Effect of Cathode Position on Hall-Effect Thruster ... - MTU Aerospace

Effect of Cathode Position on Hall-Effect Thruster Performance and Near-Field Plume Properties Jason D. Sommerville∗ and Lyon B. King∗ Michigan Technological University, Houghton, Michigan 49931, USA Thruster efficiency and plume properties, including ion energy distributions and beam current density profiles, of a Hall-effect thruster are compared when the cathode is placed in nine radial positions relative to the thruster and at three cathode mass flow rates. The cathode was mounted such that its orifice normal was at a right angle to the thruster axis. Plume properties were measured at a radius of 250 mm from the intersection of the thruster axis and the exit plane. Cathode coupling voltage, beam divergence, and voltage utilization are strongly affected by cathode position.

Nomenclature Dprobe f Ib Id Iprobe j m m ˙ m ˙c m ˙ ing R r T V v

Diameter of the Faraday probe electrode The ion energy distribution function (IEDF) Total ion beam current Anode supply current Current measured by Faraday probe Ion beam current density Xenon atomic mass: 131.29 amu Anode mass flow Cathode mass flow rate Ingested propellent mass flow rate Probe sweep radius: 250 mm Radial cathode position Thrust Voltage Ion velocity

I.

Vcg Vd "x# "θ# η ηadj ηθ ηI ηV ηVcg ηvdf θ

Cathode coupling voltage: the voltage at which the cathode floats below ground Anode supply voltage The expectation (average) value of any quantity x Beam divergence Thruster efficiency Measured efficiency corrected for estimate of ingested propellent Beam divergence efficiency Current utilization efficiency Voltage utilization efficiency Cathode coupling efficiency Velocity distribution efficiency Off-thrust-axis angle

Introduction

Hall-effect thrusters (HETs) are a class of electric propulsion devices that use electric and magnetic fields to create a plasma and expel the ions at high velocity in order to generate thrust.1 A critical component of the HET is the cathode. The cathode is a plasma source which provides free electrons which serve two purposes. The first purpose is beam neutralization—sufficient electrons are expelled via the cathode to balance the charge emitted by the ion beam. The second purpose is to provide the “seed” electrons which initialize and sustain the plasma discharge near the exit plane of the HET. The flow of the seed electrons is known as the recycle current. The process by which the free electrons in the plume of the cathode are coupled to the anode of a Hall thruster and how this process affects cathode coupling voltage and thruster performance is not well understood. A few researchers have studied the effects of cathode type2 and mass flow rate2, 3 on HET performance. Albaréde, et al. compared three types of thermionic orificed cathodes and found only small differences in behavior.2 Both Albaréde, et al. and Tilley, ∗ ME-EM

Dept., 815 R.L. Smith Bldg., 1400 Townsend Dr.

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et al. observed increases in cathode coupling voltage with increasing flow rate, and Albaréde, et al. also noticed nonmonotonic changes in anode current fluctuation frequency with changes in cathode mass flow.2 It has been repeatedly noted that cathode placement has an effect on thruster performance.3–8 Hofer, et al.4 and Jameson, et al.,8 noticed significant performance improvements by placing the cathode in the center of the HET rather than outside, and Beal, Gallimore and Hargus have inferred from probe measurements that cathode placement and number in a cluster of HETs will affect performance.6 To the best of our knowledge there are two studies available in the literature that specifically address the effect of cathode position on thruster performance across a range of cathode locations. In the first, by Tilley, et al. the authors note an increase in cathode coupling voltage as the cathode is moved forward of the exit plane.3 In the second, by Walker and Gallimore, the authors note decreasing performance as the cathode is moved away from the thruster.7 This is in contradiction to our own work in which we see generally improved performance with increasing cathode separation for cathodes mounted outside of the thruster body.9, 10 The discrepancy may be due to the difference in thruster size, magnetic field configurations, and the difference in overall scale over which the two experiments were performed. In our continuing effort to understand cathode to HET coupling, we have undertaken a series of experiments studying the performance and plume properties of a Hall thruster as a function of radial cathode position and mass flow rate. In prior work, we showed a definite change in thrust, cathode coupling voltage and efficiency as a function of cathode position.9 We showed further that the change in efficiency resulting from the change in coupling voltage was insufficient to explain the total change in efficiency seen. This experiment is designed to further illuminate how a change in cathode position affects thruster performance. By measuring the thruster performance along with the ion current densities and ion energy distribution functions (IEDFs), we can break the efficiency into constituent loss mechanisms and uncover which mechanisms are changing as cathode position changes.

II. A.

Experiment

Setup

The HET was mounted on a thrust stand, and the cathode was mounted on a linear motion stage and could be moved from 40 mm to 200 mm radially away from the thrust axis, at a fixed axial distance of 30 mm from the thruster exit plane (see Figures 1 and 2). A Farday probe and a retarding potential analyzer (RPA) were placed on a boom mounted on a rotational stage directly above the intersection of the thrust axis and the exit plane. The probes were mounted at a distance of 250 mm. A possibly significant difference between this work and the prior work is that the cathode was mounted with its orifice normal at a 90 degree angle to the thrust axis. This change was done to enable the cathode to be placed at radial locations closer to the thrust axis (r = 0) than was possible with the cathode mounted with its orifice normal vector parallel to the thrust axis. The implications of this change will be discussed later. B.

