Influence of applied magnetic field in an air-breathing microwave plasma cathode

The air-breathing electric propulsion concept refers to a spacecraft in very-low Earth orbit (VLEO) ingesting upper atmospheric air as propellant for an electric thruster. This compensates atmospheric drag and allows the spacecraft to maintain its orbital altitude, removing the need for on-board propellant storage and allowing an extended mission duration which is not limited by propellant exhaustion. There is a need for development of a robust, high current density and long life cathode (or neutralizer) for air-breathing electrostatic thrusters as conventional thermionic hollow cathodes are susceptible to oxygen poisoning. An Air-breathing Microwave Plasma CAThode is proposed to overcome this issue through the use of a microwave plasma discharge, producing an extracted current in the order of 1 A with 0.1 mg s−1 of air. In this paper, the effect of varying magnetic-field strength and topology is investigated by using an electromagnet coil, which reveals a significantly different behaviour for air compared to xenon. The extracted current with xenon increases by 3.9 times from the zero-field value up to a peak around 150 mT magnetic-field strength at the antenna, whereas an applied field does not increase the extracted current with air at nominal conditions. A non-zero magnetic-field with air is however beneficial for current extraction at reduced neutral densities. A distinct increase in extracted current is identified at low bias voltages with air for a field strength of around 50 mT at the internal microwave antenna, consistent across varying field topologies. The effect of a lowered magnetic-field strength in the orifice region is investigated through the use of a secondary coil, resulting in an extracted current increase of 25% for a relaxation from 6 mT to 1 mT, and demonstrating the beneficial impact of a locally reduced field strength on electron extraction.


Introduction
Air-breathing electric propulsion (ABEP) describes a spacecraft in very-low Earth orbit (VLEO), using the rarefied air at these upper atmospheric altitudes as propellant for an electric * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. thruster. Previous mission analysis studies have indicated 180-200 km as a feasible VLEO altitude range for an ABEP system [1,2]. The generated thrust is used to compensate atmospheric drag and maintain the desired orbit. In this way, a spacecraft with an ABEP system achieving full drag compensation does not require onboard propellant storage, allowing long-duration missions in the VLEO altitude range by removing propellant capacity as a limit on operating lifetime [3,4].
Several recent mission analysis studies of the ABEP scenario conclude that high specific impulse (I sp ) is a key desired characteristic of the thruster, with a minimum I sp requirement of at least around 3000 s [1,2,5]. This is driven primarily by the tangential drag of the spacecraft and solar array surfaces, which is significant even if these surfaces are aligned with the VLEO air flow. This suggests that the performance of thruster designs based on electrostatic ion acceleration, which require a cathode (or neutralizer) and typically demonstrate I sp values in the 2000-6000 s range with conventional propellants, is suited for an ABEP system. A high-specific impulse electrostatic thruster design has been proposed by several ABEP studies, for instance based on adapting conventional electric propulsion technologies such as Hall-effect (HET) and gridded-ion (GIT) thruster types [6][7][8]. Such thrusters require a cathode to provide a negative current for supporting the thruster discharge and neutralizing the ejected ion beam, and this therefore motivates the development of a neutralizer capable of operating on air.
The cathode presented in this study is developed as part of the AETHER H2020 project, which aims to design an airbreathing thruster and intake system that is capable of achieving drag-compensation in VLEO and can be tested in a VLEOrepresentative lab environment [1]. This application prescribes several of the cathode target operating parameters based on a dawn-dusk Sun-synchronous orbit at altitudes between 190 and 240 km, such as: an extracted current in the 0.25-3 A range, maximum power of 200 W, inlet air flow of 0.04-0.1 mg s −1 , composition of 0.48O + 0.52N 2 (atomic oxygen replaced with molecular for testing) and inlet air density range of 0.5-5 × 10 18 m −3 .
