Investigation of Detachment in a Miniature Magnetic Nozzle Source

IEPC-2017-335

Presented at the 35th International Electric Propulsion Conference Georgia Institute of Technology – Atlanta, Georgia – USA October 8–12, 2017

Timothy A. Collard∗, Matthew P. Byrne,† Shadrach T. Hepner,‡ Christopher J. Durot,§ and Benjamin A. Jorns¶ University of Michigan, Ann Arbor, MI, 48109, USA

Plume detachment from a magnetic nozzle is investigated in a low magnetic field and a high magnetic field case. At each operating condition a double Langmuir probe, an emissive probe, and Laser Induced Fluorescence is used to spatially map the plasma properties and the ion streamlines. For the weak magnetic nozzle condition the centerline exit plane 17 3 plasma density was 10 m− , the electron temperature was 3.5 eV throughout the ∼ ∼ plume, and the ions expanded isotropically from the source. For the strong magnetic 16 3 nozzle case the centerline plasma density was 10 m− , the electron temperature was 6 ∼ ∼ eV throughout the plume, and the ions initially expanded isotropically from the source, but then deflected inward downstream. This implies that the plume was detached from the magnetic nozzle in the near-field and then reattached downstream. Investigation of this phenomenon uncovered that the neutral density was high in the near-field leading to enhanced cross-field mobility due to large electron-neutral collision frequencies. Itis demonstrated that, due to differences in the rate of decay of the neutral density and the magnetic field strength, the plume can reattach to a strong magnetic nozzle ata downstream location. The direct implication is collisions are dominant in the near-field and the nominal magnetic nozzle referenced to the source liner geometry is not the true magnetic nozzle influencing the plume; the expanded effective magnetic nozzle that forms within the plume dictates the nozzle physics. A discussion of the ramifications on device design and performance is included.

Nomenclature

α = ion fraction β = uniformity of the density profile within the source region m˙ = mass flow rate νen = electron-neutral collision frequency Ω = Hall parameter A = local magnetic nozzle cross-sectional area A0 = magnetic nozzle throat cross-sectional area B = magnetic field strength F0 = thrust generated within the source region FP = thrust generated by the nozzle me = electron mass Mdet = detachment Mach number

∗Ph.D. Candidate, Department of Aerospace Engineering, [email protected]. †Ph.D. Pre-Candidate, Department of Physics, [email protected]. ‡Ph.D. Candidate, Department of Aerospace Engineering, [email protected]. §Post-Doctoral Fellow, Department of Aerospace Engineering, [email protected] ¶Assistant Professor, Department of Aerospace Engineering, [email protected].

1 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 q = fundamental charge R = radial position Te = electron temperature Z = axial position

I. Introduction

agnetic nozzles have been proposed as thrusters due to their ability to convert thermal energy into Mdirected kinetic energy via a convergent-divergent nozzle.1–14 The magnetic nozzle contours can be generated by passing current through an inductive coil or by permanent magnets. In these devices neutral propellant is injected into an ionization region where radio frequency (RF) power is coupled via an antenna. The resulting plasma then accelerates through the converging-diverging magnetic nozzle topology and trans- mitting thrust through internal diamagnetic plasma currents and interaction with the magnetic circuit. To produce net thrust the plasma must detach from the closed magnetic nozzle field lines. This notional process is depicted in Figure 1. By being inherently electrodeless magnetic nozzles exhibit limited wear, long lifetimes, and are propellant blind, making them ideal devices for long duration missions or missions requiring the use of in-situ propellants. However, the measured performance of low power magnetic nozzles have been poor, with state-of-the-art nozzles achieving a total efficiency of 8% at 2 kW.2 Performance models for magnetic∼ nozzles∼ with magnetized15 and un- magnetized16 ions have been proposed, but neither model accurately captures the plume physics. In both models the plasma detachment determines the amount of expansion the plume undergoes within the nozzle, which is directly related to the thrust production in the nozzle. In terms of these mod- Figure 1: The nominal magnetic nozzle referenced els two of the primary questions are: What are the to the plasma liner (solid black) and the effective expanded magnetic nozzle that forms within the upstream and downstream bounds defining the mag- plume due to neutral collisions near the source. netic nozzle? And what are the physical parameters driving performance within the nozzle? To answer these questions an understanding of the mechanism(s) driving detachment and its interaction with the nozzle is required. A number of detachment theories have been proposed8, 10, 17–20 ranging from resistive detachment21 to three body recombination22 to finite Larmor radius effects,23 but the mechanism by which the plasma detaches from the magnetic nozzle remains unclear due to the lack of experimental measurements. These models tend to predict that the ions diverge more slowly than the nozzle field lines, while the electrons remain tied to the nozzle lines up to the detachment point. However, while the electrons remain attached to the field lines they exert a force on the ions deflecting them outward slightly. Beyond the detachment point the electron and ion streamlines coincide. Several criteria defining the detachment point have been proposed, including when the ion Larmor radius exceeds the local cross-sectional area of the magnetic nozzle,15 when the divergence of the ion streamlines from the magnetic nozzle field lines exceeds 4%,7 and when the ion streamlines become ballistic.20 In experiments utilizing the latter two methods the ion streamlines are inferred from far-field Faraday probe traces. This technique has several limitations including that Faraday probes are inherently perturbative and restricted to far-field, and the analysis assumes that the ion density profile evolves self-similarly downstream. Toiden- tify the start of the magnetic nozzle near-field measurements are required, precluding the use of Faraday probes, while determining the downstream edge of the nozzle requires making direct, far-field ion streamline measurements or validating the assumptions inherent to the far-field Faraday probe techniques. In this work a suite of plasma diagnostics is used to spatially map the plume of a new, flexible magnetic nozzle source with four degrees of freedom (power, flow rate, magnetic field strength, and liner geometry), to determine the upstream limits of the magnetic nozzle region. In Section III the experimental apparatus and measurement methods are described. The results of the spatial maps are presented in Section IV.A near-field phenomenon is identified and the design and performance implications are discussed inSection V.

