Monte Carlo studies of non-conservative electron transport in the steady-state Townsend experiment

An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.

[1]  J. Behnke,et al.  Nonlocal electron kinetics and densities of excited atoms in S and P striations , 2000 .

[2]  J. Behnke,et al.  On the bunching effect of electrons in spatially periodic resonance fields , 1998 .

[3]  J. Boeuf,et al.  Monte Carlo simulation of electron swarm motion in SF6 , 1984 .

[4]  D. Loffhagen,et al.  Spatial Transition of the Electron Gas from the Active to the Remote Plasma State , 2003 .

[5]  R. Robson,et al.  Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis , 2002 .

[6]  Y. Golubovskii,et al.  On the Nonlocal Electron Kinetics in s- and p-Striations of DC Glow Discharge Plasmas: I. Electron Establishment in Striation-like Fields , 1998 .

[7]  Robert Robson,et al.  Transport phenomena in the presence of reactions: definition and measurement of transport coefficients , 1991 .

[8]  J. Urquijo,et al.  Data and modeling of negative ion transport in gases of interest for production of integrated circuits and nanotechnologies , 2007 .

[9]  D. Marić,et al.  Measurements and analysis of excitation coefficients and secondary electron yields in Townsend dark discharges , 2003 .

[10]  Sommerer,et al.  Self-consistent kinetic model of the cathode fall of a glow discharge. , 1989, Physical review. A, General physics.

[11]  R W L Thomas,et al.  Monte Carlo simulation of electrical discharges in gases , 1969 .

[12]  Robert Robson,et al.  Colloquium : Physically based fluid modeling of collisionally dominated low-temperature plasmas , 2005 .

[13]  D. Uhrlandt,et al.  Space-dependent kinetics of electrons in the anode region of a glow discharge , 2001 .

[14]  D. Uhrlandt,et al.  Strict calculation of electron energy distribution functions in inhomogeneous plasmas , 1997 .

[15]  Y. Sakai,et al.  The variation of steady state electron mean energy between parallel plates in argon , 1972 .

[16]  Uwe R. Kortshagen,et al.  On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasmas , 1996 .

[17]  Robert Robson,et al.  Kinetic Theory of Charged Particle Swarms in Neutral Gases , 1980 .

[18]  F. Sigeneger,et al.  On the Nonlocal Electron Kinetics in s and p Striations of DC Glow Discharge Plasmas: II. Electron Properties in Periodic States , 2000 .

[19]  Y. Sakai,et al.  The development of electron avalanches in argon at high E/N values. II. Boltzmann equation analysis , 1977 .

[20]  G. Sukhinin,et al.  Kinetics of the Electrons in Striations of Spherical Glow Discharges , 2000 .

[21]  J. Boeuf,et al.  A Monte Carlo analysis of an electron swarm in a nonuniform field: the cathode region of a glow discharge in helium , 1982 .

[22]  Y. Sakai,et al.  The development of electron avalanches in argon at high E/N values. I. Monte Carlo simulation , 1977 .

[23]  A. Takeda,et al.  Analyses of spatially resolved electron energy distribution and transport properties in Steady State in CF4 , 1997 .

[24]  J. Lucas,et al.  A comparison of a Monte Carlo simulation and the Boltzmann solution for electron swarm motion in gases , 1975 .

[25]  B. V. D. Pol,et al.  Tchebycheff polynomials and their relation to circular functions, Besselfunctions and Lissajous-Figures , 1934 .

[26]  Parker,et al.  Comparison of Monte Carlo simulations and nonlocal calculations of the electron distribution function in a positive column plasma. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Z. Petrović,et al.  Kinetic phenomena in charged particle transport in gases, swarm parameters and cross section data , 2007 .

[28]  Y. Golubovskii,et al.  On the formation of electron velocity distribution functions in striation-like fields , 2002 .

[29]  J. Fletcher.  Non-equilibrium in low pressure rare gas discharges , 1985 .

[30]  A. B. Wedding,et al.  A benchmark model for analysis of electron transport in non-conservative gases , 1997 .

[31]  T. Makabe,et al.  Plasma Electronics: Applications in Microelectronic Device Fabrication , 2006 .

[32]  Toshimitsu Musha,et al.  Monte Carlo Calculations of Motion of Electrons in Helium , 1960 .