Neutralizers for electric propulsion are most commonly based on the hollow cathode design, typically producing a high electron current density at low input power via thermionic electron emission from the surface of low work function material. However, exposure of the emitter materials, such as barium-oxide impregnated tungsten (BaO-W) or lanthanumhexaboride (LaB6), to oxygen results in poisoning of the material surface and prompts a significant decrease in the current density at even minimal values of air pressure [9,10]. Additionally, the combination of an oxidising environment and the high temperatures associated with thermionic emission, typically in the 900 • C-1700 • C range for BaO-W and LaB6 hollow cathodes, can lead to significant degradation of components such as the heating element and therefore a reduced cathode lifetime. This is demonstrated in [1], where operation of a LaB6 hollow cathode to xenon containing a 12% fraction of a 0.48O 2 + 0.52N 2 mixture results in significant erosion of the emitter and cathode structure. Hollow cathodes are consequently not viable as a neutralizer for a fully air-breathing propulsion system, in which the cathode operates on a subset of the total intake flow of oxygen and nitrogen species.
Several types of neutralizers have been investigated in the literature as alternatives to hollow cathodes, typically comprising a plasma electron source where electrons are extracted out of a plasma sustained within the neutralizer. Based on the AETHER-derived targets introduced previously, a microwave plasma cathode is selected as the approach for this study, due to: (a) microwave cathodes achieving an extracted current in the 1 A order (with xenon) in literature, (b) high power and propellant utilisation efficiencies demonstrated in literature at the low power and flow rate intended for the AETHER cathode, and (c) more compact microwave components than RF equivalents, important since a feasible ABEP system must fit in the post-intake volume to minimise platform drag. The prototype developed within this study is termed the Air-breathing Microwave Plasma CAThode (AMPCAT), which was previously introduced in [11]. Through iterative prototype testing, this work investigates the influence of the applied magneticfield on extracted current behaviour. In particular, section 2 presents the prototype design and test setup, before the differences between air and xenon propellant are detailed in section 3. The effect of magnetic-field strength at varying neutral density is presented in section 4 and the influence of varying applied field topologies in section 5. Finally, the impact of a reduced magnetic-field strength in the orifice region is investigated in section 6.

Microwave cathodes in literature
Excitation using microwaves is an approach extensively used in the plasma cathode literature, commonly operating in the 2-5 GHz range. Typically, microwave neutralizers make use of the electron cyclotron resonance (ECR) mechanism for efficient electron heating, which aims to produce high-energy electrons that boost the degree of plasma ionization and so allow an increased current to be extracted. ECR refers to a matching of the input microwave frequency and the frequency of electron motion within the plasma, which is determined by the applied magnetic-field strength inside the neutralizer. Kamhawi et al [12] investigate two methods of feeding microwave power into an ECR cathode: (a) a coaxial line with an antenna directly inserted into the plasma, and (b) a waveguide input to the neutraliser volume. The plasma-interfacing antenna configuration demonstrates higher extracted current, with a maximum of 2.6 A at a power cost of 98 W A −1 recorded with xenon.
Another ECR microwave cathode with significant research maturity is the µ10 neutralizer developed by JAXA and flown on the Hayabusa-1 and 2 asteroid sample return missions. Studies include those in [13,14] and, more recently, [15]. The µ10 operates at a nominal current of 0.18 A with 0.07 mg s −1 of xenon flow rate, at an input 4.2 GHz microwave power of 8 W and total bias of 32 V between the neutralizer and anode in standalone testing [15]. An updated neutralizer design for the µ20 configuration demonstrates a maximum current of 0.5 A with xenon at 20 W microwave power [16]. The neutralizer standalone test results are reproduced when coupled with thrusters, for both GIT and HET thruster types [16,17].
The applied magnetic-field has a significant impact on the internal plasma of microwave cathodes studied in the literature. The design of the µ10 neutralizer's magnetic circuit aims to establish a |B| = 150 mT magnetic-field strength region, corresponding to the ECR condition for the 4.2 GHz input microwave frequency, which intersects the L-shaped microwave antenna. An increasing magnetic-field strength both upstream and downstream of the antenna produces a magnetic-mirror to confine electron motion between the |B| maxima, allowing a localised region where electrons are efficiently accelerated by both skin-depth antenna heating and ECR [13]. The design is based on the fact that a high density of electrons confined within the magnetic-mirror acts as a virtualcathode, which supports efficient coupling of the microwave power from the antenna to the plasma [13]. Analysis concludes that the propagation of microwave power is likely limited to the 2-5 mm skin-depth region around the antenna, since the electron density measured inside the neutralizer is significantly larger than the 2.2 × 10 17 m −3 cut-off value (n c ) above which 4.2 GHz waves do not propagate [18]. This rationale of electron heating in the antenna vicinity is also supported by the plasma light emission visible through the orifice, which shows an azimuthally non-uniform intensity with significantly stronger emission around the antenna, indicating that the most direct ionization of xenon neutrals occurs in this region.
