G.J. Parker

Radiation trapping simulations using the propagator function method: complete and partial frequency redistribution

An integral method for solving the problem of imprisonment of resonance radiation based on propagator functions is further developed. Earlier work was restricted to plane parallel and spherical geometries, to a Lorentz lineshape, and to the approximation of complete frequency redistribution. This work extends the method to cylindrical geometry, to a Voigt lineshape, and to include the effects of partial frequency redistribution. The method is ideal for calculating both the time-dependent and the steady-state densities of resonance atoms which result from an arbitrary production rate per unit volume. An emission spectrum is also generated in calculations involving partial frequency redistribution. The propagator function method is at least 50 times faster than the Monte Carlo method. The greater speed of the propagator function method makes it well suited to fully self-consistent kinetic simulations of glow discharge plasmas.

Physical and numerical verification of discharge calculations

Calculations of radio frequency discharge parameters, and to a lesser extent DC discharge parameters, are apparently highly sensitive to the physical model used. The testing of numerical schemes for error, considering alternative formulations and simple physical models, is carefully considered. Within kinetic models a number of options exist, having different capabilities, the implications of which are examined. Particle simulations are discussed, and mesh-based kinetic calculations are considered in detail. An efficient and accurate mesh-based kinetic model which closely replicates the physical processes taking place is presented. Ways to improve its accuracy, which is limited by the resolution of the mesh, and their effects are presented. Cross-checking of various numerical formulations shows that the results for each are essentially the same. Physical reasoning and simple estimates of discharge parameters are used to further substantiate the predictions for a particular discharge, and the processes taking place in an RF discharge in helium are described in detail. >

Self-consistent kinetic model of an entire dc discharge

Abstract A dc discharge in helium has been modeled from electrode to electrode, fully kinetically using a self-consistent electric field and including all the physical processes believed to be important for ions, electrons and neutral atoms. The cathode fall, negative glow, and cathode fall-negative glow boundary develop naturally in the simulation without an internal boundary condition and without breaking the electron energy distribution function in components. Results of the simulation are compared to precise experimental results for the electric field profile, species densities, and average electron energy. Excellent agreement is obtained demonstrating that the physical model used is both correct and complete.

Radiation trapping simulations using the propagator function method

Abstract An integral method of solving the Holstein-Biberman equation based on a propagator function is described. This method is used to solve the equation with a Lorentz lineshape in an infinite plane parallel geometry and a hollow spherical geometry. The method is ideal for solving for both the time dependent and the steady state density of resonance atoms which results from an arbitrary production rate per unit volume. The propagator function method is 100 times faster than the Monte Carlo method. The greater speed of the propagator function method makes it well suited to fully self-consistent kinetic simulations of glow discharge plasmas.

Kinetic modeling of the α to γ transition in radio frequency discharges

An accurate and comprehensive self‐consistent kinetic model is applied to a helium radio frequency (rf) discharge which in experiments exhibits an ‘‘α to γ’’ transition. The main conclusions are (i) there is good agreement (factor of 2) between the experiment and simulation in plasma density, power density, and current density across two orders of magnitude of the applied voltage. (ii) The bulk electron temperature exhibits a transition from high at low driving voltages to low at high voltages. The low‐voltage regime exhibits a larger bulk electric field in the simulation. (iii) Multistep ionization is important under all conditions studied.

Accurate models of collisions in glow discharge simulations

Very detailed, self-consistent kinetic glow discharge simulations are used to examine the effect of various models of collisional processes. The effects of allowing anisotropy in elastic electron collisions with neutral atoms instead of using the momentum transfer cross-section, the effects of using an isotropic distribution in inelastic electron-atom collisions, and the effects of including a Coulomb electron-electron collision operator are all described. It is shown that changes in any of the collisional models, especially the second and third described above, can make a profound difference in the simulation results. This confirms that many discharge simulations have great sensitivity to the physical and numerical approximations used. Our results reinforce the importance of using a kinetic theory approach with highly realistic models of various collisional processes. >