2 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 II. Performance Model Overview

Previously, quasi-1D performance models have been proposed by Lafleur15, 24 for devices in which the ions are magnetized and by Collard et. al.16 for devices in which the ions are partially magnetized. In both models the thruster is treated as two distinct regions: the upstream ionizing source and the downstream magnetic nozzle section. In the upstream source region the models state that the performance of the thruster is dependent on the equilibrium electron temperature required to balance ionization within the source and all losses within the region, and that the efficiency is largely dictated by the magnitude of the radial wall losses. In this work we are focused on the downstream magnetic nozzle section, and, specifically, how to define the bounds of nozzle. For completeness, an overview of the model of the magnetic nozzle section is included in this section. In the diverging nozzle section continuity and the species (ion and electron) momentum equations can be combined to relate the ion acceleration and the expansion of the nozzle:

1 2 A (Mdet 1) ln(Mdet) = ln , (1) 2 − − A0! where A is the local cross sectional area of the nozzle, A0 is the area of the nozzle throat, and Mdet is the detachment ion Mach number. This equation holds until ions no longer follow the imposed field lines - the plume becomes detached. Inherent to this formulation is that the plasma is perfectly confined by the bounding magnetic field line referenced the source geometry and that the plasma is everywhere collisionless within the expanding nozzle. These assumption imply that the plasma is attached everywhere upstream of the far-field plume detachment point. If the detachment point can be determined then the corresponding local cross sectional area of the nozzle, A, can be calculated and the Mach number of the ions at this point can be found. The additional thrust produced by the nozzle can be determined, resulting in

2 Mdet + 1 FP = F0. (2) 2Mdet ! where F0 can be interpreted as the upstream thrust:

F0 = qβn0TeA0. (3)

This formulation for FP comes from the ion and electron momentum equations and integrating over the cross sectional area at the detachment point. Note that q is the fundamental charge, β captures the uniformity of the plasma within the source, n0 is the plasma density within the source, and Te is the electron temperature. In the case of partially magnetized ions Collard et. al.16 assume that the detachment point coincides with the turning point of the magnetic nozzle because beyond the turning point minimal momentum is transferred to the thruster. In summary, the downstream magnetic nozzle is defined as starting at the throat (ator slightly upstream of the device exit plane), perfectly following the vacuum interface line defined by the source geometry, and terminating at the detachment point (in this case the turning point of the magnetic nozzle). Within this section the plume is assumed to be everywhere attached and collisionless. In the following sections we investigate the validity of these assumptions.

III. Experimental Setup

In this section the experimental apparatus used to investigate the validity of the assumptions in Section II is described. A magnetic nozzle plasma source is detailed and the diagnostics used to make the measurements presented in Section IV are outlined.

