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A theoretical model for the kinetics of the processes for production and destruction of atom excited states in microwave discharges sustained in helium gas at reduced pressures by surface wave propagation is developed. The excited state population densities and the line intensities at the axis of the discharge are obtained from the stationary Boltzmann equation and the set of the rate balance equations for the excited states solved in a semi-analytical - semi-numerical manner. The numerical evaluation of the results accounts for the experimental conditions investigated in part I of the study. The comparison of the theoretical results with the experimental data (part I) for the population densities of the , , and excited states allows one to deduce the values of the mean electron energy and the electron density at the axis of the discharge. By these means, the two parts of the study complete a procedure for determination of these two plasma parameters in discharges sustained by propagating surface waves. This procedure for plasma diagnostics is extended to obtaining the radial and axial profiles of the electron density. The measured radial and axial distribution of the 504.7 nm line emitted intensity and radial distribution (through line absorption) of the and population densities (part I) are used. The axial density distribution obtained from completing the optical spectroscopy measurements with the theoretical model is in good agreement with that evaluated from radial decay measurements of the surface wave electric field intensity.

Surface-wave gas discharges sustained under the conditions of a diffusion controlled regime are studied on the basis of the fluid plasma model. The self-consistent behaviour of the plasma density and of the field intensity along the discharge length is obtained. It is shown that the nonlinearity in the particle balance equation due to stepwise ionisation determines the plasma density in terms of the field intensity and ensures self-consistent behaviour of the wave ⟺ discharge characteristics in a diffusion controlled regime.

Recent activity on a volume-production negative-hydrogen-ion source with the design of a matrix of small-radius discharges inductively driven by a planar coil is reported. A single discharge of the matrix has been studied by employing probe-and laser-photodetachment diagnostics. The measurements have been carried out in the first - small-size - chamber of a two-chamber discharge vessel, with rf power introduced by a planar coil positioned on its front wall. The measured profiles of the negative ion density show strong axial dependence, with two maxima located at the positions corresponding to the maxima of the dc potential, where the maxima of the electron density are also located. The first maximum is in the vicinity of the rf power input and the second one is close to the interface between the two chambers of the discharge vessel.

A two-dimensional (2D) model of a low-pressure hydrogen discharge is presented in the study. Gas-discharge description based on the fluid-plasma theory is self-consistently coupled to electrodynamics of a planar-coil driven inductive discharge, with the coil included in the modeling domain. A discharge with a small radius is considered regarding development of the concept for a source of negative hydrogen ions completed as a matrix of small-radius discharges. Confirming previous results for the spatial distribution of the plasma parameters and, in particular, the result for a strong accumulation of the negative ions in the region around the maximum of the potential of the dc electric filed in the discharge, the model specifies the behavior of the TE-mode sustaining the discharge as well as of the rf current density and of the rf power input to the plasma. Comparison with results for the plasma parameters obtained by simulating the rf power deposition via a half of a super-Gaussian profile shows that the latter is a good approximation. Analytical estimations and comparison with numerical results from a model, in which the accounting for the coil is via a surface current applied as a boundary condition, are involved in discussion on the role of the finite – small – radius of the discharge in determining the skin depth of the TE-mode producing the plasma.

The dispersion relations of two nonlinearly interacting LP 01 modes are derived from a perturbation procedure. A step-index optical waveguide is considered here, but it should be emphasized that other index profiles can be introduced without any increase in conceptual difficulty. The cross-phase modulation couples waves with the same polarization and different frequencies. The nonlinear contributions to the linear wavenumbers arising from the effects of both self-phase and cross-phase modulation are obtained. The method used for deriving the nonlinear dispersion coefficients is novel because it uses nonlinear changes in the wave-field distribution in the transverse direction. As a consequence, the results differ from those obtained by the usual method of determining the nonlinear wavenumber shift. A set of coupled nonlinear Schrodinger equations is considered and a new nonlinear effective area involved in the cross-phase modulation effect is defined.

