Breakdown of a Space Charge Limited Regime of a Sheath in a Weakly Collisional Plasma Bounded by Walls with Secondary Electron Emission

D. Sydorenko, I. Kaganovich, Y. Raitses, and A. Smolyakov

Phys. Rev. Lett. 103, 145004 – Published 1 October 2009

Abstract

A new regime of plasma-wall interaction is identified in particle-in-cell simulations of a hot plasma bounded by walls with secondary electron emission. Such a plasma has a strongly non-Maxwellian electron velocity distribution function and consists of bulk plasma electrons and beams of secondary electrons. In the new regime, the plasma sheath is not in a steady space charge limited state even though the secondary electron emission produced by the plasma bulk electrons is so intense that the corresponding partial emission coefficient exceeds unity. Instead, the plasma-sheath system performs relaxation oscillations by switching quasiperiodically between the space charge limited and non-space-charge limited states.

Received 21 May 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.145004

Authors & Affiliations

D. Sydorenko^1,*, I. Kaganovich², Y. Raitses², and A. Smolyakov¹

¹Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada
²Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA

^*At present time, D. Sydorenko is at the University of Alberta, Edmonton T6G 2G7, Canada.

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Vol. 103, Iss. 14 — 2 October 2009

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Images

Figure 1
Schematic diagram of the simulation model. Positions of the walls are $x = 0$ and $x = H$ .Reuse & Permissions
Figure 2
Relaxation sheath oscillations. Temporal evolution of emission coefficient at $x = H$ (a), primary electron flux at $x = H$ (b), plasma potential at $x = H / 2$ (c), and energy of an electron averaged over all particles (d). Dashed vertical lines mark the beginning and the end of the RSO period and the transition from SCL to non-SCL state. Arrows mark times $t_{1} = 9057 ns$ , $t_{2} = 9095 ns$ , and $t_{3} = 9269 ns$ when the EVDFs shown in Fig. 4 are taken. Dashed horizontal line in (a) marks a theoretical value of the critical emission coefficient $γ_{cr} = 0.983$ for a xenon plasma with a Maxwellian EVDF [2].Reuse & Permissions
Figure 3
Typical profiles of plasma potential during the SCL (curve 1, red) and the non-SCL (curve 2, black) regimes. The left and right panels show details of the middle panel in the near-wall regions. The walls are at $x = 0$ and $x = 25 mm$ . Curve 1 (red) is at $t = 9038 ns$ ; curve 2 (black) is at $t = 9076 ns$ .Reuse & Permissions
Figure 4
EVDFs over $v_{x}$ and $v_{z}$ in the middle of the plasma $10 mm < x < 15 mm$ obtained (a), (d) in the SCL stage at $t_{1} = 9057 ns$ , (b), (e) in the beginning of the non-SCL stage at $t_{2} = 9095 ns$ , and (c), (f) in the end of the non-SCL stage at $t_{3} = 9269 ns$ (times $t_{1, 2, 3}$ are marked by arrows in Fig. 2). Surfaces depicted by thin (blue) and bold (red) lines in (a), (b), (c) correspond to the electrons of the plasma bulk and the secondary electron beam, respectively. Panels (d), (e), (f) are the color maps of the plasma bulk EVDFs corresponding to the thin-line (blue) surfaces in (a,b,c), respectively. White areas in (d), (e), (f) contain no particles. Ovals in (e) mark areas which are replenished during the non-SCL stage. Graphs are plotted in energy coordinates, negative energy values correspond to propagation in the negative direction. Only parts of EVDFs moving in the positive $x$ direction are shown.Reuse & Permissions
Figure 5
(a) Average energy of motion of plasma bulk electrons in the direction parallel to the walls versus the energy of motion normal to the walls. The dependencies are obtained by averaging over particles in the middle of the plasma $10 mm < x < 15 mm$ . Region $A$ corresponds to electrons escaping to walls during the SCL stage (the weakly confined electrons). Region $B$ corresponds to the range of perturbations of the plasma potential in the system. (b) Total electron current at the wall $x = H$ versus the plasma potential relative to the wall. The cross marks the actual average values of current $J_{e} \approx - 33.3 A / m^{2}$ and potential $Φ_{p} \approx 11.5 V$ between times $t_{2}$ and $t_{3}$ . Curves 1 (red) are at $t_{2} = 9095 ns$ , curves 2 (black) are at $t_{3} = 9269 ns$ (same as $t_{2, 3}$ in Figs. 2, 4).Reuse & Permissions

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