A study of the physics underlying high-velocity ion trajectories within the near-field region of a Hall thruster plume is presented. In the experimental part of the study, three diagnostic instruments were used: (1) a Faraday probe for measuring ion current density, (2) an ExB velocity filter for mapping ions with the primary beam energy, and (3) a retarding potential analyzer (RPA) for the determination of ion energy distributions.
Hall Thruster Overview
The generated ions will then be accelerated out of the channel by the axial electric field, producing an annular ion beam [5]. This is due to the "partially magnetized" nature of plasma, in which electrons are trapped in magnetic field lines while ions are not.
Previous Research
Simulations of Hall propellers have focused primarily on two areas: (1) the internal physics in the propeller duct and (2) the “far field” region, which is a few propeller diameters downstream of the exit plane. In these codes, the simulation domain usually consists of the Hall thruster channel and a small region downstream of the exit plane within the near field.
Motivation
In terms of experimental research, some studies have been conducted that focus on ion trajectories within the near-field region of the Hall thruster plume. One is the formation of the central jet and the other is the formation of high energy ions at high angles from the thruster centerline.
Problem Statement and Approach
This allowed a qualitative assessment of the impact of different parameters on the central jet. To investigate the formation of the central beam, high-speed ion current density maps were created using an ExB velocity filter.
SPT-70 Thruster
In addition, measurements of the total ion current density were taken using a Faraday probe, for comparison with the ExB and RPA data. The cathode is mounted externally, out of the thruster exit plane, at an angle of approximately 45◦, as can be seen in Figure 2.1.
Vacuum Facility
The stage is fixed in the z direction, so the height of the probes is set so that they are at the same height as the center of the thruster. In the experiment, the cathode was positioned so that it was out of the plane of motion of the probes.
Diagnostic Instruments - Faraday Probe
Although most faraday probes are of the simple "button" construction shown in Figure 2.5, employing a cylindrical outer ring, this probe has a tapered outer ring. Note that there is a small gap of 0.13 mm between the tip of the solar collector and the protective ring.
Diagnostic Instruments - ExB Velocity Filter
This trace is representative of the ion velocity distribution in the centerline of the thruster. Because of the size of the hole, it was assumed that the density inside the device was balanced with the neutral background density.
Diagnostic Instruments - Retarding Potential Analyzer
The front grille was mounted so that it was flush with the front of the RPA housing. The acceptance angle of the device was 15 degrees (full angle) and was determined experimentally [27].
Summary of Scans
In the case of the ExB filter, two types of scanning were done: transverse and axial. During the axial scan, the transverse location was fixed and the probe moved in the direction of the propeller, parallel to the propeller centerline.
Hybrid-PIC Model Overview
Deriving the electron equations, as well as the integration method, is quite complicated. One of these involves changing the way the weighting is performed on the wall, i.e. changing the way parameter values are weighted at each node of the simulation mesh adjacent to the wall.
HPHall at the Jet Propulsion Laboratory
Unless otherwise stated, this is the method used in the HPHall simulations presented in this thesis. Changes have also been made to the wall jacket model previously designed by F.
Application to the Ion Trajectory Problem
In the left drawing, most of the drop occurs just upstream of the exit plane, which means that the ion acceleration is mainly in the axial direction. First, the simulation data in the 650 W case had to be matched with the thruster performance parameters. As in the case of the Faraday probe, the ExB traces also had to be divided by the bin area to obtain a measurement that could be compared to experimental data.
Corner Sheath Model - Motivation
HPHall is insufficient to examine sheath effects because it replaces the sheath with a boundary condition and forces the ion velocity at the wall boundary to be the ion acoustic, or Bohm, velocity [32]. However, this approach cannot be directly applied to the radial acceleration problem within the envelope because it assumed a "zero-Debye length limit", i.e., the envelope was assumed to have zero thickness. This model solves the continuity, momentum, and Poisson equations iteratively to determine the density, velocity, and potential profiles within the envelope.
Sheath Equations
To solve for the sheath and determine whether it has a significant effect on ion trajectories, a 2D framework was developed to solve the standard sheath equations while including the effects of secondary electron emission due to ion collisions with the dielectric wall .
Boundary Conditions
If the potential at the end of the sheath is also known, then the sheath equations can be solved to find the thickness of the sheath. So if one knows the potential away from the wall, one can easily calculate the potential at the end of the sheath. If it was not, the model would be iterated over the thickness of the casing, until an acceptable solution was reached.
Numerical Method
Once the boundary conditions were calculated, the values of χs and χw were entered into the model, along with an estimate of the mantle thickness. Finite volumes were also used for the spatial derivatives of Poisson's equation, and the potential field was solved using an iterative Gauss-Seidel scheme (Eq. Initially, values of x are guessed, and then x is iterated using Eq.