Procedure

The experiment proceded as follows: the cathode was placed at a specific radial position and the cathode mass flow set. In each experiment, the thruster was set at an operating voltage of 250 V and a mass flow rate of 4 mg/s of xenon. These values were chose to match prior experiments conducted on cathode position with this thruster.9, 10 A magnet current value of 2.5 A was chosen to match prior values as well. In the earlier studies, this value was the optimal current value, as determined by minimizing the discharge current for the given voltage and mass flow. In these experiments, 2.5 A was slightly below the optimal point, but more importance was placed on matching prior magnetic field strengths, and thus the thruster was run with this current. After the thruster stabilized, thrust, discharge current, and efficiency of the thruster were measured over a period of two minutes. After recording the performance, the cathode was moved to a new location, randomly chosen from the nine position in 20 mm intervals between r = 40 mm and 200 mm. After all of the performance data were taken at a given cathode mass flow, RPA and Faraday probe sweeps were performed at five cathode positions: 40 mm, 60 mm, 80 mm, 120 mm, and 200 mm. In the m ˙ c =10 SCCM case, the 120 mm position was not acquired. Both probes were mounted at a constant radial distance of 250 mm from the center of the thruster exit plane. The Faraday probe was swept from -90 to 60 degrees in 2.3 degree increments. At each increment, 1000 samples were taken at a rate of 10 kHz and averaged. The RPA was swept in 10 degree increments over the same range. At each increment, 5 sweeps from 0 to 300 V were taken with 600 points per sweep. After all performance and probe data were acquired at each of the cathode positions, the cathode mass flow rate was adjusted and the experiment repeated. Cathode mass flow rates of 10 SCCM, 5 SCCM, and 2 SCCM were chosen. 2 of 20 American Institute of Aeronautics and Astronautics

Figure 1: Experimental setup

Figure 2: Photograph of experimental setup

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10 SCCM is the nominal cathode ignition flow rate, and 2 SCCM was the lowest cathode mass flow at which the cathode would stably operate. C.

Equipment

1.

Thrust Stand

The thrust stand is a NASA-Glenn style, null displacement, inverted pendulum thrust stand, with automatic leveling. The displacement nulling is provided by a solenoid driven by a closed-loop digital controller which measures the displacement of the thrust stand using an LVDT. The level is sensed by an electrolytic inclinometer, and controlled by a microstepping motor connected to an 80-threads-per-inch screw. The thrust is directly proportional to the current provided to the solenoid. Calibration is provided by a linear fit to a set of known weights applied to the thruster across a pulley and controlled via a stepper motor. The data from the thrust stand, as well as the power supplies is continually monitored by a telemetry datalogger implemented in software. Communication with the thrust stand and the power supplies is either by analog input to the datalogging computer, or via GPIB, depending on the device. Telemetry is recorded at a rate of 1 Hz. From the recorded thrust, anode mass flow rate, discharge current and discharge voltage, the measured efficiency is calculated according to T2 . (1) η= 2mI ˙ d Vd Note that m ˙ does not include cathode mass flow, and likewise, Id and Vd measure only the current through and voltage to the anode. Given the thermal drifts in the thrust stand compounded with the error in the linear fit, the error in the thrust measurement is estimated at 5%. Propagating the errors of the thrust measurement and the mass flow rate through the efficiency equation, we estimate the error on the efficiency measurements at 9% of the stated values. 2.

Faraday Probe

The Faraday probe used is a guard-ring-type planar probe. The probe electrode is a tungsten rod 2.4 mm in diameter. The guard is separated from the probe by an alumina tube with an outer diameter of 4.75 mm. The guard ring, made of stainless steel, surrounds the alumina. The outer diameter of the guard ring is 10 mm. Except for the face, the guard ring is spray coated with boron-nitride to reduce amount of current collected by the ring. The current to the probe electrode passes through a shunt resistor, and the voltage across the resistor is amplified by an op-amp circuit, and then measured with a computer-based data acquisition system. The voltage to the guard ring is controlled via a FET operating as a voltage-controlled resistor. Both electrodes are biased at -30 V below ground to repel electrons. The probe was swept from an angle of -90 degrees to +60 degrees. Beyond 60 degrees the probe would collide with the cathode. At each interval, the voltage from the shunt resistor amplifier was measured by a computerized data acquisition system, and converted into a current. Current density was then calculated from the probe current according to 4Iprobe j= . (2) πD2probe 3.

Retarding Potential Analyzer

The RPA used in the experiments is a four-grid design. The first grid is a floating grid, designed to isolate the plasma from the various potentials applied to the remaining grids. The second grid is an electron repeller, which is biased negative relative to plasma potential in order to prevent electrons from entering the remainder of the probe. The third grid is the ion repeller. This grid is swept across the desired voltage range and allows only those ions with energies above the grid potential to pass through to the collector. The final grid is a secondary electron suppression grid. This is designed to force any secondary electrons ejected from the collector by the impact of an ion to return to the collector. The grids on the RPA are made from stainless-steel mesh with 0.139-mm spacing and a 30% open-area fraction. Each grid is spaced 2.54 mm apart from the next. The orifice of the probe is a circle 12.7 mm in diameter. This diameter is maintained through the length of the probe, to the equally sized collector, which is simply a grounded, stainless-steel plate.

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Current to the collector is amplified by current amplifier/current-to-voltage converter manufactured by Femto. The resulting voltage is measured with the data acquisition system. The sweeper grid is swept from 0 to 300 V using a Keithley 2410 source-meter. The electron repeller and secondary suppression grids are biased with a DC power supply to -15 V. Test traces were also take at -30 V on centerline, where the plasma potential was expected to be highest. No differences were discernable. From this we concluded that -15 V sufficiently repelled electrons. To reduce the RPA trace, a cubic spline was fit to all of the data acquired. This process was done semi-automatically. A computer program guessed the best spline to fit the data. However, manual interaction was required to choose an appropriate number of spline knots, and to slightly modify the spline in order to achieve the best visual fit of the spline to the raw data. The spline was then scaled so that its value at 0 eV was 1, and at the maximum sweep value of 300 eV the value is 0. The negative of the derivative of the normalized spline is the IEDF: f (V) = − 4.

dIspline (V) . dV

(3)

Vacuum Facility

All experiments were run in the Xenon Vacuum Facility at Michigan Tech’s Ion Space Propulsion Laboratory. The facility is a 4-m-long chamber 2 m in diameter. It is evacuated by two 48-inch cryogenic pumps capable of 60,000 L/s each. The base pressure during these experiments was 5 × 10−6 Torr and operating pressures were 2.4 × 10−5 Torr as measured by an ion gauge corrected for xenon and located on the top of the downstream third of the chamber. 5.