A plasma density above n c inside the neutralizer plasma volume is sustained by diffusion of the high-energy electrons beyond the localised antenna region. In particular, this electron mobility is required for maximizing the electron current extracted through the neutralizer orifice. The magnetic-field strength is a trade-off in this regard, between increasing the volume for ECR-heating and ensuring electron motion is not excessively impacted by a high |B|. This is supported by observations in [12,19]. The identified impact of magnetic-field strength motivates the study in [20], which adds an electromagnet coil around the orifice of the µ10 neutralizer to partially counteract the primary field imposed by the samariumcobalt (SmCo) permanent magnet. Lowering |B| at the orifice in this way, from 23 mT to 12 mT, results in an extracted current increase of around 40% above the nominal value of 0.18 A, and this behaviour is maintained with varying xenon flow rate.

Principle of operation
In the air-breathing cathode, microwave power at 2.45 GHz is supplied to the plasma via a molybdenum L-shaped antenna inserted directly into the plasma volume. Neutral propellant particles fed into the cathode impinge on the high electricfield region in the antenna vicinity, resulting in ionization and generating a plasma within the cathode. The plasma electron source principle of extracting a negative current I extr from this plasma relies on equal ion current I i collection on the plasma-interfacing internal surfaces, in order to preserve charge quasi-neutrality. The electron and ion fluxes are sustained by a positive potential gradient applied between the cathode internal surfaces and the region downstream of the cathode orifice. In fully-representative operation, this potential gradient is achieved with negative biasing of the ion-collecting surfaces, relative to the typically positive space potential V s of the thruster discharge. For the standalone test configuration used in this study, the cathode is grounded and a positive bias is applied to an extracting anode plate, located downstream of the orifice. The total bias potential between the neutralizer and anode is termed V b .
The dissociation energies of the O 2 and N 2 components of the inlet air are 5.11 eV and 9.76 eV respectively [21,22], resulting in the production of two atomic particles for every molecule experiencing a dissociation collision with an electron of sufficiently high energy. Collisions between high-energy electrons and neutrals form the primary cathode ionization mechanism, for which the first ionization energy values are 13.62 eV, 14.53 eV and 12.13 eV for O, N and Xe respectively [23]. A consideration of these dissociation and ionization energies for the neutral air particles inlet to the cathode plasma, in which microwave energy is first transferred to electron heating and then to propellant ionization via electron-neutral collisions, suggests a predominantly atomic (rather than molecular) ion population due to the significantly lower dissociation energy values.
