A Continuum Kinetic Investigation into the Role of Transport Physics in the Bohm Speed formulation

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Virginia Tech


When plasmas come in contact with the boundaries that confine them, various complex processes occur between the plasma and the materials in the boundary. These processes, called plasma-material interactions (PMI) lead to physical and chemical modifications in the materials and in the plasma. In the case of a tokamak, a magnetic confinement fusion reactor, the interactions between the plasma and the material in the bounding walls can negatively impact the performance and service life of the reactor. Furthermore, PMI are also found in other areas of significant engineering interest, such as plasma-based spacecraft propulsion engines, where interactions affect the transport properties of the plasma and consequently the performance of the engine. Therefore, gaining a fundamental understanding of the various plasma-material interactions is necessary for the development and improvement of these devices.

PMI are dictated by the plasma sheath, a layer of net positive charge that forms at the plasma-boundary interface. The sheath regulates the energy and particle fluxes to the boundary, mediating the interactions. Sheaths, however, are only stable and well-developed when the ions enter the sheath with a speed equal to or greater than the Bohm speed'. The Bohm speed is a landmark result in sheath theory and various mathematical expressions for it have been derived from fluid and kinetic treatment of plasmas. Although these models are widely used, they are only accurate in cases where the thickness of the sheath is negligible when compared to the scale length of the plasma in consideration. These cases are said to satisfy the asymptotic limit'.

To resolve this, a new Bohm speed model that considers the effects of transport terms such as the electron heat flux, thermal force, and temperature isotropization has been recently proposed [Y. Li et al., Physical Review Letters (2022)]. The model is verified using particle-in-cell (PIC) kinetic simulations and is shown to accurately predict the Bohm speed in cases away from the asymptotic limit. This thesis investigates the new model using the continuum kinetic approach on the Gkeyll software framework. The continuum kinetic approach numerically solves the Vlasov-Maxwell equations using the discontinuous Galerkin method and captures the kinetic phenomena of the plasma without needing to track individual particles. Multiple collisional cases ranging from a Knudsen number of 20 to 5000 are considered in a 1X3V simulation domain using the Lenard-Bernstein collisional operator.

The results of the continuum kinetic simulations are benchmarked to the PIC simulation results. It is concluded that across a wide range of collisionalities, the continuum kinetic method captures much of the same physics as the PIC method while offering noise-free results. However, there is a discrepancy between the Bohm speed prediction and the simulation results in the continuum kinetic case. This discrepancy is explored and significant error in the collisional integral derived transport terms between the continuum kinetic method and PIC method is found, suggesting that the difference in collisional operator may be the source of the discrepancy. Nevertheless, the sheath profiles developed in the PIC simulations and the continuum kinetic simulations are in reasonable agreement.



Plasma Sheaths, Bohm speed, Plasma Transport, Continuum Kinetics, Computational Plasma Dynamics