A stability analysis is presented of the electrothermal modes of perturbation of a spatially homogeneous, two-temperature and fully ionized plasma with wave-vector K perpendicular to the magmetic field. It is found that the wavelength of the fastest growing unstable, non-convective mode is of the order of (mi/ me)½ ae, with maximum growth rate of the order of (me/ mi) vei, where ae and vei are the electron Larmor radius and electorn-ion collision frequency respectively. Depending on the values of ωτ and β, this analysis also shows the presence of a convective mode which persists in the limit of long wavelengths. This theory has been consistently examined with homogeneous equilibrium plasma models constructed under the assumption of either a scalar or a tensor electric conductivity. A comparison of these results with the previous steady-state profiles obtained in parts 1 and 2 of this series indicates that current filamentation can take place as a result of electrothermal instabilities in the plasma.

The ½ subharmonic excitation is studied for the ionization wave in a positive column glow discharge. When an oscillation with about twice the frequency (and twice the wavenumber) of the resonant one is applied by modulating the discharge current, the ½ subharmonic is excited if the applied voltage exceeds a certain critical value. However, the excitation phenomenon differs from that of the ion-acoustic wave, since the ionization wave has a backward wave property in contrast to the forward one. Such an excitation mechanism is theoretically explained by the Van der Pol equation.

A model equation for nonlinear drift Alfvén waves in the region where they do not couple to the electrostatic drift wave branch is derived. Two conservation relations are derived and the results are compared to that of the Hasegawa—Mima equation. The spectrum is found to cascade to both smaller and larger k. The convective cell formation is studied for two different orderings of the parameters. The relation between characteristic scale lengths parallel and perpendicular to the drift flow for the onset of cell formation has been found.

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

The propagation of a superluminous plane wave of fixed profile through a cold electron plasma, in a direction perpendicular to the ambient magnetostatic field, is considered. The polarization is such that the electric vector has no component parallel to the magnetostatic field. The analysis is referred to the frame of reference in which all the field quantities are uniform in space, and the exact governing equations are cast into the form of an autonomous system of four nonlinear, first-order, coupled differential equations. The equations contain the parameter n that specifies the wave speed, c/n, in the laboratory frame, and inspection reveals that the limiting case n = 0 admits two exact solutions, which are monochromatic, of arbitrary amplitude, and recover the standard solutions of linear theory in the small-amplitude limit. The possibility of the existence of corresponding period solutions for the case n ≫ 1 is then investigated by a perturbation treatment. I t is found that the analysis can be carried through explicitly, and, to the first order in n, the outcome confirms the existence of periodic solutions, and yields the dependence of the period'on an amplitude parameter. The results are checked against a direct numerical integration procedure that incorporates a method of searching for periodic solutions, and close quantitative agreement is found for sufficiently small values of n.

A stability analysis which directly uses particle distribution functions determined from experiments or transport theory, rather than model distributions, is carried out. The features of distribution functions relevant to whistlers, ion cyclotron waves, including their low-frequency extensions for propagation along the magnetic field, and to ion-acoustic waves are analyzed in detail. The dependence of wave growth on the precise shape of the distributions and the numerical feasibility of the method is demonstrated by the use of measured solar wind distributions.

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.

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.

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.

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.

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.