Hall Thruster

The HET used in this experiment is an Aerojet BPT-2000, 2 kW class thruster.11 The thruster has an outer diameter of ∼100 mm and a channel width of ∼10 mm. It operates at a nominal voltage of 300 V and a mass flow of 5 mg/s xenon. At these conditions its specific impulse is ∼1700 s with ∼50% efficiency. 6.

Cathode

The cathode used in these experiments is a laboratory cathode similar to the MIREA cathode used by Albadére.2 It is shown schematically in Figure 3. The cathode consists of a 1-inch-diameter titanium cylinder approximately 100 mm long. A 2-mm diameter orifice was drilled in one face. Pressed against this hole is a molybdenum pellet holder which holds a lanthanum-hexaboride (LaB6 ) emitter. Xenon is introduced into the cathode via a feed tube attached to the side of the cylinder. Filling the length of the cathode from the pellet holder to the base is a tungsten heater coil which heats the emitter to its operating temperature. Radiation insulation loosely wraps the heater and pellet holder to maximize emitter heating. A keeper electrode is positioned approximately 3 mm outside of the orifice and is used to ignite the cathode discharge. After the main HET discharge was ignited, the keeper was unpowered and allowed to float. In these experiments, the cathode was placed near and within the ion beam. In early trials it was found, not surprisingly, that this caused the cathode to heat up. While the temperature of the cathode was not directly monitored, the heater voltage was seen to increase while it was held at constant voltage, a sure indication of a temperature increase. Any heating of the cathode causes the emitter pellet to more freely give electrons, which affects cathode coupling voltage. While this is interesting and may bear further research, in these experiments, we wanted to avoid this affect and focus on the effect of where the cathode gas and electrons are introduced. To alleviate the thermal loading of the cathode, we constructed an actively cooled shield. The shield, pictured in Figure 3(c), is a copper fin which is slightly wider than the cathode diameter and extends the length of the cathode. 1/4-inch copper tubing is soldered to the base of the fin, through which water flows during operation. The exposed portion of the fin is covered in graphite foil to prevent copper from contaminating the thruster or other equipment. Tests with the heat shield showed significant reduction of the cathode heating, though did not completely alleviate the problem. Without the shield, moving the cathode from outside the beam at 120 mm to inside the beam at 60 mm resulted in a change in of 0.6 V on a nominally 10.5 V heater voltage. With the shield in place, the same change in position caused a 0.1 V change in heater voltage. Heater currents were 6 A in both cases. 7.

Mass Flow Controllers

Flow of xenon to the thruster and the cathode was controlled by MKS Type 1479a mass flow controllers. Their accuracy has been tested by monitoring the rise in pressure of a small calibration tank of known volume while flowing 5 of 20 American Institute of Aeronautics and Astronautics

(a)

(b)

(c)

Figure 3: (a) Schematic representation of the laboratory cathode. (b) Photograph. (c) The heat shield.

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gas into the tank. The mass flow controllers are accurate to 2% of the full scale reading: 200 SCCM (19.5 mg/s xenon) for the anode controller, and 20 SCCM (1.95 mg/s xenon) for the cathode controller.

III. A.

Results

Performance

4.4 4.2

Thrust (mN)

4.6

4

-18 -20 -22 -24 -26 -28 -30 -32 80 100 120 140 160 180 200 Efficiency Cathode - Ground

60

r (mm)

-12 -14 -16 -18 -20 -22 -24 -26 80 100 120 140 160 180 200 Efficiency Cathode - Ground

40

60

z = 30 mm

r (mm)

Efficiency (%)

Thrust (mN)

(a) m ˙ c =2 SCCM

z = 30 mm

(b) m ˙ c =5 SCCM 72 70 68 66 64 62 60 58 56 54

5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8

Thrust Discharge Current

0.54 0.52 0.5 0.48 0.46 0.44 0.42 0.4 0.38

-8 -10 -12 -14 -16 -18 -20 -22 80 100 120 140 160 180 200 Efficiency Cathode - Ground

40

60

r (mm)

Current (A)

40

0.5 0.48 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0.32

Coupling (V)

0.52 0.5 0.48 0.46 0.44 0.42 0.4 0.38 0.36

Efficiency (%)

3.8

5.2 5 4.8 4.6 4.4 4.2 4 3.8

Thrust Discharge Current

Current (A)

66 64 62 60 58 56 54 52 50

4.8

Coupling (V)

5

Thrust Discharge Current

Current (A)

68 66 64 62 60 58 56 54 52

Coupling (V)

Efficiency (%)

Thrust (mN)

The thruster performance data as a function of cathode position is plotted for the three cathode mass flow rates in Figure 4. The data show a consistent trend with thrust, cathode coupling voltage, and efficiency highest near thrustcenterline, and falling off to ∼120 mm. Beyond this point, these parameters rise slightly. The current, meanwhile, decays rapidly from 40–80 mm, afterwhich it is constant. The decay is more rapid as cathode mass flow decreases.

z = 30 mm

(c) m ˙ c =10 SCCM

Figure 4: Thruster performance as a function of cathode position.

