Solving the spatially dependent Boltzmann’s equation for the electron-velocity distribution using flux corrected transport

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Abstract
Boltzmann’s equation(BE) for the electron-velocity distribution (EVD) in partially ionized plasmas is not usually directly integrated as an initial value problem using finite differences. This circumstance is a result of numerical effects which blur sharp density boundaries in the position-velocity plane. To address this issue, we have applied flux corrected transport (FCT) to solving BE and demonstrated the method by calculating the EVD in the cathode fall of a He glow discharge by direct integration. Unidirectional and bidirectional EVDs are considered, and comparisons are made to conventional multibeam and Monte Carlo simulations to validate our method. We find that using FCT to solve BE is a significant improvement over conventional finite difference methods, being both more accurate and computationally faster.

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