A. The Magnetic Detachment Experiment (MDX) The Magnetic Detachment eXperiment (MDX) is a flexible testbed magnetic nozzle source designed to investigate the physics underlying plasma detachment from the nozzle field lines. MDX is 13 cm in diameter and can accept plasma liners up to 3 cm in diameter. This compactness enables us to∼ use smaller

3 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 vacuum facilities without the diverging nozzle field lines intersecting the facility walls near the source. The diverging magnetic nozzle section is generated by a 149-turn solenoid constructed of 10 AWG square, enamel- coated copper magnet wire. In this configuration the solenoid is capable of producing peak axial magnetic fields of up to 900 G. The coil current is driven by an external DC laboratory power supply. The radio frequency (RF)∼ power is generated external to the facility and is coupled to the plasma via a hollow copper 3-turn inductive antenna. Both the RF antenna and the electromagnet spool are open-loop water cooled to dissipate heat and maintain maximum steady-state operating temperatures below the maximum source operating temperature of 240 ◦C. Finally, the propellant is fed to MDX from an external reservoir. A Faraday mesh surrounds MDX, with openings for connections and the plasma expanding through the magnetic nozzle. Figure 2 is a rendering of MDX, without the external supporting subsystems.

Figure 2: A rendering of the MDX electro- Figure 3: A side view of MDX operating at magnet, plasma liner, and RF antenna assem- the high magnetic field condition. bly.

Based on previous findings15, 16 suggesting that limiting source wall losses is a critical to enhancing overall performance we chose to integrate a quartz plasma liner with a diameter of 24 mm and an aspect ratio of (R/L) = 0.75 for initial operating envelope checkouts of MDX. During these initial tests we observed that MDX repeatedly transitioned from a dim, pinkish (likely capacitive) operating mode to a bright, whitish (likely inductive) mode at 120 W net input power and xenon flow rates at or above 2 mg/s for electromagnet coil currents up to 30 A.∼ This observed mode transition was accompanied by a 2 3 order of magnitude plasma density increase. To investigate the extremes of this operating envelope we− present results from MDX operation at coil currents of 5 and 30 A, or peak axial field strengths of 98 and 584 G, respectively. For both operating conditions the xenon flow rate was fixed at 3 mg/s and the net deposited powerwas allowed to float to accommodate changes in the plasma-antenna match due to the increased magnetic field strength within the ionization region. For the 5 and 30 A conditions the net deposited power was 118.7 and 136.4 W, respectively. A picture of MDX operating at the high magnetic field condition is shown in Figure 3. Both operating conditions were repeatable and demonstrated stable operation exceeding 14 continuous hours with deviations of less than 1% in the steady state net deposited power and temperature telemetry over the duration of operation.

B. Vacuum Facility All experiments were conducted in the Junior Test Facility connected to the Large Vacuum Test Facility at the University of Michigan. Junior is a 3 meter long, by 1 meter diameter stainless steel clad vacuum 7 5 chamber capable of achieving base pressures of 1 10− Torr and a background pressure of 4 10− Torr during MDX operation at neutral flow rates up× to 3 mg/s. The chamber was maintained× at high vacuum by a turbopump and a cryo pump, nominally rated at 38, 000 L/s on xenon. The effective pumping speed for the experiments described in this paper was 10, 000 L/s on xenon.

C. Diagnostics To answer the question are the assumptions that the plasma is attached everywhere upstream of the detachment point and collisionless throughout the nozzle valid? a complete description of the expanding plume is required, including the spatial plasma density, electron temperature, potential, and ion velocity structures. These properties were measured using a combination of electrostatic probes, namely planar double Langmuir and emissive probes, and non-invasive Laser Induced Fluorescence (LIF). Due to the small

4 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 size of MDX both probes were constructed of 1/16” diameter double-bore alumina, with the double probe collecting surfaces each measuring 0.25 mm in diameter and the emissive probe hairpin loop measuring 1 mm in diameter. The emissive probe was operated in the the limit of high emission. To map ion streamlines 2D time-averaged LIF, based on the setup used by Durot et. al.,25 was used to measure the axial and radial ion velocity distributions at throughout the plume. As Figure 4a demonstrates, the LIF injection and collection optics were fixed to preserve alignment and MDX was moved using a pair of linear translation stages, allowing the 1 mm diameter LIF measurement spot to move throughout the plume. To minimize changes to the experimental setup and to prevent probe cross-talk the double and emissive probes were fixed 30 cm apart and MDX was moved around each probe to produce a plume map, as depicted in Figure 4b. The magnetic topology at various coil currents was measured in atmosphere using a 3-axis Gaussmeter with a resolution of 0.01 G. A Stabil ion gauge, mounted in place of the emissive probe in Figure 4b, was used to measure the axial neutral pressure distribution of MDX while flowing 3 mg/s of xenon without plasma.

