Anisotropy of the electron component in a cylindrical magnetron discharge. I. Theory of the multiterm analysis.

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.

Anisotropy of the electron component in a cylindrical magnetron discharge. II. Application to real magnetron discharge.

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.

Two-dimensional nonlocal model of axially and radially inhomogeneous plasma of cylindrical magnetron discharge.

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.

Nonlocal electron kinetics and excited state densities in a magnetron discharge in argon.

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.

Kinetic simulation model of magnetron discharges.

A self-consistent kinetic model of plasma in the entire gap of a magnetron cylindrical discharge, with all quantities varying in radius and with the uniform magnetic field being directed axially, is presented. The discharge modeling is performed on the basis of a numerical solution of the spatially inhomogeneous Boltzmann kinetic equation together with equations of ion motion, current balance, and Poisson's equation. The model represents an example of discharge description from cathode to anode with respect to strong nonlocality effects in the distribution function formation. Based on the results for a typical magnetron discharge condition, the distribution functions, field, and macroscopic properties calculated for the entire discharge in argon, are presented and discussed.