Numerical study of isotope separation phenomena of noble gases by dc discharge as rarefied gas dynamics

Abstract

A numerical simulation was undertaken on argon and krypton isotope separation in their dc arc discharges through a thin capillary. The mass transport phenomenon of neutral particles as well as of ions in the positive column was treated by direct simulation Monte Carlo method, whereas electrons were treated as background particles, and their behavior was assumed to be already given to evaluate the effects of electron collisions onto neutral particles. The numerical results agreed qualitatively with the isotope separation phenomena of argon and krypton dc discharges. The heavier isotopes were enriched into the region of the cathode, whereas the lighter ones into that of the anode. It was also found that the numerical results explained the pressure difference between the cathode and the anode observed experimentally. The characteristics of drift motion of ions also qualitatively agreed with existing experimental results.

Numerical Study on Acceleration and Deceleration Mechanism of Weakly Ionized Plasma Flowing Supersonically Through Open Field Line

“…Not only the ions, but also neutral particles must be treated as rarefied flow, since the Knudsen number of the system is larger than 0.01 or sometimes becomes up to 1.0, where the fluid dynamic treatment is not desirable. We should describe such rarefied systems by the Boltzmann equations, which can be solved statistically by particle-based method, and typically, by the direct simulation Monte Carlo (DSMC) method [14]- [16]. Upon our previous experimental and numerical study [10]- [13], we must carry out numerical simulation of the expanding plasma jet as rarefied gas dynamics based not on fluid approximation but on particle modeling, which is precisely the objective of this paper.…”

“…To solve the rarefied flow with its Knudsen number Kn ≥ 0.02, it is well known that the NavierStokes equation should be avoided but that the Boltzmann equation should be applied to, where DSMC method is one of the particle-based simulations to obtain a stochastic solution [14]- [16]. In the present simulation, we treat cold helium plasma with low-ionization degree ∼1%, and therefore, we must solve the neutral flow simultaneously with the electrons and ions since the structure of the neutral flow strongly couples with the flow of ions.…”

“…Next, for collisions between an ion and a neutral, we consider two kinds of collisions, that is, the charge transfer collision and the elastic collision [15], [16]. We applied rigidsphere model, and therefore, the total cross section was cited from [28], and the probability of charge transfer cross section was set as 1/2 also after Nanbu [28].…”

“…where F is the force on the particle, V is the particle velocity, m is the particle mass, q is the charge of particle and q = 0 for neutrals and q = e, elementary charge, for ions because we now consider only singly charged He ions owing to the low electron temperature of the present plasma [10], and E and B are the electric and the magnetic fields, respectively, at the position of each particle at the time t. Both of their velocity and their position are treated in 3-D space, whereas the collisions are treated in 2-D space with the rotational transformation from (r, θ, z) to (r, 0, z) according to the Riechelmann-Nanbu method because the system is axially symmetric [15], [16], [24], [25]. We treated the collisions of a sample particle with other sample molecules by the maximum collision number method [26].…”

“…Concerning collisions of two neutral particles, the cross section was calculated from the self-diffusion coefficient, which was assumed to be constant [27]. They are treated as an isotropic scattering in a center of mass system [15], [16]. That is, the velocities of the particle pair i, j after the collision V i , V j is calculated from those before the collision V i , V j by the following:…”