Development of a modelling tool for performance optimization in pulsed plasma thrusters

该项目的总体目标是为脉冲等离子体推进器开发一个数值模型，使其性能得到优化。该模型涉及几个部分，包括固体特氟龙推进剂的烧蚀和由此产生的蒸汽的子序列化，从而产生等离子体，放电电流通过等离子体在两个电极之间流动。这种电流与自感磁场的相互作用产生JxB力，使等离子体加速到高速。为了开发数值优化工具，需要一个等离子体模型，这被认为是建模中最具挑战性的部分。学术贡献在于这种等离子体模型,其造型的三个关键方面:1)如何electrodes2电流片高度)电流片的几何形状变化的电子往往分散away3)假设是什么做的的热力学状态plasmaThe前两个密切相关的计算电流片的尺寸而后者涉及等离子体,但不太可能一个平衡状态（LTE），但在一个高度非平衡状态与电子远不是麦克斯韦。如果将这三个结合在一起，就可以得到等离子体电阻，这是整个数值模型（一个改进的扫雪机模型）的关键输入，该模型将PPT表示为RLC电路，但其参数在空间和时间上都是不同的。大学对数值优化工具的整体项目目标的贡献的新颖性在于等离子体建模的方法，特别是在允许电子的非平衡分布，检查阴极的电子发射以及阴极的电流附着和薄片中电子密度的非均匀分布。这是以前从未研究过的，以及这些将对使用数值工具的性能的整体优化产生的影响。第一步将是批判性地检查先前在文献中发表的等离子体建模方法。这将使我们能够准确地确定差距在哪里，并使我们的详细方法具体化。然而，我们目前的观点是，关键方面似乎在于阴极发射和电流附着以及电子的非平衡性。我们的方法是从一个简化的假设开始，假设一个给定的气体质量从烧蚀固体表面流出，给我们上游边界，避免解决特氟龙的烧蚀问题。这就有效地减少了这个问题，变成了一个气体输入的PPT，普林斯顿大学在这个PPT上进行了重要的基础研究，让我们可以使用这些结果。对于非平衡电子分布，我们将从现有的介质阻挡放电的漂移扩散数值模型开始，该模型假设了群体分布，并修改了电子分布（最初的想法包括使用双麦克斯韦方程组和/或一次加麦克斯韦方程组）或求解电子浓度和能量的守恒方程。对于电子发射，我们假设有两种可能的机制，场发射和离子轰击，尽管我们也会研究第三种爆炸点。为了估计电流片厚度，将使用以前的建模方法和基于测量的半经验方法。

The overall aim of the project is to develop a numerical model for pulsed plasma thrusters that will allow their performanceto be optimized. This model involves several parts including, ablation of the solid Teflon propellant and subsequentionization of the resulting vapour creating a plasma, through which a discharge current flows between the two electrodes.The interaction of this current with the self-induced magnetic field produces JxB forces, which accelerate the plasma to ahigh velocity. In order to develop the numerical otimisation tool a plasma model is required and this is envisaged as themost challenging part of the modelling. The academic contribution lies in how this plasma is to be modelled and inparticular three key aspects of this modelling:1) how the current sheet attaches at the electrodes2) how the geometry of the current sheet changes as electrons tends to diffuse away3) what assumptions are made in terms of the thermodynamic state of the plasmaThe former two are closely related to the calculation of the dimensions of the current sheet whilst the latter deals with thefact that the plasma is unlikely to be in a state of equilibrium (LTE) but in a highly non-equilibrium state with the electronsfar from being Maxwellian. If one couples these three together one can arrive at the plasma resistance, which is a keyinput to the overall numerical model ( a modified snowplow model) which represents the PPT as an RLC circuit but withparameters that vary in both space and time.The novelty of the university contribution to the overall project goal of a numerical optimization tool is in the approach to theplasma modelling, in particular in allowing for a non-equilibrium distribution for the electrons, examining the currentemission of electrons from the cathode together with current attachment at the cathode and non-uniform distribution ofelectrons density in the sheet, which have never been investigated before and the effects that these will have on the overalloptimisation of the performance using the numerical tool.The first step will be to critically examine the previous plasma modelling approaches that have been published in theliterature. This will allow us to identify exactly where the gaps are and crystallize our detailed methodology. Neverthelessour current view is that the key aspects seem to lie in cathode emission and current attachment and the non-equilibriumnature of the electrons.Our approach will be to start with the simplifying assumption of a given gas mass flow from the ablating solid surface,giving us the upstream boundary and avoiding solving for the ablation of the Teflon. This then reduces the problem in effectto one of a gas fed PPT on which there has been significant fundamental research at Princeton University and allowing us to use these results. For the non-equilibrium electron distribution, we will begin with the existing drift-diffusion numericalmodel for a dielectric barrier discharge, which assumes a swarm distribution, and modify the electron distribution (initialideas include using bi-Maxwellian and/or primary plus a Maxwellian) or solving the conservation equations forconcentration and energy of electrons . For the electron emission, it will be assumed that two mechanisms are possible,field emission and ion bombardment although a third one of explosive spots will also be looked at. To estimate the currentsheet thickness, previous modelling approaches will be used and also a semi-empirical approach based onmeasurements.