Theory and simulation of anode spots in low pressure plasmas

Abstract

When electrodes are biased above the plasma potential, electrons accelerated through the associated electron sheath can dramatically increase the ionization rate of neutrals near the electrode surface. It has previously been observed that if the ionization rate is great enough, a double layer separates a luminous high-potential plasma attached to the electrode surface (called an anode spot or fireball) from the bulk plasma. Here, results of the first 2D particle-in-cell simulations of anode spot formation are presented along with a theoretical model describing the formation process. It is found that ionization leads to the buildup of an ion-rich layer adjacent to the electrode, forming a narrow potential well near the electrode surface that traps electrons born from ionization. Anode spot onset occurs when a quasineutral region is established in the potential well and the density in this region becomes large enough to violate the steady-state Langmuir condition, which is a balance between electron and ion fluxes across the double layer. A model for steady-state properties of the anode spot is also presented, which predicts values for the anode spot size, double layer potential drop, and form of the sheath at the electrode by considering particle, power, and current balance. These predictions are found to be consistent with the presented simulation and previous experiments.Comment: Submitted to Phys. Plasma

Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs

“…This model includes the effect of electron impact ionization and shows the qualitative features of lengthening and the buildup of an ion rich layer in the sheath next to the electrode that are expected from the physical arguments above. Anode glow was also observed in the PIC simulations of [30]. These results are reproduced in the panel marked t = 9.5µs in figure 28.…”

“…Profiles of the bulk electrons n eb , electrons from ionization n eI , ions n i , and the plasma potential φ at four different times during the fireball onset. Figure reprinted from reference [30].…”

“…By balancing the ionization rate with the loss rate they predicted that the critical bias scales inversely with pressure, which was found to agree well with experiments. Reference [30] presented a slight modification of this to include the fact that sheath expansion can cause the surface area of the electron sheath associated with the anode glow to be larger than the surface area of the electrode. This leads to a slightly larger area for ion loss to the plasma than for electron loss to the electrode.…”

“…This leads to a slightly larger area for ion loss to the plasma than for electron loss to the electrode. The modified balance condition for the ionization and loss rates is [30] 1 − 1 2…”

“…This was not a part of the model from [29], which assumed a quasineutral region with a flat potential adjacent to the electrode. The remaining panels of figure 28 reveal the process that results in fireball formation [30]: A continued buildup of ions near the electrode surface results in the formation of a local maximum in the electrostatic potential just off of the electrode surface. This maximum is a potential well for low energy electrons born from electron impact ionization in its vicinity.…”