B.

Faraday Probe Data

The current density as a function of angle is plotted in Figure 5. The data are plotted on a polar graph. However, note there is a change of units at r = 250 mm. Inside this region, a representation of the thruster and cathode are plotted for reference. Outside, the radial dimension corresponds to current density. Each subfigure groups together the data taken at the same radial position but different cathode mass flow rates. 7 of 20 American Institute of Aeronautics and Astronautics

10 SCCM 5 SCCM 2 SCCM

0

0

10 SCCM 5 SCCM 2 SCCM

-30

-60

-30

-60

Current Density 2 (A/m )

Current Density 2 (A/m )

Cathode r (mm)

(a) Cathode r=40 mm

200 0 50

100

0

Cathode r (mm)

(b) Cathode r=60 mm

0

0

5 SCCM 2 SCCM

-30

-60

-30

-60

(c) Cathode r=80 mm

Cathode r (mm)

(d) Cathode r=120 mm

10 SCCM 5 SCCM 2 SCCM

0 -30

-60

Current Density 2 (A/m )

0

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

Cathode r (mm)

(e) Cathode r=200mm

Figure 5: Current densities for select cathode positions

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200 0 50

100

0

-100

-450 400 350 300 250 200 150 100 50 0 -200

100

0

200 0 50

Current Density 2 (A/m )

Cathode r (mm)

200 0 50

Current Density 2 (A/m )

-100

-90

-450 400 350 300 250 200 150 100 50 0 -200

-90

100

10 SCCM 5 SCCM 2 SCCM

-100

-450 400 350 300 250 200 150 100 50 0 -200

200 0 50

100

0

-100

-90

-450 400 350 300 250 200 150 100 50 0 -200

-90

One notes an increased broadening and decreased center-spike magnitude as the cathode is moved away from the thrust axis. There is also a decrease in the overall magnitude of the current densities with decreasing cathode mass flow, though this is less pronounced when the cathode is further from the thrust axis. C.

RPA Data

Figure 6 shows a sample I-V curve from the RPA data. Additionally, it shows the spline, the knots of the spline, and the resulting IEDF. The IEDF is plotted on the right-hand y-axis and, additionally, on the color bar. These data were acquired under the following conditions: m ˙ c = 5 SCCM, r = 60 mm, θ = −30◦ .

Figure 6: Sample RPA data, spline, and resulting IEDF Figures 7 through 9 show the IEDFs as a function of angle for each cathode position and mass flow operating point measured. Roughly speaking, it shows the probability of an ion at a given angle having an energy that corresponds to the radial dimension. To calculate the total probability, one would need to multiply the probability on the IEDF by the normalized current density at that angle. The data were taken at 10-degree intervals from -90 degrees to 30 degrees. The remaining data have been interpolated in the figures. The corresponding current density as measured by the Faraday probe is overlaid. Note that the arrangement of the radial axis is identical to that of Figure 5. Several of the plots show broad energy distributions at zero degrees. It is possible that these are due to pressure effects inside the RPA and may not, therefore, represent valid data. This will be further addressed in the discussion. The most striking feature of these graphs is that as the cathode is moved away from the thruster, the distributions become narrower in energy space. Furthermore, the broad energy distribution at 0 degrees seems to go away as the cathode is moved away from the thrust axis and as cathode mass flow is decreased. When present, the narrow spike in probability density occurs at approximately 200 V, regardless of cathode position, and extends out to about -60 degrees. It appears to vary slightly with cathode mass flow, moving from ∼200 V to ∼210 V as the mass flow is varied from 2 SCCM to 10 SCCM. Finally, one notes a low energy spike near -90 degrees. However, signal levels here are quite small, and we have low confidence in the data taken between -80 and -90 degrees.

IV. A.

Discussion

Performance

Referring back to Figure 4, we see that trends in the performance data are consistent regardless of cathode mass flow. More interestingly, they agree relatively well both in magnitude and trend with a similar experiment conducted with the cathode oriented parallel to the thrust axis and the tip even with the exit plane9 However, in this orientation, that cathode could not be moved closer than about 100 mm away from the thrust centerline.

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0.005 0

0.005 -90 -450 400 350 300 250 200 150 100 50 0 -200

200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0.01

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

(a) m ˙ c =2 SCCM, Cathode r=40 mm

(b) m ˙ c =2 SCCM, Cathode r=60 mm

0.01 0.005 0

0.01 0.005 -90 -450 400 350 300 250 200 150 100 50 0 -200

200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0.015

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

200 0

0.015

0.02 -60

0

0.02 -60

0.025

100

0.025

0.03

-30

0

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

(c) m ˙ c =2 SCCM, Cathode r=80 mm

(d) m ˙ c =2 SCCM, Cathode r=120 mm

0

0.03

-30

0.025 0.02 -60

0.015 0.01 0.005 200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0

Ion Energy Probabtility Density

-30

0

-100

0.03

Ion Energy Probabtility Density

0

0

Ion Energy Probabtility Density

0.01

0.015

Ion Energy Probabtility Density

0.015

0.02 -60

200 0

0.02 -60

0.025

0

0.025

0.03

-30

100

-30

0

-100

0.03

Ion Energy Probabtility Density

0

Current Density (A/m2) Cathode r (mm) Ion Energy (eV) (e) m ˙ c =2 SCCM, Cathode r=200 mm

Figure 7: Ion energy distributions and ion current density as a function of angle for cathode mass flow rates of 2 SCCM

