An analytic investigation is made of the nonlinear propagation characteristics of laser beams with elliptically shaped Gaussian intensity cross-sections. Explicit analytic criteria, in terms of inital conditions, are given, which determine the dynamical behaviour of the transverse dimensions of the beam, i.e. its self- focusing and defocusing properties. Approximate analytic solutions are also given, which display the characteristic features of the general variation of beam width with distance of propagation.

We report here on a two-dimensional analytical calculation of an upper bound on the space-charge limiting current for a relativistic electron beam in cylindrical geometry. Voronin and co-workers have previously obtained an analytical estimate for the maximum steady-state current that can be propagated in a solid, unneutralized electron beam which completely fills a drift tube immersed in an infinite magnetic guide field. We generalize their method to include annular beams of arbitrary thickness and length, specifying a rigorous upper bound on the limiting current in terms of an eigenvalue of Bessel' s differential equation and separated, homogeneous boundary conditions of the most general form. For the special cases of a thin solid beam in a drift tube of infinite length and a thin annular beam in a drift tube of finite length, we find closed-form analytical expressions for the upper bound which are in good agreement with numerical solutions for the actual space-charge limiting current.

Acceleration of an electron by the electrostatic field of ion wave fluctuations is considered including the external magnetic field. It is found that an accelerated electron can emit unstable electromagnetic waves which propagate along the guide magnetic field. As an example, we discuss the generation of right-handed circularly polarized whistler waves. Application of our result to laboratory and space plasmas is examined.

The relativistic Vlasov equation together with Maxwell's equations are used in a study of p-polarized electromagnetic waves incident on a warm plasma halfspace. The domain for dual propagation of longitudinal and transverse waves is derived as a function of density, temperature and incident angle at a given frequency. Expressions for the reflection and absorption coefficients are obtained in the non-relativistic limit. It is found that maximum absorption occurs at an angle dependent on the density and temperature of the plasma, above which dual propagation will not occur. It is inferred that the density–temperature space available for dual propagation diminishes with the growth of the maximum angle for such propagation.

An exact solution of the MHD flow of an incompressible, electrically conducting, viscous fluid past a uniformly accelerated infinite plate has been presented. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin friction are tabulated. At high values of the Hall parameter, wt, the velocity is found to be oscillatory near the plate.

In the present analysis, a normal mode approach is used to study waves in a plasma subjected to a spatially uniform but temporally stochastic magnetic field. The first part deals with the evolution of circularly polarized transverse waves. Making a linear analysis, it is shown that the coherent waves are damped. The nature of the damping is determined by the Kubo number. In the second part, the nonlinear interaction of three coherent waves propagating along the magnetic field is analyzed. The coupling coefficients for the interaction of two circularly polarized waves and a longitudinal one are calculated. It is shown that for coherent waves, the system is equivalent to the interaction of two damped transverse modes with an undamped longitudinal one.

Following the fluid model for the response of electrons, it is shown that a high-power whistler wave decays efficiently into a lower hybrid or a Bernstein mode and a scattered whistler wave in a homogeneous plasma. The thresholds for these channels of stimulated scattering are generally low. However, the channel of scattering involving lower hybrid waves is possible only for scattering angles exceeding ¼π. The other channel involving Bernstein modes is possible at shorter scattering angles but the growth rate is relatively small and the threshold is high.

Finite ion Larmor radius effects (ε ≡ γLi/LΙ< 1 but finite) are found to cause a branching of the Alfvén ion cyclotron mode, whereas the growth rate of the mirror mode is found to be of the order of for ωci for ε≥ 0.1 and rather moderate values of plasma beta and temperature anisotropy. For this regime its growth rate considerably exceeds that of the Alfvén ion cyclotron mode.

The effects of a self-generated magnetic field in a laser produced plasma on the parametric decay of an extraordinary electromagnetic wave into two upper hybrid plasmons is examined for arbitrary magnetic field intensity and arbitrary ratio k/k0. Owing to the presence of magnetic field, the linear Landau damping is greatly reduced and the spectrum of unstable modes is significantly modified for kλD≳ 0·2.

Plane wave propagation in temperate plasmas consisting of n ion species is calculated analytically for collisionless plasmas of arbitrary composition. Numerical results are given for the complex refractive index of plasmas including collisions between particles of any kind and at arbitrary angles of propagation. There are two waves propagating at all angles other than 90°, one wave showing resonances at each of the n cyclotron frequencies of the ions involved. High ion-ion collision frequencies combine the motions of the ions to give new mass and composition weighted hybrid ion cyclotron resonances. At right angles to the external magnetic field one wave will propagate in the ion cyclotron range showing n – 1 ion-ion hybrid resonances and n – 1 hybrid cut-offs. The ion-ion hybrid resonances can be traced down to propagation at angles smaller than 90°, disappearing for parallel propagation. The hybrid resonance frequencies are close to the cyclotron frequencies of the ions with small relative concentrations. Damping of the waves in the neighbourhood of the ion-ion hybrid resonances is strongly affected by ion-ion collisions.

