The dispersion relation (DR) has been considered for low-frequency waves in a hot magnetoactive collisional plasma with ‘longitudinal’ large-scale electric field ${\bf E}_{0} ( {t} )$ and weak spatial inhomogeneity of temperature. The electric field was assumed to be extremely weak (‘subdriecer’ field) and the quasi-static time variation of its amplitude allows us to use the ‘direct initiation’ mechanism to describe the instability development. Taking into account the ion thermal motion has not changed the form of the DR, which has remained the polynomial of the fourth order, but it has essentially complicated the form of its coefficients. As compared with previous investigations, these changes have resulted in the changes of the solutions of the DR. Two of the roots of the DR have remained of the same type (‘kinetic Alfvén-like’ waves), but another two have become quite different and get to the range of slow magneto-acoustic waves. Investigation of these new waves has shown that corresponding instability has clearly expressed threshold character, and the value of this threshold depends essentially on the reduced value of the electric field amplitude $E_{0} (t)$ and ratio of electron and ion temperatures.

We present the Rayleigh instability of low-frequency (in comparison with the ion-gyrofrequency) electrostatic waves in multi-ion species plasmas containing equilibrium density gradient and transverse ion-sheared flows caused by the dc electric field. For this purpose, multi-fluid equations are used to obtain the governing equations for two-dimensional convective cells and pseudo-three-dimensional drift waves in a non-uniform magnetoplasma. Standard procedures are then employed to study the Raleigh instability. Thresholds and growth rates are obtained. Applications to Hall thrusters are discussed.

The reactive instabilities are characterized by the absence of dissipation, algebraic dispersion relations (in slab approximation) and the existence of marginal (bifurcation) points of stability. In the vicinity of these points the reactive instabilities are amenable to a thermodynamic treatment based on the electrostatic entropy concept. After recalling the essential aspects of this concept and its connection with the linear description of the electrostatic instabilities, the theory is extended to the nonlinear domain near the marginal point. It is shownthat the marginal state is a maximum of the electrostatic entropy with respect to arbitrary variations of the bifurcation parameter (e.g. the temperature gradient). However, a nonlinear neighboring electrostatic structure is formed, which is the manifestation, on average, of large-amplitude fluctuations towards the linearly unstable side of the marginal point. A correspondence with numerical models of turbulence involving ion temperature gradient (ITG) saturation is noted. Compact analytical expressions for the mean square amplitude of the fluctuations valid in the range from the stable to the unstable side of the marginal point are presented. As an example, the theory is applied in detail to the flute modes.

The shielding of a one-dimensional, planar, permeable test charge has been studied theoretically. General expressions are derived and evaluated which show how the screening of a test charge, represented by the floating potential $\psi$, surface charge density q and screening length L, depends on various plasma parameters such as the temperature of electron and ions and particle streaming velocities. Particular attention has been given to analyzing the influence of particle trapping (reflection) in the charging and screening problem. No charging model can adequately describe the screening mechanism unless proper care is taken in choosing suitable distribution functions for both plasma species. In this paper, such a theory has been developed that provides the general idea about the charging of a grid in plasmas under different environments and conditions. As the main outcome we have found that the shielding of a non-propagating test charge is stronger, the larger the trapped ion population and the higher the temperature ratio Te/Ti are. Flux equality in the case of a propagating test charge restricts the solubility of the shielding problem to non-Boltzmann electrons and to a weak $\psi$ and q only. In the cold ion limit a lower bound for the ion streaming velocity is found than that predicted by Bohm's criterion.

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the position of the fluid element ${\bf x}^*$ is expressed as a vector sum of the position vector x of the background plasma fluid element plus a Lagrangian displacement $\xi({\bf x},t)$ due to the waves. Linear, non-Wentzel–Kramer–Brillouin (WKB) wave interaction equations are obtained by expansion of the Lagrangian out to second order in $\xi$ and $\Delta$S, where $\Delta$S is the Lagrangian entropy perturbation. The characteristic manifolds of the waves are determined by consideration of the Cauchy problem for the wave interaction equations. The manifolds correspond to the usual MHD waves modes, namely the Alfvén waves, the fast and slow magnetoacoustic waves and the entropy wave. The relationships between the characteristic manifolds, and the ray equations of geometrical MHD optics are developed using the theory of Cauchy characteristics for first-order partial differential equations. The first-order differential equations describing the singular manifolds are the dispersion equations for the MHD eigenmodes, where the wave vector ${\bf k}=\nabla\phi$ and frequency $\omega=-\phi_t$ correspond to the characteristic manifolds $\phi({\bf x},t)=$ constant. The form of the characteristic manifolds for both time-dependent and steady MHD flows are developed. The bi-characteristics for steady MHD waves in a steady background flow are related to the group velocity surface and Mach cone for the waves, and determine when the flow is elliptic, hyperbolic, or of mixed hyperbolic-elliptic type. The wave interaction equations are decomposed into coupled equations for the compressible and incompressible perturbations.