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0.005 0

0.005 -90 -450 400 350 300 250 200 150 100 50 0 -200

200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0.01

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

(a) m ˙ c =5 SCCM, Cathode r=40 mm

(b) m ˙ c =5 SCCM, Cathode r=60 mm

0.01 0.005 0

0.01 0.005 -90 -450 400 350 300 250 200 150 100 50 0 -200

200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0.015

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

200 0

0.015

0.02 -60

0

0.02 -60

0.025

100

0.025

0.03

-30

0

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

(c) m ˙ c =5 SCCM, Cathode r=80 mm

(d) m ˙ c =5 SCCM, Cathode r=120 mm

0

0.03

-30

0.025 0.02 -60

0.015 0.01 0.005 200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0

Ion Energy Probabtility Density

-30

0

-100

0.03

Ion Energy Probabtility Density

0

0

Ion Energy Probabtility Density

0.01

0.015

Ion Energy Probabtility Density

0.015

0.02 -60

200 0

0.02 -60

0.025

0

0.025

0.03

-30

100

-30

0

-100

0.03

Ion Energy Probabtility Density

0

Current Density (A/m2) Cathode r (mm) Ion Energy (eV) (e) m ˙ c =5 SCCM, Cathode r=200 mm

Figure 8: Ion energy distributions and ion current density as a function of angle for cathode mass flow rates of 5 SCCM

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Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

0.01 0.005 200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

-90

0

0.02 -60

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

0.015 0.01 0.005

-90 200 0

0.015

0.025

0

0.02 -60

0.03

100

0.025

0 -30

-450 400 350 300 250 200 150 100 50 0 -200

0.03

Ion Energy Probabtility Density

0

(b) m ˙ c =10 SCCM, Cathode r=60 mm

0

Ion Energy Probabtility Density

(a) m ˙ c =10 SCCM, Cathode r=40 mm

-30

0

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

-100

200 0

0

100

-100

-450 400 350 300 250 200 150 100 50 0 -200

0

0.005 -90

Ion Energy Probabtility Density

0.005 -90

0.01

200 0

0.01

0.015

0

0.015

0.02 -60

100

0.02 -60

0.03 0.025

-100

0.025

0 -30

-450 400 350 300 250 200 150 100 50 0 -200

0.03

Ion Energy Probabtility Density

0 -30

Current Density (A/m2) Cathode r (mm) Ion Energy (eV)

(c) m ˙ c =10 SCCM, Cathode r=80 mm

(d) m ˙ c =10 SCCM, Cathode r=200 mm

Figure 9: Ion energy distributions and ion current density as a function of angle for cathode mass flow rates of 10 SCCM

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It is interesting to see that as the cathode moves across the face, all of the performance parameters significantly increase. In particular the discharge current is seen to increase. However, away from the thruster face, discharge current is seen to be constant regardless of cathode position, both in this work and in our prior work.9 This suggests that some amount of cathode propellent is being ingested by the thruster and accelerated when the cathode is in these close locations. It is likely that propellent ingestion is a function of cathode mount angle. In the prior work, in which the cathode mounted with its orifice normal vector parallel to the thrust axis, it was not possible to move the thruster closer than r = 104 mm. In this work we see a small, but noticeable, change in the discharge current, even beyond 100 mm, particularly at the 10 SCCM cathode mass flow rate. This suggests that cathode propellent ingestion occurs more readily with the rotated cathode. To estimate the amount of ingested cathode propellent, we assume that when the cathode is at its furthest location no propellent is ingested. For closer cathode locations, any discharge current above this amount is assumed to be due to ingested propellent. These assumptions seem reasonable, given the flat discharge current vs. radial position profiles seen near r = 200 mm in this research, and the completely constant profiles seen in prior work. Note that the only other possible method for discharge current to increase is for the recycle current, the fraction of discharge current above what is expelled in the ion beam, to increase. We then assume that all “extra” current is due to singly-ionized xenon. Following these assumptions, the ingested propellent rate is given by: m (4) m ˙ ing (r) = [Id (r) − Id (200 mm)] . e We can then adjust the efficiencies to account for the ingested propellent. Referring to Equation 1 we see the “adjusted” efficiency is given by T2 m ˙ 2mI ˙ d Vd m ˙ +m ˙ ing m ˙ = ηmeas . m ˙ +m ˙ ing

ηadj =

(5) (6)

The adjusted efficiencies are plotted in Figure 10 along with the calculated ingested mass flow. Except for at 40 mm, the values calculated seem reasonable, and we believe the adjusted efficiencies to be a more accurate measure of efficiency. At 40 mm, the ingestion flow rate is higher than the cathode mass flow rate, which is obviously incorrect. In this position, the cathode partially blocks the thruster exit, and the thruster operates less stably. Severe oscillations were noted in the cathode coupling voltage and discharge current. It is likely that in this position much of the excess current is due to increased recycle current. This is further support by measurements of the current utilization efficiency, and is further discussed in Section D. B.

Beam Profile

Perhaps the most striking feature of the beam profiles is that the 5 and 10 SCCM traces at 80 mm, and the 2 SCCM trace at 120 mm [Figures 5(c) and 5(d)] all exhibit anomalous bulges between -60 and -30 degrees. Our first supposition was that this was part of the cathode plume superimposed in the beam profile. However, the IEDFs in Figures 7 through 9 do not support this theory, as one would expect to see an increased prevalence of low-energy ions. A second theory is that the bulge is due to cathode neutrals which have been ingested by the thruster and then ionized. Since the cathode provides a non-symmetric source of propellent, it would make sense to see a non-symmetric beam profile. However, the fact that it does not show up in all cases, particularly at the 60 mm case suggests another explanation. A third explanation is that the bulge is due to beam ions that have reflected off of the cathode. But, if that were the case, one would not expect the 120 mm, 2 SCCM case to show a bulge, particularly since the 80 mm, 2 SCCM case does not exhibit one. Clearly, further data are needed to understand the reason for the bulge in ion current density. Integrating the current density data to find the total beam current is necessary to calculate the current utilization efficiency discussed in Section D. The bulges cause problems when integrating the beam profiles to obtain total beam current. For the probe sweep geometry used in this study, total beam current is given by integrating the current density profile in spherical coordinates assuming azimuthal symmetry: Ib = 2π

!0

j(θ)R2 sin(|θ|)dθ.