In the vicinity of a turning point, a high-power laser radiation (in the upper- hybrid mode) is unstable for short wavelength, purely growing perturbations, viz, oscillating two-stream instability. The nonlinearity in the low-frequency response arises through the parallel pondermotive force whereas in the high- frequency response it arises through the equation of continuity. In the limits of long and short perpendicular wavelengths, κ┴ρe< 1 and κ┴ρe > 1, the growth rates are found to be γ∞ │κ┴.V0┴│2, where ρe and V0┴ are the electron Larmor radius and oscillatory drift velocity.

Nonlinear propagation of an electron-acoustic wave in a magnetoplasma is considered. Accounting for the exact electron and ion nonlinearities, we show that the equations governing the dynamics of these waves can be written in terms of the energy integral of a classical particle. A careful analysis of the potential reveals the existence of exact planar solitary waves. Application of our investigation to space plasmas is pointed out.

A hybrid-kinetic model (Vlasov ions and drift-kinetic electrons) is used to investigate the equilibrium and stability properties of collisionless linear screw-pinch configurations, assuming low-frequency perturbations (|ω|≲ωci) but making no a priori assumptions regarding the size of the ion Larmor radius (arbitrary rLi/L⊥). A general eigenvalue equation is derived for perturbations about a general equilibrium characterized by density profile N(r), isotropic ion equilibrium f0i(H), and locally Maxwellian electrons. This eigenvalue equation clearly exhibits the importance of finite electron temperature and electron kinetic effects parallel to the magnetic field direction, and reduces to the Vlasov-fluid eigenvalue equation of Freidberg in the limit of zero electron temperature.

Profile modification in the underdense region of laser-plasmas with spatially uniform temperature Te, is studied. A multiple scale method is used to describe self-consistently the plasma flow and the wave field, in (i) the scale of the field wavelength, and (ii) the overall expansion scale. For Te∝ taordinary differential equations with definite boundary conditions are obtained. For a = 0 and weak fields, we explicitly solve the equations and relate the field in the critical layer to the incident field.

It has been called to our attention that our paper on the nonlinear evolution of a temperature anisotropic plasma (T⊥ > T¶) in the absence of an external magnetic field (Lemons, Winske & Gary 1979) did not make reference to several relevant and previously published works. Specifically, the linear theory of this unstable plasma has been explored by Kalman, Montes & Quemada (1968), the quasi-linear theory by Smith (1969) and Montes, Coste & Diener (1970) while additional thermodynamic considerations were given by Montes & Peyraud (1972). We regret this oversight.

The linear stability of a uniformly imploding shell, modelled as an ideal polytropic fluid, is investigated. Two types of unstable modes are found: incompressible irrotational perturbations localized at the outer surface, ascribable to Rayleigh—Taylor instability, and compressible modes, associated with convective instabiiity. Kidder's result for the Rayleigh—Taylor modes is shown to hold independently of the form of the shell density profile. By means of a variational principle it is shown that the criterion for convective instability is the existence of a region within which d(pp-γ)/dr> 0. Analytic solutions for both spatial and temporal dependence of the perturbations are presented, and the results applied to pellets imploded by the action of a laser or charged-particle beam.

This paper presents an investigation of the excitation of an electrostatic pulse in a hot collisionless plasma by two Gaussian EM pulses at the difference frequency w1–w2, w1 and w2being the angular frequencies of two EM pulses. When the EM pulses have intensity distributions which are uniform in space and Gaussian in time, the generated electrostatic pulse is Gaussian in time with pulse width [t210 t220/ (t210+ t220)]½, where t10 and t20 are the EM pulse widths. When. the two EM pulses have Gaussian distributions in a plane transverse to the direction of propagation, the generation phenomena are considerably modified as a result of the cross-focusing of the two EM pulses.

The validity of hydrodynamic approximations for non-equilibrium plasmas is examined, with emphasis on applications to laser-driven fusion pellets. Typical density–temperature trajectories of such pellets, as predicted by hydrodynamic calculations in the published literature, are shown to lie sometimes outside the region of validity of hydrodynamic theory, which is an unsatisfactory situation. In view of this, we discuss certain criteria which can be easily used to test the self- consistent validity of any hydrodynamic result. Finally, it is noted that in the low-density, low-temperature plasma region, hydrodynamics initially breaks down because of a breakdown in conventional microscopic linear response theory. A modified microscopic theory is proposed which continues to be valid in this region. This may correspondingly extend the validity of hydrodynamics to plasmas of somewhat lower temperatures and densities.