Ion collection on the internal cathode surfaces occurs according to the Child-Langmuir law, since the potential drop through the sheath is large compared to the electron temperature T e (in eV) in the bulk plasma. The ion current density J i is therefore: where n i is the ion density, typically set equal to the electron density n e under the quasi-neutrality assumption, e is the electron charge, v is the ion velocity at the surface, ϵ 0 is the vacuum permittivity, M is the ion mass, ϕ 0 − ϕ = V is the potential drop across the sheath and d is the sheath thickness. The ion density limits the ion current which can be collected, and therefore the negative extracted current, since I i = J i A i where A i is the conducting surface area exposed to the plasma. As typical in the literature, the AMPCAT aims to exploit ECR for efficient electron heating by means of the resonance between the supplied microwave frequency f and the frequency of electron gyration ω c around lines of the applied magnetic-field: where m is the electron mass. For f = 2.45 GHz, the corresponding ECR magnetic-field strength B ECR is 87.5 mT. The electron gyration exploited by ECR occurs with a given Larmor radius r L around the B-field lines. Microwaves must travel into the plasma for electron heating to occur, however a limit exists based on the plasma frequency ω p relation for the maximum transmissible frequency at a given electron density. This determines a cut-off plasma (electron) density n c which varies with microwave frequency [24]. For f = 2.45 GHz, the cut-off density is 7.4 × 10 16 m −3 . Since the electron density observed in microwave cathodes is significantly higher than n c (see section 1), microwaves do not penetrate the bulk of the overdense plasma due to reflection at its surface. As a result, direct heating of electrons by the oscillating microwave fields occurs only in the region immediately around the antenna, approximated as the plasma skin-depth δ: where c is the speed of light. For instance, a representative n e = 10 18 m −3 predicts a region of δ = 5.5 mm thickness around the 2.45 GHz antenna in which microwave-electron energy transfer predominantly occurs. Ionization of propellant neutrals in the plasma is primarily described by the electronneutral collision frequency ν en , which is proportional to the electron-neutral collision cross-section σ en for the particular neutral species and T e . The total electron collision frequency (also including electron-ion collisions) influences the electron mobility µ e and electron diffusion coefficient D e , which describe electron transport through the cathode plasma. In the worst-case transport scenario of electron motion perpendicular to an applied magnetic-field, classical diffusion theory predicts an adjusted µ e,⊥ and D e,⊥ : where Ω e is the electron Hall parameter. Under the reasonable assumption that ω c = eB/m ≫ ν e (typically GHz compared to MHz range for microwave cathodes), it is evident that D e,⊥ , µ e,⊥ ∝ 1/B 2 . Consequently, the strength of applied magnetic-field in the cathode is a trade-off between: (a) an increased ECR-layer and beneficial electron confinement due to a reduced Larmor radius (r L ∝ 1/B), boosting electrondensity in the antenna region, and (b) excessively inhibited electron mobility and diffusion, hindering electron extraction through the cathode orifice. As well as electron diffusion, ion transport to the internal cathode surfaces is required to support negative current extraction. The ion mobility is also influenced by the magnetic-field, though significantly less than electrons due to the much larger ion mass M (e.g. since r L ∝ M).

Prototype design approach
The cathode design is depicted in figure 1, which shows a cross-section through the central axis. An L-shaped molybdenum antenna with a diameter of 1.25 mm and radiating length of λ/8 is inserted into the plasma volume, connected to a 2.45 GHz microwave generator via a coaxial microwave line. A λ/8 L-antenna is chosen as the initial design starting point due to experience in the literature [13], based on this constituting an efficient radiating length for wire antennas [25, p 200]. The antenna is encased in a boron-nitride sleeve and conductive outer collar, which minimizes microwave power loss by extending the effective coaxial line until the L-shaped radiating element. The plasma-interfacing surfaces are manufactured from grade 304 stainless steel due to its combination of: (a) good conductivity to maximize collected ion current, (b) low magnetic permeability to avoid influencing the magnetic circuit, and (c) resistance to oxidation from the air plasma at elevated temperatures. The magnetic circuit is composed of a coil with 650 turns of enamelled 0.8 mm diameter copper wire, which interfaces with two high-purity iron yokes. These act to guide the magnetic flux and form the magnetic mirror across the L-antenna. The use of an electromagnetic coil allows variation of the magnetic-field strength via a direct proportionality with the DC current supplied to the coil. An iron shield is mounted around the coil in order to reduce flux leakage and maximize |B| within the cathode. Propellant is supplied via a radial feed-tube passing through the downstream magnetic yoke. As represented by the shading in figure 1, parts not in contact with the plasma are manufactured from 6082 aluminium alloy. It should be noted that the general design methodology is motivated by the µ10 neutralizer developed at JAXA (see section 