The detailed behaviour of a beam of light propagating through a fully ionized plasma is studied near the critical density. Transient effects in the laser beam and plasma are included by taking into account, in a self-consistent manner, the proper motion of the plasma in an intense electromagnetic field. Parameters of the laser beam and plasma conditions are studied that prove most beneficial in providing a uniform deposition of energy. The behaviour of the light beams near the critical density at the three wavelengths 1054 nm, 527 nm and 351 nm are compared.

We present a method of solution of the quasi-linear diffusion equation for the averaged distribution function. The criterion for its validity is discussed. Using the solution obtained, we study the dynamics of the relaxation of a weak kinetic electron-beam instability and show that it saturates asymptotically at zero energy level. In a self-consistent manner, the distribution function for the beam particles will be shown to deform to a flat shape.

The nonlinear orbit equations are investigated analytically and numerically for a constant-amplitude electromagnetic wave (ωs, ks) with ordinary-mode polarization propagating perpendicular to a uniform magnetic field B0 êz. Relativisitic electron dynamics are essential in determining the maximum orbit excursion when the incident wave frequency ωs is near the nth harmonic of the electron cyclotron frequency Ωc. Coupled nonlinear equations are obtained for the slow evolution of the amplitude A(т) and phase ø(t) of the perpendicular orbit when ωs ≈ nΩc. The dynamical equations are reduced to quadrature and simplified analytically. At exact resonance (ωs = nΩc), if relativistic effects are (incorrectly) neglected, the maximum orbit excursion Amax approaches the unacceptably large value determined from the first (non-zero) solution to Jn(ns ΩsAmax) = 0, which totally invalidates the non-relativistic approximation. (Here ns Ωs = cks/Ωc.) As a contrasting illustrative example, for n = 1, ωs = Ωc and moderate pump strength, weak relativistic effects limit the maximum orbit excursion to the approximate value , where єs = ns ωs (Vz/c) Vq/c ≪ 1, and Vq is the axial quiver velocity in the applied oscillatory field. Physically, relativistic effects produce a nonlinear frequency shift that dynamically ‘detunes’ the particle motion from exact cyclotron resonance, thereby limiting amplitude growth.

A theoretical analysis of acoustic-like modes in a plasma consisting of two kinds of ions with different temperatures has been performed using fluid equations. The electrons are assumed to form a dynamic neutralizing background, and their perturbation has been neglected – which is permissible for k2λ2De ≫ 1. The analysis shows that an acoustic-like mode appears to propagate as a normal mode when the hotter ion concentration is very large compared with that of the colder ions.

The effect of finite Larmor radius (FLR) on the stability of m = 1 small-axial-wavelength kinks in a z–pinch with purely poloidal magnetic field is investigated. We use the incompressible FLR MHD model; a collisionless fluid model that consistently includes the relevant FLR terms due to ion gyroviscosity, Hall effect and electron diamagnetism. With FLR terms absent, the Kadomtsev criterion of ideal MHD, 2r dp/dr + m2B2/μ0 ≥ 0 predicts instability for internal modes unless the current density is singular at the centre of the pinch. The same result is obtained in the present model, with FLR terms absent. When the FLR terms are included, a normal-mode analysis of the linearized equations yields the following results. Marginally unstable (ideal) modes are stabilized by gyroviscosity. The Hall term has a damping (but not absolutely stabilizing) effect – in agreement with earlier work. On specifying a constant current and particle density equilibrium, the effect of electron diamagnetism vanishes. For a z–pinch with parameters relevant to the EXTRAP experiment, the m = 1 modes are then fully stabilized over the crosssection for wavelengths λ/a ≤ 1, where a denotes the pinch radius. As a general z–pinch result a critical line-density limit Nmax = 5 × 1018 m–1 is found, above which gyroviscous stabilization near the plasma boundary becomes insufficient. This limit corresponds to about five Larmor radii along the pinch radius. The result holds for wavelengths close to, or smaller than, the pinch radius and for realistic equilibrium profiles. This limit is far below the required limit for a reactor with contained alpha particles, which is in excess of 1020 m–1.

Oscillating two-stream instability (OTSI) of lower-hybrid pump waves has been studied in both large- and small-size devices. For large-size devices, the instability has been investigated by considering fast-ion-mode side-bands and employing local theory. The convective threshold due to the finite extent of the pump has been calculated. For small-size devices, the instability has been investigated by ignoring thermal effects on the side-bands but employing nonlocal theory. We have found that there is no important change in growth rates in both cases.

A whistler wave propagating through a preformed magnetospheric duct is susceptible to growth/amplification by an electron beam. The interaction is non-local and could be of Čerenkov or slow-cyclotron type. First-order perturbation theory is employed to obtain the growth rate for flat and Gaussian beam densities.

Nonlinear waves, solutions of the Zakharov–Kuznetsov (ZK) equation for a dilute plasma immersed in a strong magnetic field, are studied numerically. It is found that the most unstable mode rides with the carrier wave and leads to period doubling. Owing to the simplicity of the ZK equation, this and other phenomena, similar to those observed for gravity waves on a water surface, can be fully investigated. Analytical methods are also explored. An expansion in the carrier-wave amplitude leads to good estimates for growth rates, a result so far unobtainable for water waves. This paper can be read independently of parts 1 and 2, but a brief summary of all three parts is given at the end.

Surface-wave propagation along a double step is investigated within ideal compressible MHD. The occurrence of surface-wave leakage is emphasized and the relevant conditions are discussed. A numerical example is presented to illustrate the process.