Model Verification
Then, for each cell, the 2D solver was used to find the variation of the potential within the sheath, as well as the thickness of the sheath. In this way, the variation of the sheath thickness and the electric field in the axial direction could be estimated. Uncertainty is also taken into account and the results of the analysis are given in each section.
Results and Discussion - ExB Filter and Faraday Probe
In the 200 W case, as the probe angle is increased, there is significant ion current density up to 40◦ from the channel centerline. As shown in Figure 5.3, most of the ion current is confined to 20◦ of the channel centerline. Comparing this to the 100 mm example, we see a significant broadening of the beam and a reduction in the ion current density.
Uncertainty in the ExB Data
One likely cause of this anomaly is that during an axial scan, the probe spends the duration of the scan directly in front of the impeller channel. This can lead to neutral elements building up in front of the device, blocking a portion of the ion current. In contrast, during a transverse scan the probe spends only a small fraction of the scan directly in front of the thruster channel).
RPA Analysis
But even at 40◦ there is still a significant part of the ion current at the primary beam energy. As in the case of 200 W, as the angle increases from 45 to 65◦ (Figure 5.20), the low-energy CEX peak increases in height, while the primary beam energy peak decreases in height. At 65◦ there is no ion current due to the ions with the primary beam energy.
Uncertainty in the RPA Data
As for high-angle ions with primary beam energy, in the 200 W case, these ions can be seen up to 85◦ , while in the 650 W case, these ions can be seen up to 60◦ from the centerline. This begs the question: if the thruster is designed such that the electric field is predominantly axial, then how are the axial ions initially accelerated to high angles off the centerline.
Sputter Yield Analysis
In contrast to the 200 W case, in the 650 W case, the carbon plots show that the height of the high energy peak is comparable to the height of the structure corresponding to mid-range energy ions. In the case of other materials, the high-energy peak is higher than the medium-range structure, although if one were to take the integral of the curve, the contribution of the two structures would be comparable. The purpose of the HPHall simulations was to investigate the formation of the central jet, as well as to determine whether certain configurations in HPHall could come close to reproducing the high-angle, high-energy ion populations seen in experiment.
HPHall Run Conditions
Time Averaged Results from HPHall
This suggests, as with the 650 W upstream, that most of the axial acceleration occurs upstream of the exit plane. Looking at Figure 6.13, as with the 650 W upstream current, the region of high radial electric field is confined to a few centimeters from the corner. Therefore, in the 650 W downstream run, the asymmetry in the ion density appears to arise downstream of the exit plane, between z.
Faraday Probe and ExB Plots from HPHall
As with the 650 W runs, the maximum ion current density occurs at a shorter axial distance in the downstream run. This shows that, from 10 to 20◦ in the upstream run, and 10 to 30◦ in the downstream run, inward-moving ions account for a significantly larger portion of the ion current. In the downstream case, the peak corresponding to the inward moving ions is also larger in the 40◦ track.
RPA Results from HPHall
Further increasing the angle from 70 to 80◦ (Figure 6.37) upstream, continues to show a low energy peak, with a negligible proportion of ions with energies above 150 eV/q. In this direction, the low-energy peak is shorter and broader than in the 650 W direction, although it is still centered at approximately 50 eV/q. As the angle is increased above 55◦, there is no clear peak in the data; instead, there is a broad population of ions with energies from 0 to about 250 eV/q.
Repeatability of the Simulated Results
Effect of Oscillations
In all directions, the potential oscillations also show a peak in frequency corresponding to the respiratory mode, although there is significant frequency content above 100 kHz, which is not present in the current/ion density data. Looking at the potential variations, in the 650 W upstream and 200 W upstream directions, the potential changes by 15 V around an average of 95 V at the thruster output plane. However, fluctuations in the potential can explain the peak of the spread of velocities in the data, if it exists.
Boundary Conditions
As discussed in Section 4.1, values from HPHall were required to determine the boundary conditions for the mantle model. For each run, the mantle thickness and potential profile were determined using the model and plotted as a function of radial and axial location. Overall, the results showed that the sheath can change the path of the ions by about 10 to 20°.
Potential Profile
Figures 7.1 to 7.4 show the boundary conditions for the four different HPHall cases, where ΓSEE is found using Dunaevsky's power fit [43].
Ion Trajectories Through the Sheath
However, an angle change of 10 to 20◦ is not insignificant and can have an impact on the evolution of the thruster shaft. This corresponds to an area of the order of 1x10−4 m2 (i.e., the cylindrical surface extending 1x10−3 m upstream of the exit plane, with a radius of 0.020 to 0.035 m, depending on whether the wall is considered internal or external of the channel). A quick estimate of the ion current density in the exit plane can be found by dividing the total current by the exit area of the thruster.