1), enabling the literature data to be used as a reference for the performance demonstrated with xenon, however significant changes are made to target operation with air and variability of the magnetic-field (as described in later sections). The magnetic circuit is designed to impose a B ECR = 87.5 mT strength region that extends along the downstream surface of the antenna. This approach is based on maximizing electron heating from ECR via an overlap between the ECR-layer and the zone of peak electric-field produced by the antenna, as well as a high propellant neutral density resulting from the radial inlet. This is shown in figure 1 with simulations of the magnetic-field (flux density and direction), electric-field magnitude and neutral particle density inside the cathode volume, using modelling software for the case without plasma. The magnetic-field simulation is based on a magnetostatic solution using the finite-element method, the antenna-derived electricfield simulation is based on a method-of-moments solution in the frequency domain and the neutral density simulation uses the flux-based angular coefficient method for solving the free molecular flow scenario. A nominal coil current I coil = 2 A is required for the |B| pictured, the antenna |E| simulation is based on an ideally impedance-matched 50 Ω line at the nominal 60 W transmitted power and the neutral density is for the nominal 0.1 mg s −1 flow rate of 0.48O 2 + 0.52N 2 mix with the experimentally-derived background vacuum chamber pressure as the boundary condition outside the orifice. The cathode internal diameter of 33 mm is a match between: (a) an optimal ∼ 1 mm gap from the antenna-tip to the wall for a λ/8 = 15.3 mm radiating length [26], and (b) the channel diameter required for the target density of 5 × 10 18 m −3 at 0.1 mg s −1 of air in the case of a fully open orifice (see section 4.1). An orifice diameter of 5 mm is used as the baseline for the study presented in this paper, as shown in figure 1, although larger orifices are also tested to investigate the effects of varying neutral density. The nominal orifice produces a neutral density of 1.0 × 10 21 m −3 and 5.0 × 10 20 m −3 for 0.1 mg s −1 of air and xenon respectively (see section 4.1 for further detail). The length of the internal volume is based on a prediction of the ion-collecting area required for I extr in the 1 A order of magnitude, using equation (1) with plasma parameters estimated from [13].

Standalone test setup
The cathode standalone testing is performed at the Plasma Propulsion Lab of the University of Surrey. The setup inside the vacuum chamber is shown in figure 2, in which the magnetic shield surrounding the coil is removed. The extracting anode solid plate is manufactured from grade 304 stainless steel and positioned 30 mm downstream of the orifice. It is verified that the solid anode does not significantly impact cathode operation, since anode designs with a large central opening result in equivalent values of extracted current and background pressure. The cathode is connected to the chamber ground via the support, and this is represented on a schematic of the test equipment shown in figure 3. The time-averaged extracted current is recorded on the anode DC power supply (MagnaPower, max 2 kW at up to 12 A). Microwave power is supplied by a 2.45 GHz generator (Kuhne KUSG2.45-250A, forward power up to 250 W), which records the forward and reflected power. A DC block is used to isolate the microwave line from any DC current collected by the antenna from the plasma, and in this way the antenna is electrically floating. A stub tuner allows impedance matching along the line for minimising the reflected microwave power, typically reduced to below 1 W. The N-type microwave connectors within the chamber are evacuated via a hole drilled through the lateral surface to avoid connector damage due to a multi-pactor breakdown. Propellant is supplied from compressed gas bottles via a mass flow controller for both the 0.48O 2 + 0.52N 2 air mixture (Bronkhorst El-Flow, max 200 sccm Ar, precision 0.1 sccm) and xenon reference (Bronkhorst El-Flow, max 20 sccm Xe, precision  0.01 sccm). Since the mass flow controller used with air is calibrated for argon, a 1.4 conversion factor is applied for an equivalent air volumetric flow rate. Background pressure is measured using a cold cathode ionization gauge (Leybold PTR90, 10 −8 to 10 3 mbar (10 −6 to 10 5 Pa) range), with a value of <1 × 10 −5 mbar (<1 × 10 −3 Pa) without flow and a range of 2.2-4.8 × 10 −4 mbar (2.2-4.8 × 10 −2 Pa) over the air mass flow rates (ṁ) tested. The full variation of input parameters used during testing is shown in table 1, for which a sweep of anode plate bias is typically conducted at each combination of the other inputs. A microwave-frequency power sensor (Anritsu MA24105) is used to measure the input microwave power to the cathode (P in ) without plasma, in order to quantify the power loss in the coaxial line (P l ). The 30, 60 and 90 W microwave source powers (P 0 ) tested are found to correspond with input powers of 24, 48 and 70 W respectively, via P in = P 0 − P l . As stated previously, the stub tuner is used to minimize reflected microwave power during cathode operation, typically to below 1 W. The true power input to the cathode is therefore reduced by the reflected power, however this is not accounted for in the P in calculation to retain conservative input power values that can act as a common reference for the standalone tests.