(a) (b)

Figure 4: (a) The internal setup used to measure the ion streamlines via LIF. (b) The internal setup used to map the plume properties, such as the electron temperature, plasma density, and plasma potential.

IV. Results

In this section experimental plasma measurements will be compared to the magnetic nozzle, as measured by the 3-axis Gaussmeter at atmosphere. The results will be presented in a manner consistent with the literature7 to identify similar features consistent with plasma detachment.

A. Magnetic Topology The magnetic topology was measured using a 3-axis Gaussmeter for electromagnet coil currents ranging from 5 A to 30 A over a 40 30 cm grid with 5 mm spatial resolution in both dimensions. Due to the flexibility of the MDX the× plasma liner was large enough to insert the Hall probe into the ionization region; the centerline magnetic field was also measured from upstream of the peak axial magnetic field locationto 30 cm downstream. Figure 5 depicts the magnetic nozzle shape with the edge field lines corresponding to the vacuum interface line intersecting the 24 mm diameter plasma liner wall and the centerline axial field strength of the MDX with a coil current of 5 A. Figure 6 shows the magnetic nozzle contour and the centerline field strength with the same plasma liner, but with the MDX operated at 30 A coil current. Forthe5A case the peak axial field strength is 98 G and for the 30 A condition the peak is 584 G. This demonstrates that the MDX electromagnet exhibits excellent linearity, with the peak field of the 30 A condition only0.7% below the expected value of 588 G.

5 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 (a) (b)

Figure 5: (a) The magnetic nozzle contour generated by the electromagnet operated at 5 A. (b) The centerline axial magnetic field strength generated by the electromagnet operated at 5 A.

(a) (b)

Figure 6: (a) The magnetic nozzle contour generated by the electromagnet operated at 30 A. (b) The centerline axial magnetic field strength generated by the electromagnet operated at 30 A.

B. Ion Streamlines The ion streamlines were determined by measuring the radial and axial velocity distributions throughout the plume using LIF. One limitation of LIF is that the signal intensity is typically proportional to the ion density, so as the density decreases the signal to noise ratio deteriorates. This limits the distance downstream of MDX that can be measured. The mean axial and radial velocities were determined by taking the moment of the sums-of-Gaussian fit to the data, like the excerpt traces shown in Figures 7 and 8 for the low and high magnetic field cases, respectively. As depicted in Figure 9a the ion streamlines for the 5 A coil current case generally diverge faster than the magnetic streamlines and are consistent with isotropic expansion of the plume. However, near the vacuum interface line at and axial distance of 15 20 mm downstream the local ion vectors deflect inwards. Note that there is a small charge exchange∼ (CEX)− peak near zero velocity in the centerline axial traces, shown in Figure 7a. This suggests that the neutral density is large near the source exit because the estimated CEX mean free path based on the back pressure is 10 cm. Interestingly, the radial velocity distributions in Figure 7b broaden as the distance from centerline∼ increases, with an observable low energy tail that includes zero velocity ions - likely more CEX ions. For the 30 A coil current case the ion streamlines undergo a more pronounced inward deflection as observed in Figure 9b. Upstream of the deflection the ion streamlines indicate that the plume is expanding isotropically. The high magnetic field condition LIF traces again exhibit a CEX ion population inthe

6 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 centerline axial velocity traces and a broadening of the radial velocity peak with increase distance from centerline, as observed in Figure 8, similar to the low magnetic field results. Note that the degraded signal- to-noise ratio in these LIF traces and the less extensive spatial map compared to the low magnetic field case is due to the lower plasma density of the MDX while operating at the high magnetic field condition.

(a) (b)

Figure 7: (a) The axial ion velocity distribution along the nozzle centerline and (b) the radial ion velocity distribution along a radial slice located at an axial distance of 40 mm while operating at a magnet current of 5 A.

(a) (b)

Figure 8: (a) The axial ion velocity distribution along the nozzle centerline and (b) the radial ion velocity distribution along a radial slice located at an axial distance of 20 mm while operating at a magnet current of 30 A.

