Kinetic Description of the Stationary Band-Like Weakly Turbulent Beam Discharge Plasma in Hydrogen II. Budget of Ions and Metastables — Analysis of the Balance Equation System

In the first part [1] of our paper a kinetic model for the band-like beam discharge plasma in hydrogen was derived, numerically obtained results on the ionization and dissociation degree were presented and a detailed explanation of the influence of the electron kinetic properties on the macroscopic plasma behaviour was given. Continuing these investigations, we now report and discuss the results on the ion- and metastable atom-budget. On this basis an analysis is made of the resulting balance equation system with a view to finding the most important physical processes, and a simplified equation system is derived which allows to interpret the essential features of the macroscopic plasma properties.     

The Impact of Direct Ionization by Beam Electrons on the Electron Kinetics of the Beam Discharge Plasma in Molecular Hydrogen

In a recent paper the stationary beam plasma discharge in partially dissociated hydrogen was investigated where the electron component was described by the Boltzmann equation for a mixture of atomic and molecular hydrogen and the main heavy charged and neutral particles by balance equations. It was assumed that, via the quasilinear beam plasma interaction, the electron beam produces only the turbulent electric field whilst an additional production of plasma electrons due to direct ionization by the beam and thus a direct influence on the balances of charge carriers were neglected. Now the additional production of plasma electrons due to direct ionization by the beam is studied on the basis of a generalized Boltzmann equation but for the simpler model of a purely molecular hydrogen plasma. For experimentally obtainable values of the turbulence energy density, beam energy, beam ionization degree and electron life time the calculation of the electron energy distribution function and of the direct beam contribution to the electron particle balance shows a marked influence of the direct beam ionization with increasing degree of beam ionization.     

Collisional — Radiative Model of Helium Plasma. I. Description of the Model

We present a collisional-radiative model of helium plasma with explicit inclusion of metastable state influences and give results of numerical calculations of population coefficients and effective reaction rates (generalization of effective ionization and recombination coefficients for the case when metastable states are not explicitly included) for a large region of electron densities and temperatures for optically thin and thick helium plasma. The model is described in this paper.     

On the Question of Increasing Maxwellization of the Electron Energy Distribution Function due to Electron — Electron Interaction with Growing Ionization Degree in the Beam Discharge Plasma

The question of the establishment of an almost complete Maxwellian energy distribution of the electrons in a given discharge plasma is of importance, especially under the aspect of a more convenient determination of transport and rate coefficients. In [5] an energy space averaged criterion for the establishment of such a structure of the electron energy distribution function in the stationary beam discharge plasma of molecular gases was formulated from a heuristic point of view. This paper investigates this question in detail starting from the adequate Boltzmann equation of such plasmas. Energy resolved conditions for the establishment of an almost complete Maxwellian distribution are derived from the kinetic equation. Using one of these conditions, the formal derivation of the mentioned averaged condition is performed and its limitations are shown. The fulfilment of the energy resolved and of the averaged conditions are illustrated and discussed using solutions of the kinetic equation in purely molecular hydrogen for two parameter sets yielding larger and smaller deviations of the real distribution function from the Maxwellian form.     

Study of the Balmer Spectrum of Hydrogen from a High-Pressure Arc Discharge. I. Spectroscopic Measurements and Plasma Analysis

The Balmer spectrum of hydrogen emitted from a wall-stabilized pulse discharge has been measured covering a pressure range between 0.1 and 1.2 MPa. The temperature achieved in the discharge varied between 13000 and 22000 K corresponding to a variation in the electron concentration between 10²³ and 10²⁴ m^?3. Special consideration is given to the problems in both diagnostics and spectroscopic data acquisition.     

Kinetics of the Electron Component in the Turbulent Electron-Beam Discharge Plasma in Diatomic Gases and Comparison of some Macroscopic Properties between the Plasmas of the Beam and the Glow Discharge

The present paper is devoted to the investigation of the kinetics of the electron component in the stationary beam discharge plasma in molecular nitrogen. Using the Boltzmann equation with the inclusion of the elastic and the main inelastic binary collisions and also the Coulomb interaction between the charged particles we have calculated the energy distribution function and some macroscopic quantities of the electrons within a large range of parameters. Using our earlier results for the beam discharge plasma in hydrogen, also the dependence of the macroscopic quantities on the kind of molecular gas is discussed. Finally, the comparison of some macroscopic properties of the beam and the glow discharge plasma was performed under the condition of equal power input per volume unit in both types of plasmas in nitrogen.     

Analysis of the Kinetic Properties and the Energy Budget of the Electrons in the Ar?Hg Glow Discharge Plasma at Varying Partial Pressures and Discharge Currents

By simultaneously solving the Boltzmann equation and the current balance for the electrons the energy distribution function, the electron concentration and resulting macroscopic electron quantities were calculated for the Ar? Hg mixture plasma under conditions typical of fluorescent lamps. Besides the usual external parameters of such diffusion determined discharge plasmas measured values of the electric field strength were employed. The investigations were performed for independent variation of the partial pressures of Ar and Hg as well as of the discharge current in wide ranges of practical interest. The results obtained are discussed and compared with various energy distributions employed up to now and measured values of the electron concentration and temperature as well as with experimental results on the energy budget of this mixture plasma available in the literature.     

Coupling Between the Discharge Plasma Instability and the Laser Oscillation in a He—Cd Laser

The investigation of the output of a He–Cd laser with electrically floating hollow electrodes shows that the discharge plasma instability plays an important role in the generation of the population inversion. The experimental evidence is presented and a qualitative interpretation is given by considering the plasma instability as equivalent to a radio frequency component of the discharge voltage.     

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory — I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X( _D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.

When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.

We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties.     

Dynamics of the Magnetospheric Cyclotron ELF/VLF Maser in the Backward-Wave-Oscillator Regime. I. Basic Equations and Results in the Case of a Uniform Magnetic Field

We consider the nonlinear dynamics of absolute instability of whistler-mode waves in the Earth's magnetosphere in the presence of a step-like deformation in the distribution function of energetic electrons. Development of this instability, implying the transition of the magnetospheric cyclotron maser to the regime of a backward-wave oscillator (BWO), was proposed earlier as a generation mechanism of magnetospheric chorus emissions. We derive simplified nonlinear equations describing the dynamics of the magnetospheric BWO in the case of low efficiency of wave-particle interactions. Numerical simulations of these equations confirm qualitative similarity of the laboratory and magnetospheric BWOs and justify quantitative estimates of parameters of chorus emissions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 719–729, September 2005.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. I. Conservation Laws of Energy and Momentum for Electromagnetic Waves in a Nonequilibrium Dispersive and Dissipative Medium in the Case of a Slow Change of Amplitude and Phase of the Wave

A formula is given for the energy and momentum conservation laws for a narrow spectrum of electromagnetic waves in an unstable dispersive and dissipative medium by any level of dissipation and on condition that the amplitude and phase change slowly in the time and space period of oscillations. It is shown that the density of energy and momentum of the motion of resonant particles, connected with the propagation of the electromagnetic wave, generally cannot be expressed by the dielectric function of the unstable system. For example it is demonstrated that the well known Landau formula for determining the density of the wave energy in a unstable monoenergetic beam-plasma system in general is not applicable as it is often done in literature.