The longitudinal permittivity of weakly ionized low-temperature inhomogeneous magnetized plasmas is derived on the basis of the kinetic plasma model. Oblique propagation (with respect to the external, comparatively weak, magnetic field) of potential perturbations in d.c. discharge plasmas sustained under conditions of a diffusion-controlled regime is modelled. The equilibrium plasma state accounts for (i) collisions of charged particles with neutrals; (ii) plasma inhomogeneity in a direction perpendicular to the external magnetic field; (iii) crossed electric and magnetic fields; and (iv) electric field parallel to the external magnetic field. The solution of the Boltzmann equation obtained in the framework of successive approximations approaches the case of a non-complete ion magnetization and comparatively strong E*B drift of the ions due to an enhanced ambipolar electric field. The methods of integration over the unperturbed trajectories and over the angle of the gyromotion are applied.

The origin of the nonlinearity of plasma permittivity in high-frequency discharges maintained by ionizing surface waves is studied. It is shown that in a diffusion controlled regime the plasma density at the discharge axis is determined nonlocally in terms of the electric field intensity by accounting for the small nonlinear effect of recombination, along with diffusion in the particle balance equation. The axial self-consistent distribution of the surface wave field intensity and of the plasma density of discharges are obtained. The transition to a 'pure' diffusion and a 'pure' recombination regime is considered. A brief discussion is included regarding the case of a nonlinearity due to a weak dependence of the ionization frequency on the plasma density (e.g. due to stepwise processes).

A stationary microwave discharge in helium gas is studied by applying optical spectroscopy (emission and absorption) methods and field radial decay measurements. The discharge is created at the frequency 2375 MHz with an applied power varied between 100 and 200 W; the gas pressure is 0.6 Torr. From optical spectroscopy measurements, the population densities of the 21P, 23P, 41S and 43S excited states, the radial distribution of the 21P and 23P level population and the gas temperature are determined. The range of variation of the electron density along the plasma column is taken from the field radial decay measurements. The experimental data obtained are the basis for developing (in part II of this study) a theoretical model which specifies the kinetics of the processes for production and destruction of excited states under the nonequilibrium plasma conditions studied. The comparison between experimental results presented here and the theoretical results given in part II is extrapolated to the determination of the electron density and the mean electron energy.

This study presents a kinetic model of microwave generated discharges sustained, under the conditions of a diffusion controlled regime, by the propagation of azimuthally symmetric surface waves. The effect of the plasma resonances, which can appear over the radial density profile in the vicinity of the walls and lead to sharp peaks in the radial component of the high-frequency wave electric field in the plasma, is introduced. This effect modifies the surface wave damping and results in a collisional as well as collisionless (quasilinear) transfer of energy from the radial field component to the plasma. In the Boltzmann equation the latter appears as a third channel of energy transfer, which is added to the Joule heating by the axial and radial wave field components. The spatially inhomogeneous Boltzmann equation for the electron-energy distribution function, which accoutns for the radial ambipolar field, is solved in the nonlocal approximation. A complete set of relations is formed by simultaneous consideration of the fluid equations for the ion motion and the field equations for the surface wave electric field. The problem is solved numerically. It yields self-consistent radial electron density profiles and radial electric field distributions. The obtained solutions evidence indeed the occurrence of plasma resonances. The study is extended also to obtaining results for the axial variation of the (radially averaged) electron density. It turns out that the widely used concept of approximate constancy of wave power absorbed by one electron in a diffusion controlled regime keeps its validity also in the presence of plasma resonances and of the corresponding collisional, as well as collisionless, power transfer to the plasma in the resonance regions.

Previous studies on the axial structure of surface wave sustained discharges are extended and generalized to accounting for different gas discharge regimes. Discharge maintenance at high electron densities leading to fast surface waves is investigated assuming Joule collisional heating. Cases of both strong and weak collisions are analyzed. The self-consistent distribution of electron density in the axial direction is studied. A quadratic law is obtained for the axial density profile which transforms into the well-known linear density profile when the density is low enough. >

The axial distribution of the electron density related to the high-frequency field penetration in gas discharges maintained, in the diffusion controlled regime, by ionizing surface waves is obtained on the basis of the energy balance equations. It is shown that under conditions of comparatively weak electron collisions, the resonance absorption of the surface wave could cause essential deviations of the axial dependence of the plasma density from the linear one at both the end and the beginning of the discharge.

Effects of plasma density nonuniformity on the surface wave propagation along plasma-plasma and plasma-dielectric interfaces are investigated. Plasma inhomogeneities in longitudinal and transverse directions with respect to the direction of wave propagation are considered. The influence of the inhomogeneity on the propagation properties (dispersion, absorption) of the surface waves and the space distribution of the wave fields is analyzed. The wave behavior in the region of the quasi-static surface wave resonance is also studied.

