ABSTRACT
We present a detailed self-consistent model of a positive column in argon glow discharge at moderate pressures and currents. This model describes the discharge transition between diffuse and constricted states. The model includes an extensive set of plasma chemical reactions and equation for inhomogeneous gas heating. The nonequilibrium behavior of an electron distribution function is also considered. One of the main features of the model is an accurate treatment of radiation trapping by solving the Holstein-Biberman equation directly. Influence of the radiation trapping on macroscopic parameters of the constricted positive column is studied. We propose a method for solving a boundary-value problem, including particle and energy balance equations for electrons, ground state atoms, atomic and molecular ions, and excited species. Unlike traditional solution approaches for similar systems, the method provides continuous Z- and S-shaped characteristics of discharge parameters, describing hysteresis in transition between diffuse and constricted discharge regimes. Performed experiments include measurements of volt-ampere characteristics and spectroscopic study of radial density profiles of excited atoms by measuring line emission and absorption, and electrons by measuring bremsstrahlung intensity. The role of resonance radiation trapping in spatial redistribution of 1s and 2pstates of argon is demonstrated. Results of modeling are compared to the experimental data.
ABSTRACT
An effect of a nonlocal plasma response caused by local laser radiation exciting atoms in resonant and metastable states is observed in a dc neon glow discharge. Starting at the perturbed position, spatially damped oscillations in the direction of the anode effecting all plasma quantities are created. Depending on the excitation of resonant or metastable atoms, the oscillations are phase-shifted by π. If the laser excites in particular a cycling transition, no nonlocal plasma response is observed. The relaxation of the plasma is investigated by means of visible light measurements using a line camera in the vicinity of the axial perturbation position. The effect is modeled in terms of nonlocal electron kinetics by solving the spatially inhomogeneous electron Boltzmann equation.
Subject(s)
Algorithms , Lasers , Models, Chemical , Plasma Gases/chemistry , Plasma Gases/radiation effects , Computer SimulationABSTRACT
Resonance formation of the electron velocity distribution function (EDF) in an inert gas dc discharge at low pressures and small currents is analyzed on the basis of an accurate numerical solution of the Boltzmann kinetic equation in spatially periodic sinusoidally modulated striation-like fields. Calculations are performed for neon at pressures around 1 Torr . The dependences of the EDF, electron density and mean energy, and excitation rate on the electric field spatial period length are investigated. In addition to resonances corresponding to S and P striations predicted by linear analytical theory, the kinetic model indicates the presence of a resonance that can be attributed to an R striation. This resonance is more pronounced at lower pressures when R striations are observed experimentally. The influence of inelastic collisions on the EDF formation in the resonance fields is analyzed.
ABSTRACT
A general multiterm representation of the phase space electron distribution function in terms of spherical tensors is used to solve the Boltzmann kinetic equation in crossed electric and magnetic fields. The problem is formulated for an axisymmetric cylindrical magnetron discharge with the homogeneous magnetic field being directed axially and the electric field between the coaxial cathode and anode varying in radius only. A spherical harmonic representation of the velocity distribution function in Cartesian coordinates becomes especially cumbersome in the presence of the magnetic field. In contrast, the employment of a spherical tensor representation leads to a compact hierarchy of equations that accurately take into account the spatial inhomogeneities and anisotropy of the plasma in crossed fields. To describe the spatially inhomogeneous plasma the hierarchy of the kinetic equations is formulated in terms of the total energy and the radial coordinate. Appropriate boundary conditions at the electrodes for the tensor expansion coefficients are obtained.
ABSTRACT
The physical processes occurring in electrode regions and the positive column of a cylindrical magnetron discharge in crossed electric and magnetic fields are investigated based on the solution of the Boltzmann kinetic equation by a multiterm decomposition of the electron phase space distribution function in terms of spherical tensors. The influence of the distribution function anisotropy on the absolute values and radial profiles of the electron density and rates of various transport and collision processes is analyzed. The spiral lines for the directed particle and energy transport are obtained to illustrate the anisotropy effects in dependence on the magnetic field. The electron equipressure surfaces are constructed in the form of ellipsoids of pressure and their transformation in the cathode and anode regions is studied. A strong anisotropy of the energy flux tensor in contrast to a weak anisotropy of the momentum flux density tensor is found. Particular results are obtained for the cylindrical magnetron discharge in argon at pressure 3 Pa, current 200 mA, and magnetic fields ranging within 100 and 400 G.
ABSTRACT
The calculations of the electron distribution function (EDF) in striationlike, sinusoidally modulated electric fields were performed to determine the dependence on spatial period length. The calculations were done for a discharge in neon at pR=2 Torr cm, i/R=5 mA/cm, and electric field E/p=1.9 V cm(-1) Torr(-1). The presence of the resonances in the EDF and macroscopic parameters has been demonstrated. These resonances correspond to S and P striations observed in experiments. An interpretation of the results is proposed based on an analytical approximation of the numerical solution. Decomposition of EDF into two factors-amplitude and body-is carried out. The amplitude of the EDF is shown to be resonantly dependent on the value of the spatial period. One maximum in the EDF is formed at the value of the spatial period corresponding to the S striation, and two maxima at the value which corresponds to the P striation. The experimental measurements of the EDF in S and P striations with high spatial resolution showed agreement between the theoretical and the experimental results. Resonance effects in the EDF formation are considered based on the linear theory in the weakly modulated electric fields.
ABSTRACT
A cylindrical magnetron discharge (CMD) with two coaxial electrodes, a uniform axially directed magnetic field, and discharge ends closed by the shields biased at the cathode potential is considered. The presence of the shields creates axial inhomogeneity of plasma, which is taken into account in this study. At low pressures and small magnetic fields the pronounced nonlocal regime of the electron distribution function (EDF) formation is realized. The electron component is analyzed on the basis of radially and axially inhomogeneous Boltzmann kinetic equation. Unmagnetized electrons that move in axial direction are trapped in the axial potential well, their energy relaxation length exceeds the discharge vessel length, and the kinetic equation can be averaged over axial flights of electrons. Using a model two-dimensional potential profile, the EDFs at the different axial positions are obtained and two-dimensional distributions of the electron density, ionization rate, and current on cathode are calculated. The results of the modeling and experiments are compared for the dc CMD in Ar at a pressure of 3 Pa, magnetic field strength of 10 mT, and current of 150 mA.
ABSTRACT
The densities of argon metastable (3)P(2), and resonance (1)P(1), (3)P(1) states were measured along a cylindrical magnetron discharge radius by absorption spectroscopy using a narrow bandwidth single mode diode laser. The theoretical treatment includes calculations of the rates of numerous excitation and decay processes based on nonlocal electron kinetics, and analysis of the transport equations for the resonance and metastable atoms. The solution technique of the Biberman-Holstein equation of radiation transport is developed in conformity with magnetron discharge geometry. The radial profile of the effective lifetime is obtained, taking into account radiation escape on the inner and outer electrodes. The distinction in formations of the radial profiles of the resonance and metastable atoms caused by specifics of radiation transport and diffusion is demonstrated. The results of experiments and calculations are compared.