C. Densities The plasma density was extracted from planar double Langmuir probe I-V traces throughout the plume. 17 3 In the case of MDX operation at 5 A coil current the density varied from high 10 m− at the source exit 13 3 plane to 10 m− far downstream; Figure 10a shows the centerline evolution of the plasma density close ∼ 16 3 to the source exit plane. In contrast, the density varied from low 10 m− at the source exit plane to 13 3 ∼ 10 m− far downstream when the coil current was 30 A. The 10 decrease in density between the two operating conditions is likely a symptom of the RF match quality∼ degrading.× The electron temperature was also extracted from the double probe I-V traces; in the 5 A condition T 3.5 eV and in the 30 A condition e ∼ Te 6 eV. In both operating conditions the electron temperature was approximately constant throughout the∼ plume, within errorbars, indicating the the plume can be approximated as isothermal. In terms of plasma density profiles the primary difference between the two operating conditions appears when the radial slices of the plume are examined. As illustrated in Figures 10b & 10c the density does not sharply decrease off centerline, rather it decreases gradually and uniformly. This suggests that theplumeis

7 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 (a) (b)

Figure 9: A comparison of the magnetic nozzle streamlines, the ion streamlines, and the local ion velocity vectors measured using LIF for MDX operation at magnetic currents of (a) 5 A and (b) 30 A.

(a) (b)

(c)

Figure 10: (a) The axial evolution of the plasma density within the plume with an MDX magnet current of 5 A. These results should be used to benchmark the density magnitudes in the remaining two subfigures herein. (b-c) The plasma density, normalized to the centerline value, along aradial slice at axial locations of 0 30 mm. Note that the vertical dashed lines denote the vacuum interface − magnetic field line.

8 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 (a) (b)

Figure 11: (a) The axial evolution of the plasma density within the plume with an MDX magnet current of 30 A. These results should be used to benchmark the density magnitudes in the other subfigure herein. (b) The plasma density, normalized to the centerline value, along a radial sliceat axial locations of 0 30 mm. Note that the vertical dashed lines denote the vacuum interface magnetic − field line.

simply expanding isotropically, and that the magnetic nozzle does not affect the plume in the 5 A case. For the 30 A condition the density follows the same trend close to the source exit plane. However, as shown in Figure 11b further downstream the density is peaked closer to centerline. This shift in trend suggests that the plume initially expands isotropically from the MDX, but then the magnetic nozzle begins to guide the plasma further downstream. Recalling the axial magnetic field strength in Figure 6b this indicates that a phenomenon is preventing the plume from attaching close to the exit plane, but decays more quickly than the magnetic field strength. To supplement the plasma density profiles the neutral density along the MDX centerline axis was measured using a Stabil ion gauge. As illustrated in Figure 12 the neutral density exponentially decreases as a function of axial distance from the MDX exit plane. Due to the size of the Stabil gauge housing the closest measurable location was 35 mm; everything upstream of this location was extrapolated using the exponential fit through the data. 5 In the far-field the background pressure was 4 10− Torr. All results reported here are for a neutral∼ flow× rate of 3 mg/s and are corrected for xenon.

D. Plasma Potential Figure 12: The neutral pressure as measured The plasma potential was measured using an emissive by an internal Stabil gauge and the corre- probe operated in the limit of high emission. Figure 13a sponding exponential fit. shows a contour of the plasma potential throughout the 5 A condition plume. For this condition the potential generally remains peaked at the centerline and plateaus around 1 2 source radii from centerline. This potential structure is consistent with the LIF results in Figure 9a and supports− the notion that the plume is expanding isotropically downstream. As illustrated by the contour in Figure 13b the plume of the MDX operating at a coil current of 30 A initially exhibits the same peaked centerline then plateau trend close to the exit plane, consistent with the LIF measurements in Figure 9b and suggests that the plasma does not leave the source region attached to the magnetic nozzle. However, the formation of a potential well is observed close to the source, starting at 10 mm. Previously, Little observed ion confining wells when the plume was attached to the magnetic nozzle.∼ 7 The potential well strength is 1 V and the radial location approximately corresponds to the vacuum interface line, consistent with what∼ was observed by Little.7 The potential well disappears at an axial location of 45 50 mm (not shown in Figure 13b to highlight the potential well structure), suggesting ∼ −

9 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 detachment from the magnetic nozzle. Ultimately, this high magnetic field case exhibits behavior suggesting the plume is initially detached from the magnetic nozzle, reattaches at an intermediate distance downstream, then detaches from the nozzle further downstream.