Unified description of a volume-production based source of negative hydrogen ions, including its three regions--the driver, the plasma expansion through the magnetic filter, and the extraction of the ions at the position of the first electrode of the extraction system--is presented within a two-dimensional fluid plasma model. The results display the crucial role of the potential of the first electrode of the extraction system and show that the optimized conditions for the source operation should ensure proper balance between the local and non-local processes in the discharge. The role of the material of the plasma electrode is also discussed.

Based on experience from a work--both theoretical and experimental one--on negative hydrogen ion beam sources studied regarding fusion applications, a novel design of a rf source with volume production of the ions is proposed. The suggestion is for a source constructed as a matrix of small-radius tandem discharges (with magnetic filters largely extended over the discharge length), inductively driven (by a single coil, for the whole matrix) and with a single aperture extraction from each of them.

Self-consistent nonlinear changes of plasma parameters and characteristics of electromagnetic guided waves are studied with regard to the effect of self- focusing and waveguided channel formation in a cylindrical plasma waveguide. Besides the nonlinearity due to the ponderomotive force action usually involved, ionization nonlinearity specified for different regimes of particle loss mechanisms is considered. An azimuthally symmetric electromagnetic surface wave is the guided mode that forms and sustains the wave channel.The nonlinear dispersion law and the nonlinear changes in the wave field distribution and power flow are obtained, describing the effect of the self-focusing of the waves under conditions of weak nonlinearity.

A planar plasma waveguide with a single interface between an isotropic homogeneous plasma, considered as a nonlinear medium and a linear dielectric (vacuum), is studied theoretically with respect to the nonlinear effects of self-action of surface waves. Striction and ionization nonlinearities within a weakly nonlinear limit are the mechanisms providing a plasma inhomogeneity. The nonlinear wavenumber shift and the modifications of the wave field distribution and power flow are the results obtained for the nonlinear wave behaviour. The analytical and numerical analysis covers the whole, electromagnetic, range of the surface waves.

The influence of absorption of wave energy in regions of local plasma resonances in inhomogeneous (in the transverse direction) plasmas on the axial structure of discharges sustained by surface waves is studied analytically. The two regimes of charged-particle loss, namely diffusion- and recombinationcontrolled regimes, are considered. First, to extract the basic features of the phenomena, the discharge is modelled by a slab configuration and the case of slow surface-wave propagation is investigated. It is shown that it is resonant absorption that determines the properties of the discharge in the region towards its end. In the case of a cylindrical waveguide, which is the real configuration in experiments, the influence of the mechanism of resonant absorption is studied in both regions of fast and slow surface-wave propagation. With respect to the discharge behaviour, these cases correspond respectively to the regions at the beginning of the discharge close to the surface-wave launcher and at the discharge end.

A new simple method for computing the attenuation (due to dielectric losses) of weakly damped electromagnetic waves in a wide class of wave-guiding structures is suggested. The wave guiding structures considered contain time dispersive dielectric media, and restrictions are set neither on the type of modes nor on the cross-section geometry. Only one of the dielectrics of the structure is supposed to be lossy. The wave attenuation coefficient results directly from the slope of the wave dispersion presented as a dependence of the wave number on the permittivity of this dielectric at fixed wave frequency. The method is demonstrated on structures containing cold isotropic plasmas. For this case the method was found to be applicable even for some configurations with inhomogeneous plasma filling.

Recent investigations on the nonlinear dispersion law and the nonlinear wavenumber shift of the LP01 mode in step-index optical waveguides are extended to determining the effective area of the mode. The obtained result differs from that conventionally used and defines more precisely the characteristics of the nonlinear effects of self-phase modulation and soliton formation.

The features of surface wave propagation along a sharp plasma-vacuum boundary are investigated numerically for the case of plasmas that are non-uniform in the direction of wave propagation. On the basis of the full set of Maxwell's equations for cold plasmas with collisions, the distributions of the electromagnetic wave fields are calculated. The results obtained demonstrate enhancement of the intensities of the electric field components and absorption, without reflection, of surface wave energy in the vicinity of the quasistatic resonance region. This is in agreement with previous qualitative predictions.

