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

The overall aim of the project is to develop a numerical model for pulsed plasma thrusters that will allow their performance
to be optimized. This model involves several parts including, ablation of the solid Teflon propellant and subsequent
ionization 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 a
high velocity. In order to develop the numerical otimisation tool a plasma model is required and this is envisaged as the
most challenging part of the modelling. The academic contribution lies in how this plasma is to be modelled and in
particular three key aspects of this modelling:
1) how the current sheet attaches at the electrodes
2) how the geometry of the current sheet changes as electrons tends to diffuse away
3) what assumptions are made in terms of the thermodynamic state of the plasma
The former two are closely related to the calculation of the dimensions of the current sheet whilst the latter deals with the
fact that the plasma is unlikely to be in a state of equilibrium (LTE) but in a highly non-equilibrium state with the electrons
far from being Maxwellian. If one couples these three together one can arrive at the plasma resistance, which is a key
input to the overall numerical model ( a modified snowplow model) which represents the PPT as an RLC circuit but with
parameters 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 the
plasma modelling, in particular in allowing for a non-equilibrium distribution for the electrons, examining the current
emission of electrons from the cathode together with current attachment at the cathode and non-uniform distribution of
electrons density in the sheet, which have never been investigated before and the effects that these will have on the overall
optimisation 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 the
literature. This will allow us to identify exactly where the gaps are and crystallize our detailed methodology. Nevertheless
our current view is that the key aspects seem to lie in cathode emission and current attachment and the non-equilibrium
nature 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 effect
to 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 numerical
model for a dielectric barrier discharge, which assumes a swarm distribution, and modify the electron distribution (initial
ideas include using bi-Maxwellian and/or primary plus a Maxwellian) or solving the conservation equations for
concentration 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 current
sheet thickness, previous modelling approaches will be used and also a semi-empirical approach based on
measurements.

Potential economic beneficiaries include the consortium, manufacturers and end users of cubesats and nano/micro
satellites(eg SSTL, EADs Astrium, Clyde Space and UKSA), small machine shops which will manufacture the mechanical
components needed for the thruster and the UK economy in general. The SME partner in the consortium, Mars Space Ltd
will benefit by increasing its profits.
There may social impacts in terms of the increased capabilities(manoeuvrability and formation flying) of multiple cubesat
missions depending on the mission application. For example, cubesat missions of this type could be used for remote
sensing or probing of the Earth's upper atmosphere and hence increase our understanding of global warming. This would
not only be of benefit to scientists involved in this type of research but also members of the public by leading to an
increased understanding of this phenomenon and its impacts on civilisation.
Downstream users of possible cubesat missions with a range of applications including science, telecommunications, earth
observation and possibly even position, navigation and timing.