(a) (b)

Figure 13: The spatial plasma potential maps for the (a) low magnetic field and (b) high magnetic field cases. Note the appearance of the potential well near the vacuum interface line inthehigh magnetic field case.

V. Discussion

The measurements in Section IV outline compelling evidence that our assumption regarding low power magnetic nozzle physics, in that the plasma exits the ionization region attached to the nozzle, is invalid. This traditional concept of a magnetic nozzle does not include a phenomenon that prevents the plasma from initially attaching to the nozzle. This section will explore a possible explanation, examine the formation of the potential well observed in attached plumes,7 and discuss the implications to nozzle design and performance.

A. Downstream Reattachment Based on the plasma potential results in Figure 13b and the LIF data in Figure 9b the high magnetic field operating condition (30 A coil current) exhibits a transition from plume expansion behavior consistent with a completely unmagnetized plasma to behavior suggesting the plume is confined by the magnetic nozzle. This gives rise to the question what mechanism is preventing plume attachment to the magnetic nozzle as the plasma exits the ionization region? Given that the plume reattaches to the magnetic nozzle downstream this mechanism must decay as a function of downstream position. The presence of a low velocity CEX population of ions in the LIF traces (Figure 8) near the source exit, whose presence is not predicted based on the measured far-field back pressure, hints at the culpable mechanism: high neutral density near the source exit. The neutral pressures measured by the Stabil gauge, shown in Figure 12, confirms that the neutral density is high near the exit of the MDX. A highneutral density in the near-field results in large ion-neutral and electron-neutral collision frequencies resulting inCEX collisions and enhanced cross-field electron mobility. Assuming that the neutral gas expands isotropically the neutral pressure throughout the plume can be modelled as a hemisphere minus a hemispherical cap. When coupled with the measured axial magnetic field strength (Figure 6b) and the quasi-isothermal electron temperature measured throughout the plume the local Hall parameter (Ω = qB/meνen) can be estimated. This parameter captures the strength of the local magnetic field relative to the cross-field mobility-enhancing electron-neutral collision frequency. As illustrated in Figure 14a the Hall parameter is small near the exit plane, indicating that electron- neutral collisions dominate compared to the magnetic field. The corresponding enhanced cross-field electron mobility allows the expanding plasma to ignore the magnetic nozzle. As the plume continues to expand downstream the Hall parameter rapidly increases, as shown in Figure 14b, resulting in reattachment to the magnetic nozzle at around 15 20 mm. This is consistent with the inward deflection of the ion streamlines (Figure 9b) and the∼ formation− of a potential well near the vacuum interface line (Figure 13b).

10 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 This reattachment may be due to the neutral density decreasing more rapidly than the magnetic nozzle strength. The increase in Hall parameter and the reattachment of the plume suggests that there is a critical Hall parameter value of 10 below which the plume is detached and above which the plume is attached to the nozzle. Due to the disparity∼ between the isotropic expansion of the neutral population and the more uniform magnetic nozzle strength this critical Hall parameter threshold is achieved closer to the the exit plane along the vacuum interface line compared to the centerline, as seen in Figure 14b. This implies that the plume begins to reattach to the outermost nozzle field lines before reattaching to the lines in the center, consistent with the outermost ion streamlines deflecting closer to the source in Figure 9b.

(a) (b)

Figure 14: (a) The estimated Hall parameter spatial map. Note that the map is estimated because the map is based on centerline neutral pressure measurements that is revolved around the centerline such that a hemisphere minus a cap is swept. (b) The Hall parameter spatial evolution along the nozzle center and nominal vacuum interface lines.

B. Formation of a Confining Potential Well Since the plume appears to detach in the near field, the natural question is what impact does the near-field detached region have on the downstream magnetic nozzle geometry? To study this question the far-field plume must be interrogated. Beyond 25 mm downstream the LIF signal to noise ratio deteriorated,∼ making it unsuitable for far-field measurements. However, the emissive probe could be used to obtain downstream plume information. In Figure 14 the Hall parameter remains large in the plume far-field due to Earth’s ambient magnetic field dominating the low background neutral density. However, as shown in Figure 15 the plasma potential plateaus in the far-field, indicating that the plume again detaches far from the source exit. In the intermediate space a potential well forms near, and Figure 16: The nominal magnetic nozzle referenced downstream of, the reattachment point close to the to the plasma liner (solid black) and the effective expected vacuum interface magnetic field. As illus- expanded magnetic nozzle that forms within the trated by the radial slices in Figure 15 the potential plume due to neutral collisions near the source. well is much more pronounced in the higher magnetic field (30 A coil current) case than the low(5 A coil current) condition. This suggests that the onset of reattachment occurs closer to the source exit as the magnetic nozzle strength increases. Figure 15 also shows that the potential well extends beyond the expected vacuum interface field line, implying that the effective magnetic nozzle downstream is larger indi- ameter than the nominal magnetic nozzle referenced to the plasma liner. This is caused in part by the high

