Boltzmann equation and Monte Carlo analysis of electron-electron interactions on electron distributions in nonthermal cold plasmas

Abstract

Electron distribution functions in nonthermal cold plasmas generated by classical electrical discharges have been calculated from a powerful Boltzmann equation solution and an original Monte Carlo simulation. In these two methods both classical (i.e. , elastic, inelastic, and superelastic) electron-atom (or molecule) collisions and electron-electron interactions are taken into account. The approximations considered to include long-range (electron-electron) and short-range (electron-atom) interactions in the same Monte Carlo algorithm are first validated by comparing with Boltzmann equation results. Then, the influence of electron-electron interactions on electron distribution functions, swarm parameters, and reaction rates under nonthermal cold plasma conditions are analyzed and discussed as a function of reduced electric field E/N and ionization degree n, /N for different atomic and molecular gases. PACS number(s): 52.20.Fs, 51.50.+v and time-dependentBoltzmann equation solution proposed in this paper is based on a stable and powerful numerical scheme. It is different from the classical scheme of Rockwood (used by numerous authors) since, due to the iterative nature of the present work scheme, there is no restriction for the treatment of any kind of collisions involving electrons (elastic, superelastic, inelastic, and also ionization stepwise or Penning ionization). Concerning the treatment of electron-electron interactions with

Weighted Particles in Coulomb Collision Simulations Based on the Theory of a Cumulative Scattering Angle

“…(16a) as t = (n 1 /n 12 )( t ) 12 . We chose the system time increment ( t ) 12 to be ( t ) 12 = t /Z , where t = 1.25 × 10 −9 s. Note the t is the (given) system time and ( t ) 12 is its subinterval. Choosing the subinterval is arbitrary.…”

“…Nanbu [10,11] proposed a quite different formulation on a cumulative property of Coulomb collisions in plasmas; he determined the probability distribution for a cumulative deflection angle resulting from many small-angle collisions. The idea of grouping is also discussed in the Boltzmann equation analysis of electron-electron collisions [12]. The nature of Nanbu's formulation yields a drastic decrease in computational effort that is realized in the Monte Carlo particle simulation of Coulomb collisions.…”

Electron Energy Distributions in Inductively Coupled Plasma: Comparison of Chlorine Discharge with Argon Discharge

“…36) It is believed that Coulomb collisions are important for plasmas with the electron density greater than 10 11 cm À3 . The role of Coulomb collisions is the equilibration of electron kinetic energy.…”

Plasma excitation processes in flue gas simulated with Monte Carlo electron dynamics

“…These cross sections are well-established ones. The cross sections for H 2 O were collected from many references [20][21][22][23][24][25]. The calculated rotational cross section for H 2 O of Itikawa [21] was scaled until the electron drift measurements of Pack et al had been reproduced [26].…”

“…The trajectory of electrons in a reactor configuration can be computed by means of a Monte Carlo algorithm [4][5][6][7][8]. The so called 'zero-collision' Monte Carlo method, originally developed by Skullerud [9], is frequently used to compute plasma parameters, see [10][11][12]. This algorithm, based on collisional frequencies of the electron, is currently mostly used for noble gases.…”