Erosion and Transport of Erosion Products in Hall Thrusters
The main life-limiting factor for Hall thrusters is the erosion of the channel walls. As Hall thrusters are beginning to be used on more extended missions (10000 hours+), lifetime issues become a priority. In addition, wall erosion produces free material that may redeposit elsewhere in the thruster or on a spacecraft. Characterizing the erosion experimentally in ground-based vacuum chambers is a long and costly process. Thus, there is a growing need for a fast, inexpensive, and accurate model of the channel erosion and transport of erosion products in Hall thrusters.
Modeling Hall thruster erosion consists of three steps: computing the flux of ions to the walls, estimation of the differential and integrated sputter yields, and predicting the transport of the erosion products through the discharge and plume.
Previous efforts within NGPDL focused on the use of a hydrodynamic plasma model of a Hall thruster discharge in order to predict the flux of ions to the channel walls. This method is being supplanted by the use of the state-of-the-art hybrid-PIC model HPHall . HPHall models the ion and neutral species in a Hall thruster using a particle-in-cell description and the electrons as a quasi-1D continuum. Because of the detailed kinetic treatment of the ions, estimation of the ion flux to the walls is expected to be more accurate using this method than with the previous hydrodynamic model.
Integrated and differential sputter yields will be determined using a detailed molecular dynamics (MD) model of the sputtering process. This model was developed within NGPDL and has been used in the past to compute integrated sputter yields of boron nitride, one of the most common wall materials used in Hall thrusters. The model describes the behavior of a small section of boron nitride that is in contact with the plasma as it is bombarded by energetic xenon ions. An example crystal that has undergone several thousand ion impacts is shown below in Figure 1. Note the amorphous layer that forms at the top surface of the lattice and the clear hexagonal structure further down where atoms are sheltered from the plasma.
Figure 1: Example domain consisting of a boron nitride crystal. Boundary conditions are periodic in x and y directions.
Two principal refinements have been made to the model in order to improve its capabilities:
The Molière potential previously used for xenon interactions has been replaced with the more physically correct Ziegler-Biersack-Littmark (ZBL) potential . This refinement serves to increase the accuracy of the computed sputter yields.
The model has been implemented within the GPU-accelerated open-source code hoomd-blue . GPU acceleration improves the speed of the computations by up to two orders of magnitude, allowing the code to process many more ion impacts in the same amount of real time. This makes the calculation of differential sputter yields, which require a large number of ion impacts to generate the necessary statistics, a much more reasonable goal.
Transport of Erosion Products
With the ion flux to the walls and the corresonding sputter yields now determined two things can be done: (a) macroscopic erosion rates can be computed from the integrated sputter yields and used to adjust the mesh in the discharge model and (b) the differential sputter yields can be used to generate new heavy species within the discharge with some initial velocity distribution. The new heavy particles can be followed as they move through the discharge to determine whether they redeposit elsewhere in the thruster or make their way into the plume. By coupling the discharge model to a plume model, the transport of the wall species in the plume can be tracked as well.
Figure 2a below shows preliminary results for differential sputter yields (mm3/C/sr) of boron nitride under bombardment by 3000 xenon ions with 100 eV kinetic energy impacting at 45° incidence with respect to the surface normal. Note that despite the large number of ion impacts already processed there are no clear trends in the distribution of the sputtered products. Not all ion impacts result in a sputtering event, so the number of sputtered atoms is considerably less than 3000. This suggests that many more ion impacts are necessary in order to accurately resolve the differential sputter yields. Figure 2b shows the spatial distribution of reflected ions (g/C/sr), which exhibits the benefit of an improved sample size. Since the majority of incident ions are reflected from the BN surface, there are sufficiently many samples for a clear trend to appear. With the GPU-accelerated MD model, well-resolved calculations of differential sputter yields are expected to be feasible.
Figure 2: Differential sputter yield of boron nitride (a) and distribution of reflected ions (b) for a BN crystal under bombardment by 100 eV xenon ions at 45° incidence. The positive x-axis is aligned with the x-component of the incident ion's velocity vector.
InvestigatorsBrandon Smith and Horatiu Dragnea
This work is currently supported by a NASA Space Technology Research Fellowship.
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