Testing Models of Sheaths and Instabilities with Particle-in-cell Simulations
Beving, Lucas
2023
Abstract
Sheaths and presheaths represent the response of a plasma to boundaries and are an instance of plasma self-organization. They are commonly utilized in plasma technologies and reduced models of plasmas across a range of gas pressures. This thesis leverages the particle-in-cell method to explain discrepancies between models and measurements of ion temperature at low pressures, test untested models of high pressure sheaths, and explore a novel electron plasma wave instability driven by an ambipolar electric field. Simulations reveal that ion-acoustic instabilities excited in presheaths can cause significant ion heating. Ion-acoustic instabilities are excited by the ion flow toward a sheath when the neutral pressure is small enough and the electron temperature is large enough. A series of 1D simulations were conducted in which electrons and ions were uniformly sourced with an ion temperature of 0.026 eV and different electron temperatures (0.1 - 50 eV). Ion heating was observed when the electron-to-ion temperature ratio exceeded the minimum value predicted by linear response theory to excite ion-acoustic instabilities at the sheath edge (T_e/T_i ~ 28). When this threshold was exceeded, the temperature equilibriation rate between ions and electrons increased near the sheath so that the local temperature ratio did not exceed the threshold for instability. This resulted in significant ion heating near the sheath edge, which also extended back into the bulk plasma because of wave reflection from the sheath. The instability heating was found to decrease for higher pressures, where ion-neutral collisions damp the waves and ion heating is instead dominated by inelastic collisions in the presheath. Simulations using the direct simulation Monte Carlo method were used to study how neutral pressure influences plasma properties at the sheath edge. The high rate of ion-neutral collisions at pressures above several mTorr were found to cause a decrease in the ion velocity at the sheath edge (collisional Bohm criterion), a decrease in the edge-to-center density ratio, and an increase in the sheath width and sheath potential drop. A comparison with existing analytic models generally indicates favorable agreement, but with some distinctions. One is that models for the edge-to-center density ratio need to be made consistent with the collisional Bohm criterion. With this and similar corrections, a comprehensive fluid-based model of the plasma boundary was constructed that compares well with the simulations. Ambipolar electric fields are commonplace in plasmas and affect transport by driving currents and in some cases instabilities. Simulations demonstrate that an instability, named the electron-field instability, can be driven by an ambipolar strength electric field. The instability excites waves of 30 Debye-lengths and has a growth-rate that is proportional to the electric field strength. Unlike other instabilities, the electron-field instability only requires that the electrons interact with the field and does not result from the relative drift between electron populations (beam instability) or electrons and ions (ion-acoustic instability). In fact, the instability occurs near the electron plasma frequency which is much higher than most drift instabilities. Low-temperature and space-based plasmas are found to be likely systems where the instability may be excited. We find that our simulations and linear theory agree until a non-linear state is reached in the simulations. These results demonstrate that low pressure sheaths are susceptible to instabilities that can significantly affect plasmas properties, while fluid model accurately capture collisional effects at higher pressures.Deep Blue DOI
Subjects
low-temperature plasmas particle-in-cell simulations plasma instabilities
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Thesis
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