The effect of the Trivelpiece-Gould mode on the behaviour of a low-frequency drift instability in a weakly ionized magnetized plasma is studied experimentally in a DC argon discharge. The ions are weakly magnetized, i.e. Omega ci approximately nu i, rho i approximately R ( Omega ci and rho i are the ion gyrofrequency and gyroradius, nu i is the ion-neutral collision frequency and R is the plasma radius). With increasing amplitude of the high-frequency field, the frequency and the amplitude of the instability decrease. Since the anomalously enhanced ambipolar field is considered as a very important factor in the mechanism driving the instability, special attention is paid to its variation with increasing high-frequency power. The nonlinear mechanisms of the dynamical control of the instability are discussed.

The kinetics of plasmas sustained by surface wave propagation at a frequency 2375 MHz in argon gas are studied experimentally. A simple manner for estimating the plasma parameters on the basis of general relations is given. The measured electron energy distribution functions are compared to numerical results from a kinetic modelling of surface wave produced plasma. Good agreement is found. By averaging over the measured electron energy distribution functions, the plasma macroscopic parameters (electron density and temperature, as well as frequencies of different processes initiated by electron impact) are obtained.

Low-frequency drift wave-type instability of weakly ionized, weakly magnetized plasma in a DC discharge in argon is studied experimentally. The instability exists in the intermediate region Omega ci approximately nu i, rho i approximately R between the conditions defining magnetization and unmagnetization of the ion plasma component ( Omega ci and rho i are the ion gyrofrequency and gyroradius, nu i is the ion-neutral collision frequency and R is the radius of the plasma column). The observations pertain to the appearance of the instability as a threshold effect and its dispersion properties. The behaviour of the instability is interpreted in relationship with the variation of the ambipolar field and its anomalously enhanced values. The effect of the longitudinal electric field sustaining the discharge is also discussed.

Unified description of the expansion (through a magnetic filter) and extraction regions, including also the driver, of volume‐production based sources of negative hydrogen ions is presented in the study. The model is one‐dimensional, developed within the fluid plasma theory. It covers description of both the second chamber of the tandem sources and a single inductively‐driven (with a planar coil) discharge of a matrix source. Four parameters have been varied in the analysis of the results: type, position and magnitude of the filter field and rf power applied for the discharge maintenance. The obtained results for the spatial distribution of the plasma parameters as well as for the electronegativity, for the negative ion beam current and its ratio to the electron current at the position of the extraction are discussed regarding optimum conditions for the source operation. The conclusion is that a magnetic field extended over a large region till the extraction favors locality in the discharge behavior and, respectively, the local production of the negative ions. This leads to high density of the extracted negative ion beam current at reasonable values of its ratio to the electron current density.

The study combines experiments on probe diagnostics with laser‐photodetachment‐technique and Faraday‐cup measurements directed towards determination of the position of the extraction device and its influence on the discharge structure. The measurements have been carried out in the second chamber of an inductively‐driven tandem plasma source performed as small scale arrangements, with a magnetic filter located just after the transition between the two chambers of the source. Results for the axial profiles of the plasma parameters display the correlation of the ratio n_/ne of the densities of the negative hydrogen ions and of the electrons and of the concentration of the negative ions with the electron density and temperature: The maxima of the (n_/ne)‐ratio and of the density of the negative ions obtained are located at the position of maximum of the electron density behind the filter, in the region of the low electron temperature. Results from probe diagnostics and laser photodetachment measurements at a ...

An analytical model for predicting the axial structure of weakly collisional plasma columns sustained by a propagating electromagnetic surface wave has been developed. It considers both the ambipolar diffusion and volume recombination regimes. The results are expressed as electrodynamical similarity relations and show the respective influence of the wave's dispersion and damping of discharge conditions and of the charged particle loss mechanisms upon the axial gradient of electron density.

Two radiophysics diagnostic methods (interferogram measurements and field radial decay method) are used for determining the plasma behaviour in microwave discharges sustained by surface wave propagation. The interferogram technique which is slightly modified and simplified is used as a reference method for verifying the applicability of the method of the field radial decay. Comparison with theoretical results for the axial density gradient is given and discussed.

