beta reduced magnetohydrodynamics (RMHD) are considered anew in order to elucidate the relationship between compressible MHD and RMHD and also to distinguish RMHD from recently developed models of nearly incompressible MHD. Our results, summarized in two theorems, provide the conditions under which RMHD represents a valid reduction of compressible MHD. The equations for low-beta RMHD and high-beta RMHD are shown to be identical. Furthermore, as a direct consequence of our analysis, the conditions under which both two-dimensional incompressible MHD (in terms of the spatial co-ordinates as well as the fluid variables) and 2½ dimensional incompressible MHD (i.e. only two-dimensional in the spatial co-ordinates) represent a valid reduction of three-dimensional compressible MHD are also formulated. It is found that the elimination of all high-frequency and long-wavelength modes from the magneto-fluid reduces the fully compressible MHD equations to either two-dimensional incompressible MHD in the plasma beta (β) limit β ≪ 1, or 2½-dimensional incompressible MHD for β ≈ 1. Our approach clarifies several inconsistencies to be found in previous investigations in that the reduction is exact. Our results and analysis are expected to be of interest for plasma fusion and space and solar physics.

The method of multiple scales is used to derive a nonlinear Schrödinger equation describing the nonlinear evolution of an ion wave packet propagating along a cylindrical plasma-filled waveguide. Numerical evaluation of nonlinear and dispersive terms shows that the wave is modulationally unstable if the wavenumber exceeds a certain critical value. On comparing with the case of an unbounded plasma, it is shown that finite geometry causes a significant shift of this critical value towards smaller wavenumbers, where Landau damping is relatively small.

This paper presents an analysis of the self-focusing of a rippled Gaussian laser beam in a plasma when the nonlinear part of the effective dielectric constant is arbitrarily large. Considering the nonlinearity to arise from ponderomotive, collisional or thermal-conduction phenomena and following the approach of Akhmanov, Sukhorukov and Khokhlov (which is based on the WKB and paraxial-ray approximation) the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. For ponderomotive and collisional nonlinearities, the present theory leads to two values of the critical power for self-focusing of the beam, Pcrl and Pcr2, which depend on the amplitudes and phase difference of the main beam and the ripple. When the beam power P lies between the two critical values (i.e. Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, again converges, and so on. For P < Pcr2, the beam first diverges, then converges, then diverges, and so on. When thermal conduction is the dominant mechanism of nonlinearity of the dielectric constant, only one value of the threshold critical power Pcr for self-focusing of the beam exists. When the beam power P < Pcr, the medium behaves as an oscillatory waveguide.

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.

The nonlinear interaction of an arbitrarily large-amplitude circularly polarized electromagnetic wave with an unmagnetized electron-positron plasma is considered, taking into account relativistic particle-mass variation as well as large-scale density perturbations created by radiation pressure. It is found that the interaction is governed by an equation for the electromagnetic wave envelope, which is coupled with a pair of equations describing fully nonlinear longitudinal plasma motions. The dynamics of the nonlinear electromagnetic wave packet is studied.

The decay rate of an Alfvén or plasma surface wave propagating along an inhomogeneous layer of plasma is calculated. The inhomogeneous profile is thin and odd, but otherwise arbitrary. The wave's decay rate is determined using two fundamentally different methods, the integro-differential equation approach of Sedl´ček and the Sturm-Liouville expansion technique of Cally, and found by both to depend only on the slope of the Alfvén or plasma frequency profile at the ‘resonant point’, and not on other details of its shape. The result is verified numerically. This problem represents a good example with which to compare and contrast the two methods.

We use a one-dimensional quasi-neutral fluid model to study the formation of an electrostatic shock associated with the lower-hybrid mode propagating almost perpendicularly to the magnetic field that exists in the auroral zone of the magnetosphere containing cold downward-streaming electrons, cold upward-streaming ions and beam electrons. We examine the effects of finite electron-beam temperature by describing the beam electrons with fluid equations. We then show how exact time-stationary shock solutions may be found when quasi-neutrality is considered.

A kinetic theory of nonlinear currents, quasi-stationary electric and magnetic fields and the ponderomotive effect of high-frequency electromagnetic radiation on a collisionless plasma is developed. General expressions for nonlinear current densities, fields and ponderomotive forces that are applicable in a broad range of space-time scales, characteristie of low-frequency motion in plasma, are obtained. These expressions are compared with the results of previous papers.