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Probes. Sheath Potentials. Hall Thruster Overview.
Hall Thruster Overview
Determination of sheath potentials is complicated by the presence of secondary electron emission from the wall. The Hobbs and Wesson solution describes the sheath potential under space-charge limited emission. Emission from the opposing wall could traverse the channel and “cancel” out part of the emission effects.
Large measured sheath potentials (~ 5Te) indicate the presence of high-energy electrons and a thermalization process that supports the use of Hobbs and Wesson.
Hall thrusters are an electric propulsion device typically used on satellites for orbit station-keeping, but is a promising option for deep-space missions that require an efficient, long-lasting propulsion system.
Typical Hall thrusters consist of four primary components: an anode; cathode; discharge channel; and magnetic circuit. Electrons emitted from the cathode migrate towards the anode, but get trapped by the applied magnetic field. The resulting electric field and magnetic field cause the electrons to drift azimuthally. Neutral gas, typically xenon, is injected through the anode and is ionized by the trapped electrons. The ions are then accelerated out of the channel by the electric field, forming thrust.
Erosion Characterization via Ion Power Deposition Measurements in a 6-kW Hall ThrusterRohit Shastry, Professor Alec D. Gallimore, and Dr. Richard R. Hofer
Ion Current Density in the Near-field Plume
Ion Power Deposition to Channel Walls
Ion power deposition can be calculated with the measured ion current density and estimated ion energy, which is found from the plasma potential and electron temperature. Average
Sheath Expansion Model
The flush-mounted nature of the probes requires a dedicated model of sheath expansion in the ion saturation regime to account for the special geometry and boundary conditions.
By simulating various conditions to characterize the effective area increase as a function of bias voltage, the ion saturation regime can be corrected to recover the “true” ion saturation current.
power to the walls was found to be 11% of the discharge power, with excess power being measured at 150 and 500 V.
Ion beam spreading in the plume is characterized by the divergence angle (see above). The larger the axial component of the ion beam, the smaller the spreading and the lower the divergence angle. The divergence angle can be deduced from ion current density measurements in the thruster plume.
A similar angle can be defined within the channel by comparing the total ion current that hits the walls to
A primary failure mechanism of Hall thrusters is erosion of the discharge channel wall by ion bombardment. Present characterization of erosion involves long, expensive life-testing which will become cost prohibitive in the future. Thus, a comprehensive model of Hall thruster erosion and channel wall physics would facilitate rapid lifetime predictions.
While significant advancements have been made in understanding wall physics, there is a lack of experimental validation. Measurements of plasma
Large ion currents and ion energies were found at low and high discharge voltages. At high voltage, the acceleration zone recedes and exposes the wall to more current and high energy ions. At low voltage, the ion beam diverges more readily and sheath energies are higher.
that exiting the thruster. This angle is shown to have a rough correlation with the plume divergence angle.
parameters at the wall are best obtained using Langmuir probes flush-mounted along the channel walls, since traditional methods cannot obtain the required proximity (see right).
Extrapolation of Plasma Properties
The data from this study must be compared to current simulation results in order to validate/refine existing wall physics and erosion models. The hybrid-PIC code HPHall-2 is used at JPL to simulate channel and near-field physics of Hall thrusters.
The measured ion current densities and energies can be used to estimate the wall erosion rate at each position. The sputtering yield is the volumetric rate of erosion per unit charge to the surface, and is dependent upon ion impact energy, incident angle, and wall material. This yield is usually derived from limited experimental data and contains large uncertainties.
Figure from: Reid, B. M. and Gallimore, A. D., "Langmuir Probe Measurements in the Discharge Channel of a 6-kW Hall Thruster," Presented at the 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA-2008-4920, Hartford, CT, July 21 - 23, 2008.
Due to the limited size of the interrogation zone, extrapolation of the data set to the entire channel length was performed using fitting functions. The functions were derived from proper fits to other data taken within the channel that had higher spatial resolution and a wider range.
In particular, near-wall plasma properties and erosion rate predictions must be compared between experiment and simulation. The existing sheath and sputtering models must then be refined to better match observations.
Future flush-mounted probe studies may also be done to enhance the current data set at desired operating conditions.
Five Langmuir probes were flush-mounted onto each channel wall, concentrated near the thruster exit plane. Data were taken across nine operating conditions under a wide range of discharge voltages and powers.
Plasma and floating potentials were extrapolated using sigmoid functions, while electron temperature was calculated using the difference between the two potentials. Ion current density was extrapolated using a combination of Gaussian and Lorentzian functions.
The estimated wall erosion rate exhibits the expected shape based on observed profiles. It also loosely follows the calculated ion power deposition density, although this does not strictly hold in all instances. The recession rate is ~10X greater than expected, indicating the sputtering model requires refinement.
Relevant properties near the wall were measured: ion current density; electron temperature; floating potential; and plasma potential. These properties were then used to characterize the ion power deposited onto the channel walls as well as to predict erosion rates.
Questions? Contact R. Shastry at firstname.lastname@example.org