Die vorliegende Arbeit stellt einen Vergleich zwischen den Bildungssystemen von Bulgarien und Österreich an, wobei das Interesse hauptsächlich darin liegt, die Eingliederung der Sonder– und Heilpädagogik in das Bildungssystem der verglichenen Länder zu analysieren. Gleichzeitig wurden die Triebkräfte erforscht, die zur Etablierung integrativer Strukturen in den beiden Bildungssystemen geführt haben. Die besonderen lokalen Ausprägungen der schulischen Integration in den verglichenen Ländern konnten dargestellt werden. Dabei wurde versucht festzustellen, in wie weit die Geschichte und die Bildungspolitik der beiden Länder die gegenwärtige Situation des Bildungsbereichs beeinflusst haben. Um sich ein klares Bild darüber zu verschaffen, wurden die geschichtliche Entwicklung des Bildungswesens in Österreich und in Bulgarien sowie der gesetzliche Rahmen der Bildung in den beiden Ländern untersucht, indem der Inhalt von relevanten Literaturquellen sowie offizieller Dokumente (Gesetze, Verträge, etc.) sorgfältig analysiert wurde. Zusätzlich wurden Experteninterviews mit Fachleuten und Entscheidungsträgern in Bulgarien durchgeführt, wobei jedoch der Bearbeitung dieser Interviews nicht ein ganzes Kapitel gewidmet wurde, sondern es fließen die dabei gewonnenen wichtigen Informationen an entsprechenden Stellen in die Arbeit ein. Auf Interviews mit österreichischen Experten wurde verzichtet, da es in Österreich, im Gegensatz zu Bulgarien, viel mehr Informationsquellen gab und die notwendigen Daten auch auf diese Weise zu finden waren. Die Untersuchung zeigte, dass in beiden Ländern integrative Prozesse und Strukturen vorhanden sind. Neun Faktoren, die zur Etablierung dieser Prozessen und Strukturen geführt hatten, konnten isoliert werden. Diese wurden dann am Ende der Arbeit präsentiert., The present study makes a comparison between the educational systems of Bulgaria and Austria, whereby the interest lies principally in the integration of the special education in the education systems of the compared countries. At the same time the reasons for the establishment of integration structures in the two educational systems were investigated. It was also tried to find the special local characteristics of the school integration in the compared countries. It was attempted to determine to what extent the history and the education policies of the two countries have affected the current situation of the education system. The historical development of education in Austria and Bulgaria as well as the legal framework of education in the two countries were examined and the content of relevant literature sources and official documents (laws, contracts, etc.) was carefully analyzed. In addition, interviews with experts and decision makers in Bulgaria were conducted. However not a whole chapter was devoted to the editing of the interviews, but the important information, gained through them, was incorporated in the proper passages of the study. No interviews with Austrian experts were conducted, because in Austria, unlike in Bulgaria, there were many other sources through which the necessary data could be gained. The research showed that integrative processes and structures are present in both countries. Nine Factors, which had led to the establishment of these processes and structures, could be isolated. These were presented at the end of the study.

The nonlinear carrier wave dispersion relation at weak nonlinearity is derived for the linearly polarized (LP) modes of a step-index optical fibre that has both a nonlinear core and a nonlinear cladding. The calculation begins with the exact equations for the nonlinear fibre and the nonlinear shift (coefficient), from its linear value, of the propagation wave-number is given in closed analytical form. The nonlinear coefficient is completely general and accounts both for the nonlinearity and the structure of the guided mode. Some numerical results for the LP01 mode are presented which show that significant deviations occur from the conventionally accepted (averaged) nonlinear coefficient.

The study presents results from a 2D model of hydrogen discharges in a tandem type of a plasma source. Analysis of the particle and electron‐energy balance outlines the pattern of the source operation: (i) discharge production in the driver governed by the mechanisms ensuring self‐consistency of hydrogen discharges in regions with rf power deposition, however, here influenced by the fluxes going to the second chamber of the source, and (ii) plasma existence in the expansion volume of the source completely determined by the particle fluxes from the first chamber. The influence of varying applied power and gas pressure is discussed.

For surface wave produced argon plasmas in the 60-180 MHz range, electron energy distribution functions are calculated from the electron Boltzmann equation solved in the Lorentz approximation. Breakdown and maintenance field strengths are determined self-consistently by satisfying additional balance equations. The influence of space charge fields and the limits of the approximations used are discussed.

