Hybrid PIC-MCC Computational Modeling of Hall Thrusters

Hall thrusters use an axial electric field to accelerate ions. A radial magnetic field interacts with the axial electric field to generate an azimuthal Hall current. This current partially confines the electrons leading to greater ionization efficiency inside the discharge chamber. We have developed particle models of the plasma plumes of Hall thrusters such as the SPT-100 and the TAL-D55 (see papers below). The exhaust plume is modeled by a combination of the direct simulation Monte Carlo (DSMC) and Particle-In-Cell (PIC) techniques.

Hall Thrusters have existed since the 1960s, with most of the serious early development taking place in the former Soviet Union. With technology transfers since the early 1990s, considerable worldwide interest has been sparked in the use of Hall thrusters in commercial applications for satellite station-keeping due to the high efficiency/thrust of these devices and their relatively robust nature.

We are now turning our attention to modeling the plasma flow inside the thruster where the ions are created and accelerated. This research is being conducted by Justin Koo, a graduate student funded under a Krell Fellowship by the Department of Energy (http://www.krellinst.org/CSGF).

Modelling the Interior of Hall Thrusters

We have been developing a 2-D axisymmetric model of a Hall Thruster acceleration channel. This work is based on earlier unsteady code by Laurent Garrigues (laurent@cpa01.ups-tlse.fr) developed during the spring of 2000. It is presently a single processor code which takes around 1 day to simulate a few milliseconds of operation.

The magnetic field configuration of the Hall Thruster is assumed to be static and is initialized at the beginning of the simulation with experimental or theoretical magnetic field data. Neutral transport is performed via a Particle-In-Cell (PIC) approach. At each timestep, a Monte Carlo Collision (MCC) algorithm is used to calculate ionization rates throughout the domain. From the local ionization rates, neutral macroparticles are replaced with ion macroparticles. These ion macroparticles are then electrostatically accelerated out of the thruster and their contribution to the thruster performance is evaluated.

The plasma electrons are modelled with a 1-D electron fluid model. Relevant properties are averaged radially and the electron energy is evaluated along the channel centerline. This provides the electron energy needed to evaluate ionization rates. Finally, a form of electron momentum conservation is used evaluate the electric field and potential along the centerline. The potential is then extrapolated along field lines and corrected with a thermal term to get the actual potential throughout the 2-D domain.

 

2-D Hydrodynamic Model of the Hall Thruster Plasma


Under development:

 


Figure 1. Plasma density distribution in the Hall thruster channel.


Figure 2. This current-voltage characteristic shows the effect of the dielectric wall material.


Figure 3. Here the magnetic field effect is shown in the near anode region. Plotted above are the velocity vectors.

Validating the Code

The NGPDG group has the unique ability for frequent collaboration with the Plasmadynamics & Electric Propulsion Laboratory (PEPL) of Prof. Alec Gallimore. Part of the ongoing work with the experimentalists of the PEPL group is rationalizing the thesis work of Dr. James M. Haas on the P5 thruster (http://www.engin.umich.edu/dept/aero/spacelab/pdf/AIAA-00-3422_Harp.pdf) with numerical simulations of our code.

Some Movies of the P5 in operation
(Just click on the image to download the zipped .avi movie.)

These are movies of some of the 15-20 kHz range oscillations observed in higher power Hall Thrusters. Asymmetrical magnetic fields are largely responsible for the plasma being pushed towards the outer wall of the Hall Thruster.

Acknowledgments

Funding for this work is generously provided by the U.S. Department of Energy through the Computational Graduate Student Research Fellowship.
Additional funding for this work provided by the TRW Foundation.