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，以优化其性能。该模型包括几个部分，包括固体Teflon推进剂的烧蚀和由此产生的蒸汽的电离产生等离子体，通过该等离子体，放电电流在两个电极之间流动，该电流与自感磁场的相互作用产生JxB力，该力将等离子体加速到高速。为了开发数值优化工具，需要等离子体模型，这被认为是建模中最具挑战性的部分。学术贡献在于如何对这种等离子体进行建模，特别是该建模的三个关键方面：1）电流片如何附着在电极上2）当电子趋于扩散时，电流片的几何形状如何变化3）在等离子体的热力学状态方面做出了哪些假设前两个与电流片尺寸的计算密切相关，而后者则涉及这样一个事实：等离子体不太可能处于平衡状态（LTE），但与电子处于高度非平衡状态，远非麦克斯韦状态。如果将这三者结合在一起，就可以得到等离子体电阻，这是整个数值模型的关键输入（一种改进的雪犁模型），它将PPT表示为RLC电路，但参数在空间和时间上都不同。大学对数值优化工具的总体项目目标的贡献的新奇在于等离子体建模方法，特别是考虑到电子的非平衡分布，检查电子从阴极的电流发射以及阴极处的电流附着和片中电子密度的非均匀分布，这些问题以前从未被研究过，以及这些问题对使用数值工具的性能总体优化的影响。第一步将是批判性地研究了以前的等离子体建模方法，已发表在theliterature。这将使我们能够准确地确定差距在哪里，并明确我们的详细方法。尽管如此，我们目前的观点是，关键问题似乎在于阴极发射和电流附着以及电子的非平衡性质，我们的方法将从烧蚀固体表面的给定气体质量流的简化假设开始，给我们上游边界，避免求解Teflon的烧蚀。这就有效地将问题减少到了一个气体馈送的PPT上，普林斯顿大学对此进行了重要的基础研究，并允许我们使用这些结果。对于非平衡电子分布，我们将开始与现有的漂移-扩散介质阻挡放电的数值模型，它假定了一个群体分布，并修改电子分布（最初的想法包括使用双麦克斯韦和/或主要加麦克斯韦）或求解守恒方程的电子浓度和能量。对于电子发射，将假设两种机制是可能的，场发射和离子轰击，尽管第三个爆炸点也将被考虑。为了估计电流片的厚度，以前的建模方法将被使用，也是一个半经验的方法基于测量。

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.