There are three types of computational models that are commonly applied to simulate Hall thruster plasmas: the fluid model, the kinetic model, and the hybrid model.

In this laboratory the research is mainly focused on the fully kinetic and hybrid models.

A typical hybrid model will assume that the heavy species, i.e. ions, are represented as particles while the electrons are represented as a fluid. This method maintains the accuracy of modeling the heavy species kinetically, and as a result, captures rarefied, non-Maxwellian features of the thruster plasma. The hybrid method also trades the more accurate particle modeling of the electrons for a fluid model, avoiding the severe computational cost that is associated with modeling the electrons kinetically. Various fluid models are available for modeling the electrons, ranging from the simple Boltzmann relation applied throughout the domain to more sophisticated fluid models based on conservation laws.

A new approach using a hyperbolic-equation system (HES) is developed to solve for the anisotropic diffusion equation of magnetized electron fluids in quasi-neutral plasmas and Hall thrusters. The conventional approach using an elliptic equation suffers numerical instabilities stemming from the cross diffusion terms. The HES approach avoids treatments of cross-diffusion terms. The HES is constructed by introducing new variables which contain gradient of another variable. A test calculation reveals that the HES approach can robustly solve problems of strong magnetic confinement by using an upwind method.

The hybrid PIC method using the HES approach is able to reproduce the fundamental characteristics of the Hall thruster discharge.

Fig. 1 The distributions of equipotential lines of thermalized potential and magnetic lines of force. (a): Near-anode region. (b): Channel-exit region. (c): Plume region.

1. R. Kawashima, K. Komurasaki, T. Schonherr, "A flux-splitting method for hyperbolic-equation system of magnetized electron fluids in quasi-neutral plasmas," Journal of Computational Physics, Vol. 310, pp. 202-212, 2016.
2. R. Kawashima, K. Hara, K. Komurasaki, H. Koizumi, "A Unified Model for Axial-Radial and Axial-Azimuthal Hall Thruster Simulations," AIAA Propulsion and Energy, Salt Lake City, UT, July 25-27, 2016.
3. R. Kawashima, K. Komurasaki, T. Schonherr, "A hyperbolic-equation system approach for magnetized electron fluids in quasi-neutral plasmas," Journal of Computational Physics, Vol. 284, pp. 59-69, 2015.
4. R. Kawashima, T. Schonherr, K. Komurasaki, "Modeling of Electron Fluids in Hall Thrusters Using a Hyperbolic System," AIAA Propulsion and Energy, Cleveland, OH, July 28-30, 2014.

Unlike the hybrid model the simulations utilizing kinetic models do not make any assumptions and both the ions and the electrons are represented as particles. Kinetic models have the advantage over fluid models of not assuming the continuum hypothesis, and as such, are better suited to plasmas in the transition or rarefied regimes. Kinetic models are at a significant disadvantage, however, in the amount of computational time required. Since electrons are several orders of magnitude lighter than ions, their motion must be resolved using much smaller timescales, typically on the order of 600 times smaller than the timescales required to resolve ion dynamics alone. To overcome this problem of large computational time different assumptions are usually made like for example mass ratio and aritificial permittivity.

A 2D fully kinetic particle-in-cell model was developed for Hall thruster discharge and lifetime simulation. Because the fully kinetic lifetime simulation was yet to be achieved so far due to the high computational cost, the semi-implicit field solver and the technique of mass ratio manipulation was employed to accelerate the computation. However, other artificial manipulations like permittivity or geometry scaling were not used in order to avoid unrecoverable change of physics.

Additionally, a new physics recovering model for the mass ratio was presented for better preservation of electron mobility at the weakly magnetically confined plasma region. The validity of the presented model was examined by various parametric studies, and the thrust performance and wall erosion rate of a laboratory model stationary plasma thruster was modeled for different operation conditions. The simulation results successfully reproduced the measurement results with typically less than 10% discrepancy without tuning any numerical parameters.

Fig. 2 Potential distribution

Fig. 3 Electron number density for magnetic flux density 14? mT (left) and 21 ?mT (right).

1. S. Cho, K. Komurasaki, Y. Arakawa, "Kinetic particle simulation of discharge and wall erosion of a Hall thruster," Physics of Plasmas, 20, 063501, 2013

Although PPT is expected to applied to microsatellites due to its simplicity and compactness, there are some difficulties in Solid Propellant PPT. Following difficulties are concerned for PPT using solid propellant (PTFE) for its propellant.

1. Excessive propellant supply from the PTFE surface after the main discharge (late time ablation).
2. Uneven propellant consumption on the PTFE surface (uneven propellant consumption).
3. Contamination of other parts of the satellite by carbon or fluorine in the exhaust gas (contamination).

Problem 1 is considered to be one of the main reasons degrading the thrust efficiency of PPT. Propellant supplied after the main discharge are not accelerated to high velocity because they do not experience the electric acceleration sufficiently.
Problem 2 is caused by the passive propellant supply function of solid propellant PPT. Uneven propellant surface can decay the thruster performance in long-term missions.
Problem 3 doesn't affect the thrust efficiency, but this problem can be crucial for real applications. Black carbon and chemically reactive fluorine can cause unexpected effects on other parts, or other satellites in constellation missions.

In order to solve these difficulties, we are suggesting a liquid propellant PPT (LPPT) utilizing water for its propellant. The following picutre shows the concept of LPPT.

The big difference between solid propellant PPT and LPPT is propellant supply function. LPPT pour an optimal amount of liquid between the electrodes, and fire the igniter with slight delay from injector.
Accorgin to this active propellant supply function, LPPT has solutions for the difficulties mentioned above.
1. Due to its active propellant supply, LPPT avoid the problem of excessive propellant supply by late time ablation.
2. The probem of uneven propellant supply can be solved as well.
3. Water doesn't affect other parts of the satellites.

As described above, LPPT can solve the crucial problems of solid propellant PPT. However, there are also some difficulties in LPPT like management of liquid in vacuum condition, design of an injector with a good responce, and evaporation of water for ionization. We are trying to find solutions for these problems of LPPT.