The nonlinear behaviour of surface waves propagating along a plasma column is investigated. The experiments include (i) measurements of the nonlinear dispersion of the waves and (ii) observation of the evolution of the shape of the wave envelope and of the wave spectrum when the waves are excited with an amplitude-modulated signal. Comparison with theory shows that (i) the measured nonlinear wavelength shift corresponds to increasing wave phase velocity with increasing wave amplitude, (ii) the observed narrowing of the wave envelope can be associated with the formation of periodic nonlinear waves described by dn Jacobi elliptic function solutions of the nonlinear Schrödinger equation and (iii) the observed strong changes of the wave spectrum are mainly related to a nonlinear effect of phase modulation.

Most industrial wastes contain different organic mixtures, making important the investigation on the microbial destruction of composite substrates. The capability of microbes to remove harmful chemicals from polluted environments strongly depends on the presence of other carbon and energy substrates. The effect of mixtures of phenol- and methyl-substituted phenols (o-, m-, p-cresol) on the growth behaviour and degradation capacity of Trichosporon cutaneum strain was investigated. The cell-free supernatants were analysed by HPLC. It was established that the presence of o-, m- and p- cresol has not prevented complete phenol assimilation but had significant delaying effect on the phenol degradation dynamics. The mutual influence of phenol and p-cresol was investigated. We developed the kinetic model on the basis of Haldane kinetics, which used model parameters from single-substrate experiments to predict the outcome of the two-substrate mixture experiment. The interaction coefficients indicating the degree to which phenol affects the biodegradation of p-cresol and vice versa were estimated. Quantitative estimation of interaction parameters is essential to facilitate the application of single or mixed cultures to the bio-treatment of hazardous compounds.

For pt.II see ibid., vol.21, p.1605 (1988). Non-linear effects of the field of high-frequency surface waves on the ionisation instability in gas discharge plasma presented previously are applied to gaseous lasers. It is shown that suppression of the ionisation instability by the high-frequency field can be considered as an effective method for improving the output characteristics of He-Ne lasers.

The phenol-degrading strain Trichosporon cutaneum R57 utilizes various aromatic and aliphatic compounds as a sole carbon and energy source. The intracellular activities of phenol hydroxylase [EC 1.14.13.7] of a Trichosporon cutaneum R57 strain grown on phenol (0.5 g/l) were measured. Different toxic phenol derivatives (cresols, nitrophenols and hydroxyphenols) were used as substrates in the reaction mixture for determination of the enzyme activity. The data obtained showed that the investigated enzyme was capable to hydroxylate all applied aromatic substrates. The measured activities of phenol hydroxylase varied significantly depending on the aromatic compounds used as substrates. The rate of phenol hydroxylase activity with phenol as a substrate (1.0 U/mg total cell protein) was accepted as 100%.

A fluid-plasma model description of the operation of a magnetic filter for electron cooling in gas-discharge plasmas is presented in the study. Directed to the use of weak magnetic fields in the sources of negative hydrogen ion beams for additional heating of fusion plasmas, hydrogen discharges have been considered. The numerical results obtained within a 2D-model are stressed. The 1D-model presented aims at showing the main trends whereas the results obtained within the 3D-model, also developed, confirm the 2D-model description. The models outline the importance of the transport phenomena: electron-energy and charged-particle fluxes. Reduction of the thermal flux across the magnetic field together with thermal diffusion and diffusion, acting in combination, is the basis of the electron cooling and of the spatial distribution of the electron density. Effects due to the (E × B)-drift and the diamagnetic drift form a fine spatial structure of the plasma-parameter variations.

Involving the idea for the Biermann effect known from space physics as well as recent discussions on non-ambipolarity of the electron and ion fluxes in low-pressure discharges, the study builds the discharge pattern in a source with localized RF power deposition outside the region of high electron density. A vortex dc current flowing in an RF discharge and a steady-state magnetic field induced by this current govern the discharge behavior. Owing to a shift in the positions of the electron-density and plasma-potential maxima, the dc current is driven with the purpose of keeping the conservativity of the dc field in the discharge. The results present the spatial structure of a discharge in a regime of non-ambipolarity of the electron and ion fluxes, including its modifications by the magnetic field.

A hydrodynamic theory of non-local plasma heating by high-frequency fields in gas discharges, sustained for instance by surface waves, is presented. Radial distributions of electron temperature are obtained for arbitrary radial profiles both of electron density and of electric field intensity.}