An investigation is made of wave generation and radiation of third harmonics by s-polarized electromagnetic waves incident on a narrow inhomogeneous layer of a magnetoactive plasma. The amplitudes of the radiated third-harmonic waves are calculated. In contrast with second harmonics, third harmonics are radiated for the case of normally incident waves on an unmagnetized plasma.

We have considered the effect due to the presence of two-temperature electrons on the formation and propagation of cnoidal waves in a weak relativistic plasma. Since the cnoidal wave is equivalent to an infinite series of solitary waves, it is worthy of study for the situation where more than one solitary wave is important. The phase velocity of the modulated periodic wave is plotted as a function of the amplitude. The form of the wave for small values of ellipticity of the cnoidal wave shows up as a series of harmonics. Such cnoidal excitations are important in determining the anomalous transport coefficients of a plasma.

The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov (1987b), who assumed a linear exponential attenuation behaviour.

The previously obtained analytical solution to the Boltzmann equation for nonhomogeneous plasmas with relative large temperature and density gradients is generalized in the following sense. (i) The relatively simple Bhatnagar, Gross and Krook collision operator is replaced by the Fokker-Planck operator expressed in terms of relaxation rates (slowing down, energy exchange, etc.). (ii) The simple Lorentzian plasma model is replaced by a multi-component plasma model with realistic masses and temperatures.

Reflection of ion-acoustic waves from the ion sheath in front of the separation grid in a double-plasma device has been investigated experimentally. The plasma potential φ of the source plasma was controlled relative to that of the target plasma. When eφ < κΤe, where Τe is the electron temperature, no reflection was observed. The reason for this is that ions are drifting towards the grid with the Bohm velocity, i.e. the ion-acoustic velocity. When eφ > κΤe the reflected wave consists of the ion-acoustic wave and the ion beam mode. The reflection coefficient for the ion-acoustic wave is about unity. This high efficiency is due to reflection of the ions themselves.

An expression for the nonlinear wavenumber shift of an obiquely propagating ion-cyclotron whistler in the presence of negative ions are derived. The effects of the intensity of the wave, the ion-cyclotron frequency, the negative-ion concentration and the propagation angle on the wavenumber shift of whistlers is discussed. Numerical estimations are also made of the wavenumber shift.

The effect of parallel electron dynamics is incorporated in the study of the Varma mode, which is a flute-like electrostatic ion drift perturbation in an inhomogeneous magnetic field. Starting from the electron and ion continuity equations, an equation for the conservation of the ion magnetic moment, the generalized Ohm's law, and Faraday's and Ampère's laws, we derive a set of four nonlinearly coupled differential equations. The nonlinearities arising from the E × B0 convection of the density and magnetic-moment variations, nonlinear ion polarization drift and Lorentz force, and the coupling of the parallel electron flow to the perturbed magnetic field are included. In the linear limit we find that the Varma mode becomes coupled with the modified-convective-cell and Alfvén modes. The instability of the coupled system is analysed and an expression for the growth rate is obtained. In the nonlinear regime we present the localized dipole vortex solution of the coupled Varma and convective-cell modes as well as the coupled Varma and Alfvén modes. It is found that for the former case the nonlinear structure is a solution of a second-order partial differential equation, whereas for the coupled Varma and inertial Alfvén waves the dipole vortex belongs to a family of fourth-order differential equations. Our results can be useful in understanding the electrostatic and electromagnetic fluctuations in mirror reactors, tokamaks and astrophysical plasmas.

From the Vlasov-fluid model, a set of approximate stability equations describing the stability of a cylindrically symmetric z–pinch is derived. The equations are derived in the limit of small gyroradius and include kinetic effects such as finite Larmor radius, particle drifts and resonant particles. In the limit of zero Larmor radius and short wavelengths, we apply the equations to the internal m = 0 and m = 1 modes. If the drift term mωD + kVD is neglected in the resonant denominators, we find stability criteria that are more optimistic than the corresponding stability criteria for perpendicular MHD. The neglect of the drift term is, however, not justified for the m = 1 mode, where mωD needs to be retained in order to preserve the property that this approximate model should have the same point of marginal stability as the exact Vlasov-fluid model. Retaining the drift terms, growth rates have been calculated for the m = 1 mode, for a constant-current-density equilibrium and for the Bennett equilibrium. For the Bennett profile, we obtain, when compared with perpendicular MHD, a substantial reduction in growth rate γ/γMHD ≈ 0·2.

This paper presents a derivation of the nonlinear equations governing the space–time evolution of magnetic electron drift waves in an inhomogeneous magnetoplasma. The equilibrium electron pressure gradient is maintained by the gradient of an external magnetic field. An oscillatory instability is shown to arise. The existence of magnetic electron drift vortices is discussed and the limitation on the vortex speed due to the external magnetic field is pointed out.

An equilibrium model for a spherical field reversed configuration in the presence of a transverse rotating magnetic field is presented. It is shown that this quasi-static equilibrium is an exact solution of the time-dependent ideal magneto-hydrodynamic equations.

On the basis of the ideal MHD equations expressed in terms of Elsässer variables, a new set of equations has been derived that governs the dynamics of the inhomogeneous background plasma and the superimposed incompressible fluctuations. From these equations the dynamic equation for the two-point and two-time correlation tensor has been obtained, and subsequently the equations of motion for the various spectral densities related to energy, cross-helicity and residual energy or the Alfvén ratio have been established. This set of equations offers a new possibility of discussing and perhaps better understanding the mostly incompressible fluctuations observed in the solar-wind plasma and of analysing their radial evolution into interplanetary space and their spectral development. The scope of the paper is limited to giving mainly formal developments of the equations. A detailed evaluation of the many terms in the light of interplanetary observations is intended for the future, but is not presented in this paper.