11 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 (a) (b)

(e)

Figure 15: Select radial slices of the plasma potential measured in the (a) low magnetic field and (b) high magnetic field cases. (c-e) The plasma potential, normalized to the centerline value, along a radial slice at axial locations of 5, 15, and 25 mm. The vertical dashed lines denote the vacuum interface magnetic field line.

12 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 electron-neutral collision frequency-driven enhanced cross field transport upstream of the effective magnetic nozzle; a significant amount of low energy electrons are able to diffuse beyond the nominal vacuum interface field line. This results in the expanded effective magnetic nozzle shown inFigure 16. Noting the above discussion suggesting that the plume reattaches to the outer magnetic field lines the potential well may form to deflect unmagnetized, ballistically expanding ion along the nozzle to preserve plume quasineutrality due to the confinement of reattached electrons. The results in Figure 15 indicate even the low magnetic field case may briefly reattach to the nozzle based on the apparent formation of an apparent potential well 15 20 mm downstream. This appears to be consistent with the LIF measurements in Figure 9a, but due∼ to the− errorbars on the plasma potential measurements this result is uncertain. To confirm this result a more accurate and sophisticated method of measurement, such as the inflection point method, must be employed. For the high magnetic fieldcase the potential well is strong enough to indicate a clear trend, despite the large uncertainties inherent to the measurement process. At this operating condition the plume reattaches at 15 mm downstream, consistent with the LIF map in Figure 9b. Interestingly, the strength of the potential∼ well appears to start to decrease at 25 mm, but at that point the potential structure also begins to transition, as observed in Figure 15b.. Further∼ downstream of this point the far-field potential, from a radial perspective, begins to exceed the centerline potential for the first time. Upstream of this location the maximum potential always resided within the magnetic nozzle. This transition in potential structure may suggest that the plume is beginning to once again detach from the magnetic nozzle. In both magnetic field cases the plasma potential structure flattens, within errorbars, within 50 mm, as illustrated by Figures 15a and 15b, providing further evidence of far-field detachment in the ∼case of the high magnetic field operating condition.

C. Conditions to Avoid Near-Field Detachment The presence of a mechanism capable of detaching the plume from the magnetic nozzle in the near-field raises the question: in what ways can this mechanism be mitigated or eliminated? From the results above the critical threshold of the Hall parameter to observe reattachment is 10, which suggests that the magnetic field needs to dominate the neutral collisions. By invoking the∼ continuity equation to solve for the neutral density in terms of the ion fraction and the mass flow rate the Hall parameter can be manipulated intothe form B Ω , (4) ∝ m˙ (1 α) − where α is the ion fraction andm ˙ is the neutral mass flow rate. From this form the Hall parameter clearly scales with the magnetic field, neutral flow rate, and the level of ionization. However, the magnitudes of these parameters required to achieve this threshold Hall parameter may not be attainable for low power devices. Using the results for the MDX reported here and assuming that each parameter can be changed while the other values remain fixed, the magnetic field must be increased to 1 T to prevent detachment in the near-field at the reported neutral conditions, or 25 the present field∼ strength. This would require a redesign of the electromagnet to accommodate the∼ kA currents× required to generate this field and the thermal management system to reject the accompanying increase in waste heat generated by the magnet. The next scaling parameter in this system is the mass flow rate. If the flow rate into the MDX is reduced from 3 mg/s to 0.1 mg/s while the magnetic field and ion fraction were held constant the Hall parameter would marginally reach the threshold value and the plasma would be attached to the nozzle lines. However, the MDX could not be stably operated at flow rates below 0.5 mg/s within the 200 W input range studied here. For the remaining scaling factor the ion fraction must be increased to 0.96, or plasma must be nearly fully ionized, for the Hall parameter threshold to be met. Based on the available literature 2, 3, 7 the ion fraction in closer to 0.001 0.1 implying that significant breakthroughs in plasma power coupling at low power are required to attain− near full ionization. While in real devices these scaling parameters are inherently linked, the difficulties associated with achieving the critical Hall parameter required for plume attachment in the near-field suggests that near-field plume detachment may be prevalent in low power magnetic nozzles.