[33]  Z. Petrović,et al.  Electron excitation coefficients for 2p and 3p levels of Xe , 2000 .

[34]  Z. Petrović,et al.  Monte Carlo studies of electron transport in crossed electric and magnetic fields in CF4 , 2005 .

[35]  D. Uhrlandt,et al.  Radially inhomogeneous electron kinetics in the DC column plasma , 1996 .

[36]  Ronald D. White,et al.  Spatially periodic structures in electron swarms and the Franck-Hertz experiment , 2000 .

[37]  K. Kumar.  Short-time development of swarms-approach to hydrodynamic regime for charged particles in neutral gases , 1981 .

[38]  K. Ness,et al.  Anomalous anisotropic diffusion of electron swarms in a.c. electric fields , 1995 .

[39]  F. Sigeneger,et al.  Relaxation of the electron gas in spatially decaying plasmas , 2001 .

[40]  J. Behnke,et al.  On the non-local electron kinetics in spatially periodic striation-like fields , 1999 .

[41]  Robert Robson,et al.  Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas? , 2003 .

[42]  D. Uhrlandt,et al.  Nonlocal behaviour of the electron component in nonequilibrium plasmas , 1996 .

[43]  Z. Petrović,et al.  Comparison of the results of Monte Carlo simulations with experimental data for electron swarms in ? from moderate to very high electric field to gas density ratios ? , 1998 .

[44]  H. Sugawara,et al.  Analyses of electron swarms in gases under steady-state Townsend conditions , 1994 .

[45]  D. Loffhagen.  Impact of Electron–Electron Collisions on the Spatial Electron Relaxation in Non-Isothermal Plasmas , 2005 .

[46]  Y. Choi,et al.  Studies of a sheath structure in an RF discharge using experimental, analytical, and simulation approaches , 1999 .

[47]  A. Napartovich,et al.  Electron swarm characteristics in Ar:NF3 mixtures under steady-state Townsend conditions , 1999 .

[48]  N. Dyatko,et al.  Spatial Electron Relaxation: Comparison of Monte Carlo and Boltzmann Equation Results , 2003 .

[49]  H. Blevin,et al.  Electron Transport and Rate Coefficients in Townsend Discharges , 1984 .

[50]  D. Loffhagen,et al.  Temporal and spatial relaxation of electrons in low temperature plasmas , 2002 .

[51]  H R Skullerud,et al.  The stochastic computer simulation of ion motion in a gas subjected to a constant electric field , 1968 .

[52]  Winkler,et al.  Response of plasma electrons to a spatially embedded electric field impulse. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[53]  Z. Petrović,et al.  The role of heavy particles in kinetics of low current discharges in argon at high electric field to gas number density ratio , 1998 .

[54]  D. Loffhagen,et al.  Study of the electron kinetics in the anode region of a glow discharge by a multiterm approach and Monte Carlo simulations , 2002 .

[55]  K. Ness,et al.  Non-conservative electron transport in CF4 in electric and magnetic fields crossed at arbitrary angles , 2006 .

[56]  F. Sigeneger,et al.  On the mechanisms of spatial electron relaxation in nonisothermal plasmas , 1997 .

[57]  F. Sigeneger,et al.  Impact of magnetic fields on the spatial relaxation of electrons , 2000 .

[58]  F. Sigeneger,et al.  Spatial relaxation of electrons in nonisothermal plasmas , 1997 .

[59]  Z. Petrović,et al.  Monte Carlo simulation of non-conservative positron transport in pure argon , 2008 .

[60]  Toshiaki Makabe,et al.  Kinetic phenomena in electron transport in radio-frequency fields , 2002 .

[61]  G. Petrov,et al.  Multi-term treatment of electron kinetics in inhomogeneous nonequilibrium plasmas , 1997 .

[62]  R. Robson,et al.  What really happens with the electron gas in the famous Franck‐Hertz experiment? , 2003 .

[63]  M. Hannemann,et al.  The electron kinetics in the cathode region of H2/Ar/N2 discharges , 2000 .

[64]  R. White,et al.  Magnetic field effects on spatial relaxation of swarm particles in the idealized steady-state Townsend experiment. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  S. Vrhovac,et al.  Energy distributions of electrons in a low-current self-sustained nitrogen discharge , 2001 .