−90◦

(7)

When this is done on the data exhibiting bulges, beam currents in excess of the discharge current are obtained. The uncorrected beam current (Ib ) plots in Figure 11 exhibit this. Of course, it is unlikely that the bulge extends a full 13 of 20 American Institute of Aeronautics and Astronautics

0.45 10 0.4 5

0.35 0.3

0.5

60

15

10 0.4 5

0.35 0.3

80 100 120 140 160 180 200

0 40

60

80 100 120 140 160 180 200

r (mm)

r (mm)

(a) m ˙ c =2 SCCM

(b) m ˙ c =5 SCCM Efficiency Adjusted Efficiency Ingested Propellent

Efficiency

0.5

20

15

0.45 10 0.4 5

0.35 0.3

Ingested Propellent (SCCM)

0.55

0 40

60

20

0.45

0 40

Efficiency Adjusted Efficiency Ingested Propellent

80 100 120 140 160 180 200 r (mm)

(c) m ˙ c =10 SCCM

Figure 10: Cathode propellent ingestion and adjusted efficiency as function of cathode position.

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Ingested Propellent (SCCM)

15

0.55

Efficiency

0.5 Efficiency

20

Efficiency Adjusted Efficiency Ingested Propellent

Ingested Propellent (SCCM)

0.55

360 degrees azimuthally. In fact, we can see that it does not, from the portion of the current density profile at off-axis angles greater than zero, at least in the m ˙ c = 10 SCCM case at 80 mm [Figure 5(c)]. To explore the effect of the bulge, we manually excised the bulges by substituting a spline which approximated the general shape of the non-bulged profiles where the bulge was exhibited. This brought the current down to more reasonable, values, as shown in the corrected Ib plots in Figure 11. However, in the 2 SCCM case at 120 mm, and in the 5 SCCM case at 80 mm, the beam currents still exceed the discharge currents. Most likely, these bulges, which are shallower than the 10 SCCM, 80 mm bulge, actually extend in θ beyond what was visible as a departure from the normal profile and skew a much larger portion of the current density profile. 8.5

34

8

8.5

32

32

28

6.5 6

26

5.5

24

5 4.5 4 40

60

30

7 Current (A)

30

7

6.5

28

6

26

5.5

24

5

22

4.5

22

20

4

20

80 100 120 140 160 180 200

40

60

Divergence (degrees)

7.5 Divergence (degrees)

7.5 Current (A)

34

8

80 100 120 140 160 180 200

Cathode r (mm)

Cathode r (mm)

(a) m ˙ c =2 SCCM

(b) m ˙ c =5 SCCM

8.5

34

8

32 30

Current (A)

7 6.5

28

6

26

5.5

24

5 4.5

22

4

20 40

60

Divergence (degrees)

7.5 Id Ib Ib (corrected) (corrected)

80 100 120 140 160 180 200 Cathode r (mm)

(c) m ˙ c =10 SCCM

Figure 11: Beam current, discharge current and beam divergence as a function of cathode position. Beam profiles exhibiting “bulges” have been corrected. In addition to the total beam current, the beam divergence, which is a measure of the beam focus, is another important quantity which determines thruster efficiency. Here, beam divergence is quantified by the average off-axis angle of the ions, and it is calculated according to "θ# =

"0

−90◦

θ j(θ)R2 sin(|θ|)dθ Ib

.

(8)

Beam divergence is also unduly affected by the bulges, as can be seen in Figure 11. Additionally, one notes that the divergence is consistently lowest at r = 60 mm. This will be further discussed in Section D. The decrease in peak beam current as a function of increasing cathode position seen in Figure 5 corresponds with the decrease in total discharge current and beam current, as shown in Figure 11. More interesting is the increase in beam divergence. This is consistent with the observations of Hofer, et al. that center-mounted cathodes have improved 15 of 20 American Institute of Aeronautics and Astronautics

beam divergence over externally mounted ones.5 However, even mounting the cathode at 90 degrees and bringing it close to the discharge channel shows marked improvement in beam divergence. It is interesting to see that, bulges aside, as cathode mass flow decreases, the discrepancy between discharge current and beam current also decreases. This will also be further discussed in Section D. C.

Ion Energy Distribution

As we previously noted, the IEDF at angles with magnitudes less than 60 degrees is seen to broaden in energy space as the cathode is placed closer to the centerline. The most likely explanation is that the broadening is a result of cathode propellent ingestion. Because the cathode neutrals are not introduced in the back of the anode, but rather the front, they are more likely to undergo ionization further down the potential hill created by the thruster. The added population of slower, cathode-originating ions serves to broaden the IEDF. A second theory is that the change in location of the cathode causes a significant change in the potential structure inside the HET. Unfortunately, without difficult internal plasma potential and density measurements, neither theory can be robustly tested. D.

Efficiency Analysis

With ion current densities and energy distributions it is possible to break down the efficiency into its constituent efficiencies with the goal of identifying the significant causes of change in efficiency. Following, Larson12 and Ross,13 we decompose efficiency into the loss mechanisms shown in Table 1. In the following series of equations, we show how each of these efficiencies are broken out of the total efficiency. Efficiency

Symbol

Definition

Description

How to Measure

Velocity Distribution

ηvdf

"v#2 "v2 #

Inefficiency due to the spread in 1-D velocity space of the ions

Beam Divergence

Calculate this efficiency at each angle from the IEDF. Perform a weighted average of all angles, weighting by current density and solid-angle.

