Plasma Walls Beyond the Perfect Absorber Approximation for Electrons

Abstract

Abstract-Plasma walls accumulate electrons more efficiently than ions leading to wall potentials which are negative with respect to the plasma potential. Theoretically, walls are usually treated as perfect absorber for electrons and ions implying perfect sticking of the particles to the wall and infinitely long desorption times for particles stuck to the wall. For electrons we question the perfect absorber model and calculate, specifically for a planar dielectric wall, the electron sticking coefficient se and the electron desorption time τe. For the uncharged wall we find se ≪ 1 and τe ≈ 10 −4 s. Thus, in the early stage of the build-up of the wall potential, when the wall is essentially uncharged, the wall is not a perfect absorber for electrons. For the charged wall we find τ −1 e ≈ 0. Thus, τe approaches the perfect absorber value. But se is still only of the order of 10 −1 . Calculating se as a function of the wall potential and combining this expression with the quasi-stationary balance equations for the electron and ion surface densities we find the selfconsistent wall potential, including surface effects, to be 30% of the perfect absorber value.

Wall Charge and Potential from a Microscopic Point of View

“…For relaxation happening in external surface states, the length L can be absorbed in the transition probabilities and drops out in the limit L → ∞ which can be meaningfully taken in this case. If however energy relaxation takes place inside the wall, as in dielectrics with positive electron affinity, L is the penetration depth and has to be obtained from experiments or theoretically calculated [24]. A quantity characterizing trapping of an electron with wave number k is the prompt sticking coefficient [31],…”

“…Multiphonon processes contribute very little to it. Since the wall charge does not affect the relative line up of the potential just outside the dielectric and the bottom of the conduction band (potential just inside the dielectric), as mistakenly assumed in [24] but corrected in [28], this conclusion also holds for a charged dielectric wall with negative electron affinity. Relaxation after initial trapping depends on the strength of transitions from the upper bound states to the lowest bound state.…”

“…Inspired by Emeleus and Coulter [20] as well as Behnke and coworkers [10,21] who attempted to describe the dynamics of the wall charge and its coupling to the bulk plasma with phenomenological rate equations, characterized by sticking coefficients, residence times, and recombination and emission coefficients, we initiated in the framework of the TRR24 an effort to describe the plasma wall beyond the perfect absorber model [22][23][24]. With an eye on grain charging in dusty plasmas and the wall charge in dielectric barrier discharges we calculated -as a first step -for various uncharged metallic [23] and dielectric [25][26][27] surfaces electron sticking coefficients and desorption times, determined the distribution of the wall charge across the interface between a plasma and a floating dielectric surface [28], and investigated how electrons are extracted from dielectric surfaces via deexciting metastable molecules [29,30].…”

“…If however energy relaxation takes place inside the wall, as in dielectrics with positive electron affinity, L is the penetration depth and has to be obtained from experiments or theoretically calculated [24]. For relaxation happening in external surface states, the length L can be absorbed in the transition probabilities and drops out in the limit L → ∞ which can be meaningfully taken in this case.…”

The absorbing properties of one-dimensional plasma photonic crystals

“…Therefore, absorption becomes more obvious with periodic number increasing. Physical insights into absorption in plasma have been revealed that the absorption is mainly attributed to collision processes of the plasma (Bronold et al 2011). As a large number of periods introduce more plasma layers into the plasma photonic crystal, the absorption increases with the period number increasing.…”