Boltzmann equation studies on electron swarm parameters in Townsend breakdown of copper vapor plasma using independently assessed electron-collision cross sections

Abstract

Electron transport coefficients in copper vapor plasma are calculated both by two-term expansion of electron Boltzmann equation Bolsig+ and tracking the random motion of electrons using Monte Carlo collision code METHES based upon recently evaluated cross section sets. The copper atoms are evaporated from hot electrode during the post-arc phase of vacuum circuit breakers, in which Townsend breakdown between electrode gaps is probable. The electron energy probability function, electron mean energy, flux/transport mobility and diffusion coefficients, as well as Townsend ionization coefficients are shown in reduced fields 10∼1000 Td at a typical vapor temperature 2000 K. The validity of two-term approximation is checked by comparison to well benchmarked METHES code. If the electrode temperature varies between 1500∼2500 K, the influence of vapor temperature on ionization coefficients is about 5% at 200.4 Td, and drops to 0.5% at 493 Td according to Bolsig+ results. Similar to classic gas discharge theory, the Paschen curve is proposed for Townsend breakdown of metal vapor. Using the calculated ionization coefficient and a constant secondary electron yield, the Paschen minimum is determined to be 106∼122 V at a critical value of the product of vapor density and gap length (4.7∼5.7)×1019 m-2. A satisfactory agreement was found with the previously measured ignition voltage between vacuum interrupter contacts after the arcing.

Observation of prior light emission before arcing development in a low-temperature plasma with multiple snapshot analysis

“…Since the average kinetic energy of the ectons ejected from the emitting area is a few electronvolts 38 and they are accelerated by the electric field in the sheath up to several electronvolts, inelastic collisions are dominant in the non-collapsing ion sheath, ultimately producing a Townsend breakdown. We note that Yang et al 39 investigated copper vapor plasma via simulation and reported minimum breakdown voltages of 106–122 V at . Considering that (i) the electron-impact ionization cross section of aluminum is ten times larger than those of copper and argon 40 , 41 , and (ii) the aluminum density is assumed as (few hundred millitorr of vapor pressure), breakdown is initiated within a sub-millimeter region in the non-collapsing sheath where the voltage difference between the background plasma and AIP tip is a few hundred volts.…”

The comparison of two-term Boltzmann approximation and Monte-Carlo solutions for e+Ar0 plasma

“…. Researches [51,52] suggest, that background VDF becomes important in the case of small fields. The latter can be taken into account by changing u 0 term in (8): u 0 → u 0 + v bg , where v bg corresponds to thermal velocity, sampled from the background VDF.…”

Transport of electrons and propagation of the negative ionisation fronts in indium vapour

“…The left panel shows the elastic momentum transfer (1), total ionization (2), and quantities that are obtained by multiplying the total cross section for superelastic collisions with the corresponding fractional populations of the first excited metastable state at indium vapour temperatures of 1260 K, 3260 K, and 5260 K. The left panel also includes the following discrete inelastic transitions: (5s 2 5p) 2 P 3/2 (3), (5s 2 6s) 2 S 1/2 (4), (5s 2 6p) 2 P 1/2 (5), (5s 2 6p) 2 P 3/2 (6), (5s 2 5d) 2 D 3/2 (7), (5s 2 5d) 2 D 5/2 (8), (5s 2 4p) 2 P 1/2 (9), (5s 2 4p) 2 P 3/2 (10), (5s 2 7s) 2 S 1/2 (11) and (5s 2 4p) 2 P 5/2 (12). The right panel includes the following discrete inelastic transitions: (5s 2 7s) 2 P 1/2 (13), (5s 2 7s) 2 P 3/2 (14), (5p 2 6d) 2 D 3/2 (15), (5p 2 6d) 2 D 5/2 (16), (5p 2 4 f ) 2 F 7/2 (17), (5p 2 4 f ) 2 F 5/2 (18), (5p 2 8s) 2 S 1/2 (19), (5p 2 8s) 2 P 1/2 (20), (5s 2 7d) 2 D 3/2 (21), (5s 2 7d) 2 D 5/2 (22) and (5s 2 8p) 2 P 3/2 (23). Integral cross sections for electron scattering in indium vapour for atoms in the metastable state (5s 2 5p) 2 P 3/2 .…”

“…The primary driving force behind these early studies was the modelling and optimization of light sources containing mercury [8,14,15], sodium [16,17], and zinc [18,19]. Other applications include the modelling of a gas laser [20], the magnetohydrodynamics of arcs [21], and a post-arc breakdown plasma [22].…”

“…The computed cross-sections were subsequently used as input to solve the Boltzmann equation to calculate the electron swarm transport coefficients. The publicly available two-term Boltzmann equation solver BOLSIG+ [27], as well as the Monte Carlo code METHES [28], were recently used to investigate the electron transport and breakdown in a copper vapour post-arc plasma [22]. The relativistic complex optical potential method has also been used to study electron-beryllium scattering [29].…”