ηθ

"cos(θ)#2

Current Utilization

Ion velocity components not parallel to the thrust axis tend to cancel and do not generate thrust

Integrate the Faraday-probederived current densities to find the expectation value of cos(θ)

ηI

Ib /Id

Cathode Coupling

The “recycle” current “leaks” from the cathode to the anode without directly creating thrust in the form of beam ions.

Integrate Faraday-probe-derived current densities to obtain Ib and divide by discharge current (Id ) measured by power supply

ηVcg

Vd + Vcg Vd

Measure the cathode coupling voltage

Voltage Utilization

The voltage at the cathode floats below ground is not available to accelerate ions. Note that Vcg is always negative.

ηV

Not all ionization takes place at the top of the potential hill. Because of this, ions do not receive the full amount of energy available.

Integrate IEDF and current density data, similar to the process for ηvdf , and divide by the sum of the measured Vd and Vcg

1 2 2 m"v #

e(Vd + Vcg )

Table 1: Efficiency loss mechanisms

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T2 2mP ˙ 1 m"v# ˙ 2 = 2 Id Vd 1 ˙ 2# "v#2 m"v = 2 2 "v # Id Vd

(10)

=

(12)

(9)

η=

(11)

1 m"v ˙ 2# "v#2 2 2 "cos(θ)# "v2 # #!!!!$%!!!!& Id Vd #$%& ηθ ηvdf

= ηvdf ηθ

1 2 em/m ˙ 2 m"v # Id eVd #!$%!&

(13)

ηI

= ηvdf ηθ ηI

1 2 2 m"v #

Vd + Vcg e(Vd + Vcg ) Vd #!!!!!!!!$%!!!!!!!!& #!!!!$%!!!!& ηV

(14)

ηVcg

= ηvdf ηθ ηI ηV ηVcg

(15)

No attempt is made to correct for ionization fraction in these equations, or the proceding analysis. That is to say, we assume that all ions are singly charged. Because of this, ηvdf is probably slightly overstated, while ηV is understated. The various expectation values are calculated by a weighted average according to the following equation " 0 " 300 V x(V, θ) f (V, θ) j(θ)R2 sin(|θ|)dVdθ ◦ "x# = −90" 0 0 " 300 V . (16) 2 sin(|θ|)dVdθ f (V, θ) j(θ)R ◦ −90 0

Since the data integrated is discrete, the inner integral is first performed at each available angle using Simpson’s rule. The results of these integrations are then linearly interpolated, multiplied by the current densities, and integrated across θ. Strictly speaking, the separation of ηvdf and ηθ in Equation 12 is only valid if the IEDF is independent of angle. This is clearly not the case. However, because the IEDF seems to change most at high angles where the current density is small, we will procede with the assumption anyway. The bulges discussed in Section B present a particular problem for evaluating the current utilization efficiency. In the proceding analysis, we have removed the bulges from the current profile, as previously discussed. Since two data points still display calculated beam currents in excess of the discharge current (refer to Figure 11), we limit the resulting calculation of current utilization efficiency to 1. The results of this efficiency decomposition are shown in Figure 12, along with the measured efficiency, the ingestion-adjusted efficiency, and the total efficiency calculated from probe data. The total efficiency is calculated by multiplying all of efficiency components according to Equation 15 and is denoted by ηmult . Total efficiencies are plotted with solid lines, while efficiency components are plotted with dashes. The calculated efficiencies show good agreement with the measured efficiencies, except when m ˙ c = 10 SCCM and at all cathode mass flow rates when r = 60 mm. The reasons for these discrepancies are unclear. The voltage utilization efficiency is the dominant loss mechanism, with beam divergence being a close second. The remaining efficiency components are all ∼85% or better. All efficiency components show similar trends as cathode position is varied, regardless of cathode mass flow. The consistency of the trends suggests that there is no fundamental difference in thruster operation as a function of cathode mass flow rate. The voltage utilization efficiency increases as the cathode is moved away from the thruster. This is likely explained by the decrease in cathode propellent ingestion as r increases. Ingested cathode propellent is more likely to be ionized further down the potential hill and across a greater range of potentials, as it comes from outside the thruster, rather than the back of the anode. An increase in cathode propellent ingestion would therefore be result decrease in voltage utilization, as the velocity distribution was spread to lower values. The fact that the velocity distribution efficiency trends in the same fashion as the voltage utilization also supports this theory, as it measures the spread in velocity space of the beam ions. The current utilization efficiency is quite high, and relatively flat. It does drop significantly at 40 mm, which in part explains the consistently poor performance at this point. Given the high, periodic oscillations in cathode coupling 17 of 20 American Institute of Aeronautics and Astronautics

1

0.9

0.9

0.8

0.8

0.7

0.7

Efficiency

Efficiency

1

0.6 0.5

0.6 0.5

0.4

0.4

0.3

0.3

0.2

0.2 40

60

80

100

120

140

160

180

200

40

60

Cathode r (mm)

80

100

120

(a) m ˙ c =2 SCCM

(b) m ˙ c =5 SCCM

1 0.9

Efficiency

0.8 ηmeas ηadj ηmult ηβ

0.7 0.6

ηI ηvdf ηV ηVcg

0.5 0.4 0.3 0.2 40

60

80

100

120

140

140

Cathode r (mm)

160

180

200

Cathode r (mm)