D. Thruster Design Ramifications Since interest in magnetic nozzles includes incorporation into low power thrusters 2, 3, 7, 11 the detached- attached-detached nature of the plume has several direct design and performance ramifications: larger than expected liner wear due to enhanced cross-field collisional transport within the plasma liner, reduced efficiency

13 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 due to the loss of confinement near the source, and lower thrust performance due to a decrease in theeffective throat field strength. Here low power is defined as up to several kW, where ion fractions are small,giving rise to the high electron-neutral collision frequency that prevents near-field plume attachment. While these devices would remain electrodeless because a plasma-wetted electrode is not required for operation one of the main advantages is lost, namely the extended expected lifetime due to limited wear. For highly collisional plasmas within the source the magnetic field parallel to the liner walls is unable to confine theplasma resulting in higher erosion rates. This enhanced near-field plume collisionality may, in part, explain the limited measured thrust performance of magnetic nozzles ( 8% total efficiency at 2 kW2) due to the ability of the plume to collisionally diffuse beyond the nominal∼ magnetic nozzle in∼ the near-field. Due to the isotropic expansion in thisregion a fraction of the ions born within the source region will gain sufficient energy to escape the reattachment of the plume. This results in an effective waste of the energy consumed by the creation of those ions, thereby resulting in a higher ”useful” ion cost - those ions that are successfully accelerated axially. As shown in Figure 16, the nominal vacuum interface line may not be the true interface line. Rather a nearby, slightly more divergent, field line becomes the vacuum interface. This effectively enhances the plume divergence, decreasing the divergence efficiency of the plume. Additionally, due to the near-field collisionality, thethroat of the effective magnetic nozzle is located within the plume at a lower magnetic field strength. Thisresults in reduced ion acceleration. To account for this effect numerical models must account for the additional loss terms associated withthe enhanced cross-field plasma transport in the near-field and the location of the true magnetic nozzlethroat located within the plume. The expanded plume should also be included to allow for accurate prediction of plume divergence and total efficiencies. Physical system designs should also consider designing the magnetic circuit to have the actual downstream magnetic nozzle throat coincide with the peak field strength to recover some of the lost ion acceleration potential.

VI. Conclusion

A flexible testbed source was created to investigate the physics underlying plasma detachment froma magnetic nozzle. In initial experiments the MDX is operated at a constant flow rate of 3 mg/s xenon with a fixed source region diameter of 24 mm. The peak centerline magnetic field was set to 98 Ginthelow magnetic field case and 584 G in the high field condition. The net deposited RF power was allowed tofloat to accommodate changes in the antenna-plasma match caused by the change in magnetic nozzle strength. A suite of plasma diagnostics, including a double Langmuir probe, an emissive probe, and LIF are used to spatially map the plume. The resulting maps revealed that the plume is initially detached from the magnetic nozzle in the near-field and, in the high magnetic field condition, reattaches downstream. In the far-fieldthe plasma fully detaches from the magnetic nozzle. Near the reattachment point the ion streamlines transition from isotropic expansion to inward deflection near the vacuum interface field line and an ion confining plasma potential well begins to form. High electron-neutral collision frequencies due to large neutral densities in the near field are proposed to be the cause of the initial detachment from the magnetic nozzle. Assumingthat the streamlines following the magnetic field is indicative of attachment the plume reattachment may bedue to a more rapid decay in the neutral density compared to the local magnetic field strength. This detachment- attachment-detachment pattern results in the formation of an effective, expanded magnetic nozzle within the plume that differs from the nominal magnetic nozzle referenced to the source geometry. During our near-field investigation of the MDX magnetic nozzle it was discovered that the plumewas detached from the nozzle field lines. The discovery of this detached near-field region may, in part, account for the low measured thrust performance2 in low power, small ion fraction magnetic nozzle thrusters. We have discussed the performance and plasma models and they must account for the additional loss region and decrease in effective magnetic nozzle throat strength. Finally, these results suggest that the magnetic circuit of new and existing devices should be modified such that the peak field generated by the magnets coincides with the location of the downstream effective magnetic nozzle throat.

VII. Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1256260, Thank you to the members of the Plasmadynamics

14 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017 and Electric Propulsion Laboratory for their insightful discussion concerning this research.

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15 The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8–12, 2017