A fluid-plasma model of diffusion-controlled hydrogen discharges sustained in the field of propagating surface waves is presented in this study. The self-consistent description of the discharge structure achieved provides results for the inter-related variations of the discharge characteristics: the electron concentration n e , the concentrations of the three ionic species (H + , H + 2 and H + 3 ), the concentrations of the two neutral gas components (H and H 2 ), the electron temperature, the power absorbed on average by an electron, the gas temperature, the wavenumber and the space damping rate α of the wave. Wave behaviour in radially inhomogeneous collisional plasmas is taken into account because it provides the proper description of diffusion-controlled discharges. The general mechanism of nonlocal heating of the electrons in the wave field is considered. The model is extended to comparatively low gas pressures (p 0.2 Torr) by introducing effective mobilities of the ions in which, besides the ion-neutral elastic collisions, the production and destruction of ions by collisions are included. Based on these effective mobilities, the ambipolar diffusion coefficients of the charged particles are specified. The most important reactions that contribute-under the gas-discharge conditions considered-to the production of charged particles and hydrogen atoms as well as to the electron-energy and gas-energy balances are involved in the model. It is shown that in hydrogen discharges, the ( -n e )-relation, which besides the (α-n e )-relation ensures a self-consistent description of the axial structure of surface-wave-sustained plasmas, in general, stems from the dependence of on the concentrations of the neutral gas components (H, H 2 ) and their relation to the concentrations of the ions (H + , H + 2 and H + 3 ). The results obtained using the model are discussed in the context of experiments showing a peculiar behaviour of the axial structure of hydrogen discharges compared to discharges in other gases.

Abstract. 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 main trends whereas the results obtained within the 3D model, also developed, come to confirm the 2D-model description. The models outline 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 a combination, are in the basis of the electron cooling and of the spatial distribution of the electron density. Effects due to the ) ( B E × -drift and to the diamagnetic drift form the fine spatial structure of the plasma-parameter variations. IntroductionThe development of sources of negative ion beams for fusion plasma heating by neutral beam injection [1-4] is one of the stimuli motivating the active research on low-pressure hydrogen discharges. In general, the sources of negative hydrogen ions with volume-production based processes as well as the hybrid sources where surface production is employed are tandem-type sources with a construction ensuring space separation of regions of high and low electron temperature [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Thus, electron cooling in the discharge is needed and this is provided by a magnetic filter.The magnetic filter is a localized transverse magnetic field. Its effect for cooling the electrons has been proved both experimentally [3,6,7,13,[20][21][22][23][24][25][26], by probe diagnostics and measurements of the current density of the extracted negative ions, and theoretically [6][7][8][9][10][11][12]15,27] by modelling and discussions on the mechanisms governing the operation of the filter. The fluid-plasma models [6][7][8][9][10]15] of the magnetic filter involve importance of the transport processes. However, the different models stress different aspects as mechanisms of the filter operation: (i) reduction of the electron mobility and of the diffusion in magnetized plasmas acting in a combination with the temperature dependence of the Coulomb collision frequency, the latter considered as a factor ensuring lower diffusion of the hot electrons; (ii) thermal conductivity effects, again acting together with Coulomb collisions; (iii) importance of the Lorentz force showing evidence due to cancelled effects of the -) ( B E × and diamagnetic drifts; (iv) importance of the diamagnetic drift; (v) diffusion acting together with elastic electron-neutral collisions. Both 1D and 2D models have been developed, however, as it has been usually stressed, 2D models are needed for proper description of the problem. Due to the complexity of the description, simplifying assumptions, like neglecting of col...

The study presents a numerical fluid-plasma model of waveguide discharges sustained by travelling azimuthallysymmetric Trivelpiece-Gould modes. The results describe weakly-magnetized ( ª ) plasma production in a diffusion-controlled regime ( being the wave frequency, ª the electron gyro-frequency). However, with respect to the influence of the external magnetic field on the transverse ambipolar-diffusion coefficient, cases of both weak and strong impact of the magnetic field are covered. In its electrodynamical part, the model involves detailed description of the behaviour of the Trivelpiece-Gould waves in radially-inhomogeneous collisional plasmas. The gas-discharge part of the model specifies plasma production in an argon gas. The results are for the self-consistent structure of the discharge composed out of the interrelated variations of wavenumber, space damping rate, plasma density, electron temperature and power absorbed on average by an electron. The analysis is in terms of influence of gas-pressure and magnetic-field changes.

This study aims to contribute to the analysis of the mechanisms of wave-energy absorption and electron heating in waveguide discharges sustained by propagating Trivelpiece-Gould modes. The discussion is based on a derivation of the dispersion law and the wavefield distribution in cylindrical waveguides with magnetized collisional plasmas with a diffuse boundary. Through resonance absorption associated with the transformation of Trivelpiece-Gould modes into upper hybrid volume waves, the plasma-density radial inhomogeneity affects the wave behaviour. The conditions of the existence of resonance absorption are analysed and its role in the maintenance of wave-produced gas discharges in external magnetic fields is discussed.

The effects of collisions and radial inhomogeneity of the plasma density on the behaviour of the azimuthally-symmetric Trivelpiece-Gould modes (including the waveguide resonance and the wave resonance absorption at the upper hybrid frequency) are treated in this study in terms of their relation to gas-discharge production in an external magnetic field. Numerical solutions for the wave-field patterns and for the propagation properties of the waves are presented and their changes are discussed with a varying averaged plasma density, for various plasma-density profiles. First modifications due to collisions in homogeneous plasmas are presented for different values of the external magnetic field. Then, for a given magnetic field, the combined effects of collisions and Bessel-type radial profiles of the plasma density are emphasized. After which, for a given profile, the influence is discussed of varying the magnetic field. It became evident that, for low collision frequencies and a cyclotron frequency less than the wave frequency, the plasma-density profile shape has a strong impact on the results and that the wave properties, as the average density is varied for dominantly diffusive charged particle losses, are badly represented by wave properties in uniform plasmas. The behaviour discussed here should be useful in understanding the structure of diffusion-controlled discharges maintained in the fields of propagating Trivelpiece-Gould modes.