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the exact position of the fluid element ${\bf x}^*$ is expressed as a vector sum of the position vector ${\bf x}$ of the background plasma fluid element plus a Lagrangian displacement $\xib({\bf x},t)$ due to the waves. An exact theory for the wave and background stress energy tensors is developed based on the exact Lagrangian and the exact Lagrangian map. Noether's theorems are used in conjunction with the exact action and Lagrangian maps to determine the general form of conservation laws for the total system of waves and background plasma, corresponding to divergence symmetries of the action. The energy and momentum conservation laws of the system are derived from Noether's first theorem corresponding to the time and space translation symmetries of the action, respectively. As examples of the use of Noether's first theorem, we derive the conservation laws associated with the 10-parameter Galilean group admitted by the MHD equations. This includes the space and time translation symmetries, the space rotations, and the Galilean boosts. A class of solutions of the Lie determining equations for the infinite-dimensional MHD fluid relabeling symmetries are used to discuss the corresponding conservation laws. Ertel's theorem for the conservation of potential vorticity for the system of waves and background gas in ideal gas dynamics is derived from an infinite-dimensional fluid relabeling symmetry of the action.

The formation of a non-equilibrium steady-state distribution function of particles with the power law interaction potentials $U\,{=}\,\alpha/r^{\rm s}$, where $1 \,{\le}\, \beta \,{<}\, 4$, is studied numerically. Consideration is based on the one-dimensional nonlinear kinetic equation of a Landau–Fokker–Planck type in the presence of particle (energy) sources. Non-equilibrium quasi steady-state local distributions exist inside the momentum interval between the energy (particle) source and the bulk (or sink) of the particle distribution and have the form of gradually decreasing functions. Numerical calculations based on the completely conservative difference schemes are accompanied by the analytical consideration and comparison with the experimental results is given. Obtained results can be useful in connection with the development of high-power particle and energy sources and for the prediction of the semiconductors behavior with an intrinsic or extrinsic conductivity under the action of particle fluxes or electromagnetic radiation.

It was demonstrated that low pressure ($\sim$0.2 torr) water vapor plasmas generated in a 10 mm inner diameter quartz tube with an Evenson microwave cavity show at least two features that are not explained by conventional plasma models. First, significant ($\gt$2.5Å) hydrogen Balmer $\alpha$ line broadening, of constant width, up to 5 cm from the microwave coupler was recorded. Only hydrogen, and not oxygen, showed significant line broadening. This feature, observed previously in hydrogen-containing mixed gas plasmas generated with high voltage dc and rf discharges, was explained by some researchers as resulting from acceleration of hydrogen ions near the cathode. This explanation cannot apply to the line broadening observed in the (electrodeless) microwave plasmas generated in this work, particularly at distances as great as 5 cm from the microwave coupler. Second, inversion of the line intensities of both the Lyman and Balmer series, again at distances up to 5 cm from the coupler, were observed. The line inversion suggests the existence of a hitherto unknown source of pumping of the optical power in plasmas. Finally, it is notable that other aspects of the plasma including the OH* rotational temperature and low electron concentrations are quite typical of plasmas of this type.

In the present paper, the xenon plasmas containing argon and caesium as additives and pertaining to the above-mentioned type (high-pressure, low-temperature) are studied, and a theoretical evaluation of their basic transport parameters are presented. The numerical calculations were based on the assumption that the system is kept under constant pressure and temperature and has attained local thermodynamical equilibrium (LTE). Particular attention is given to the evaluation of electron collision frequencies within the temperature interval from 2000 to 20000K, and for initial pressures ranging from 0.1 to 1.5 MPa in plasmas in the mixtures of xenon, argon and caesium. The equilibrium plasma composition was evaluated with the use of the modified Debye radius.

It is found that the addition of as little as 1% of caesium profoundly alters the properties of the plasma. The presence of the added caesium in the thermal xenon and argon plasma is indeed quite significant for its transport properties, especially at temperatures below and around 10000K. Thus, electron number density, monotonically increasing with temperature (with pressure kept constant) much as in the pure noble-gas plasma, becomes considerably higher. The characteristics of the electrical and thermal conductivities are basically caused by the specificities of the processes of thermal ionization taking place in the system considered, as these processes determine the multiplier electron number density.

Photon kinetic theory provides a framework for the study of intense electromagnetic fields interacting with underdense plasmas. It is particularly useful when studying forward scattering four-wave modulational type instabilities. The most powerful features are its simplicity and its strong connection with particle beams, and the natural way in which broadband and angular spread effects can be included in the formalism. In this paper we derive the dispersion equations describing four-wave stimulated Raman and Brillouin scattering and Langmuir wave modulational instability for induced spatially incoherent pump waves.