(c) m ˙ c =10 SCCM

Figure 12: Efficiency decomposition versus cathode radial location

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160

180

200

voltage observed, it is possible that there was increased electron mobility in the HET channel, which would exhibit itself as a decrease in current utilization efficiency. A more interesting trend is seen when comparing the overall current utilization from each of the cathode mass flow rates, as was mentioned in Section B. As cathode mass flow rate increases, current utilization decreases. One possible explanation is that the increased cathode flow results in increased charge-exchange collisions. The fast neutrals, which must be captured for a completely accurate picture of current utilization, are not detected by the Faraday probe. On the other hand, if this were the only effect, one would expect the current utilization to be much worse with the cathode close to the thruster, than with it at r = 200 mm. This is not the case. But, increased ionization of the cathode propellent may offset this, making the two effects impossible to disentangle with the current data. The cathode coupling efficiency trends nicely match the trends in efficiency. This can be better seen in Figure 4, where Vcg (∝ ηVcg ) is seen to vary nearly in step with performance. However, cathode coupling efficiencies only vary by roughly 5% as the cathode position is changed, while total efficiencies vary by up to 20%. We see that the beam divergence efficiency shows roughly the same trend as the overall efficiency, and also approximately matches the coupling voltage efficiency trends. The divergence efficiency exhibits a maximum change of roughly 10% as cathode position is changes. It is surprising that even at 40 mm, where the cathode partially blocks the thruster channel, beam divergence remains good. As previously mentioned, the trend seen here is further supported by the conclusions of Hofer, et al.5 Clearly beam divergence is an important factor in explaining the trend in total efficiency.

V.

Conclusion and Future Work

The data from this experiment suggest that there is not a simple relationship between cathode position and thruster performance. None-the-less, consistent trends are seen in all of the efficiency components. These trends suggest that changes in beam divergence and voltage utilization dominate the changes in total efficiency. However, a more detailed analysis is certainly required before drawing any firm conclusions. The problems of the bulges of unknown azimuthal extent, which violate the assumption of azimuthal symmetry, as well as the violation of the assumption that IEDFs are independent of angle present complications in the present analysis. For future work, we plan to alleviate both problems. For the bulge, we plan acquire 2-D current density measurements, and to asses the effect of the violation of the assumptions in Equation 12. This work is part of a larger effort to understand the relationship between the magnetic field of the thruster and cathode position. The magnetic field of the thruster has been simulated and measured experimentally. Comparison of past data to the field proved interesting, and we expect similarly interesting results when these data are compared to the magnetic field.

Acknowledgments The authors would like to thank Marty Toth for providing quick turn-around in fabricating of various napkinsketched mounts required to set up this experiment. This work has been supported by the Air Force Office of Scientific Research.

References 1968.

1 R.

G. Jahn, Physics of Electric Propulsion. McGraw-Hill Series in Missile and Space Technology, New York: McGraw-Hill Book Company,

2 L. Albarède, V. Lago, P. Lasgorceix, M. Dudeck, A. Burgova, and K. Malik, “Interaction of a hollow cathode stream with a Hall thruster,” in 28th International Electric Propulsion Conference, vol. 03-333, Electric Rocket Propulsion Society, March 17–21 2003. 3 D. L. Tilley, K. H. de Grys, and R. M. Myers, “Hall thruster-cathode coupling,” in 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, vol. AIAA-99-2865, AIAA, June 20–24 1999. 4 R. R. Hofer and A. D. Gallimore, “Recent results from internal and very-near-field plasma diagnostics of a high specific impulse Hall thruster,” in 28th International Electric Propulsion Conference, vol. IEPC-2003-037, March 17–21 2003. 5 R. R. Hofer, L. K. Johnson, D. M. Goebel, and D. J. Fitzgerald, “Effects of an internally-mounted cathode on Hall thruster plume properties,” in 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, vol. AIAA-2006-4482, American Institute of Aeronautics and Astronautics, July 9–12 2006. 6 B. E. Beal, A. D. Gallimore, and W. A. Hargus, “The effects of cathode configuration on Hall thruster cluster plume properties,” in 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, vol. AIAA-2005-3678, July 10–13 2005. 7 M. L. R. Walker and A. D. Gallimore, “Hall thruster cluster operation with a shared cathode,” Journal of Propulsion and Power, vol. 23, pp. 528–536, May 2007.

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8 K. K. Jameson, D. M. Goebel, R. R. Hofer, and R. M. Watkins, “Cathode coupling in Hall thrusters,” in 30th International Electric Propulsion Conference, vol. IEPC-2007-278, (Florence, Italy), Electric Rocket Propulsion Society, September 17–20 2007. 9 J. D. Sommerville and L. B. King, “Effect of cathode position on Hall-effect thruster performance and cathode coupling voltage,” in 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, (Cincinnati, OH), American Institute of Aeronautics and Astronautics, July 8–11 2007. 10 J. D. Sommerville and L. B. King, “Effect of cathode position on Hall-effect thruster performance and cathode coupling voltage,” in 30th International Electric Propulsion Conference, (Florence, Italy), Electric Rocket Propulsion Society, September 17–20 2007. 11 D. King, D. L. Tilley, R. Aadland, K. Nottingham, R. Smith, C. Roberts, V. Hruby, B. Pote, and J. Monheiser, “Development of the BPT family of U.S.-designed hall current thrusters for commercial LEO and GEO applications,” in 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, vol. AIAA-98-3338, Electric Rocket Propulsion Society, July 13–15 1998. 12 C. W. Larson, D. L. Brown, and W. A. Hargus, “Thrust efficiency, energy efficiency and the role of VDF in Hall thruster performance analysis,” in 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, (Cincinnati, OH), American Institute of Aeronautics and Astronautics, July 8–11 2007. 13 J. L. Ross and L. B. King, “Energy efficiency in low voltage Hall thrusters,” in 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, vol. AIAA-2007-5179, American Institute of Aeronautics and Astronautics, July 8–11 2007.

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