Cathode plasma properties
Knowledge of the cathode plasma parameters enables an assessment of the mechanisms occurring within the plasma, therefore estimates of properties such as electron temperature and electron density are useful to the analysis presented in this study. These plasma parameters are derived from diagnostic studies of the microwave cathode using a Langmuir probe, in which the tested cathode prototype differs only marginally in the design of the internal plasma volume from the prototype described here. The diagnostics are performed without any applied magnetic-field and for a straight λ/4 microwave antenna instead of the L-shaped design. Therefore, the estimates for T e and n e are applicable for the case of |B| = 0. This reduces the need to consider the effect of the magnetic-field on the processing of the raw Langmuir probe data and eases the insertion of the probe within the plasma volume (since the electromagnet coil is not present).
The diagnostic tests use a single Langmuir probe with a conventional design based on best-practices recommended in the electric propulsion literature [27,28]. A 0.75 mm diameter tungsten wire is used, housed within an alumina sleeve. The probe is positioned both: (a) in the internal cathode volume, and (b) in the external anode-orifice discharge. Internally, the probe position is halfway to the wall radius (r w ), sampling the bulk plasma 8 mm equidistant from the antenna and chamber walls, and 7 mm upstream of the orifice (at z o ). Externally, the probe is positioned along the central cathode axis (r = 0) and 15 mm downstream of the orifice, half of the orifice-anode distance (d a ). The plasma parameters measured are detailed in table 2. The data is presented for the baseline orifice diameter of 5 mm. Results are reported for an air mass flow rate Table 2. Measured plasma parameters (average values with standard deviation from repeat readings) for internal and external Langmuir probe sampling of representative cathode prototype with no applied magnetic-field.

Magnetic-field validation
The nominal cathode magnetic-field configuration, as described in the previous section, is also termed 'mirror' due its design aiming at a magnetic-mirror around the Lantenna. The B-field achieved in the prototype is validated through comparison to the simulated values by using a magnetometer probe (Hirst GM08). The applied B is sampled along two paths in the assembled prototype, one in the radial and one in the axial direction, as shown in figure 4. These values are compared to the simulated B-field, modelled using Finite Elements Method Magnetics software [29]. The comparisons demonstrate a generally close agreement between the measured and simulated B. For a 2 A coil current, the maximum discrepancy is 2.  The variation of |B| within the cathode corresponds with a visible change in the plasma discharge between the orifice and extracting anode, which is shown for the most emissive case of V b = 120 V in figure 5. Given that the visible emission occurs primarily from excited neutrals in the cathode plume, the visible region is correlated to areas of high electron density in the discharge. The images are therefore an effective visualisation of electron confinement by the B-field spanning the internal cathode and orifice-anode regions. For instance, plume narrowing with increasing |B| is particularly visible in theṁ = 0.15 mg s −1 images of figure 5(b), with the visible plume edge found to correspond with a magnetic-flux contour of approximately 3 µWb based on B-field simulations.

Tested extraction difference between air and xenon
The effect of |B| on the cathode extracted current I extr is investigated, for the nominal 'mirror' B-field, by means of varying the coil current at a given flow rate, input microwave power and bias combination. The magnetic-field strength within the cathode volume is represented by the maximum |B| value along the downstream antenna surface (top) obtained from simulations, which is directly proportional to the current in the electromagnet coil. This metric is chosen since it reflects |B| in the intended ECR region and is used in the following results presented. As a reference, the I coil = 2 A value designed to established a B ECR = 87.5 mT layer across the antenna corresponds with a maximum |B| = 96 mT along the exact antenna downstream surface. Tests are performed for both air and xenon to assess the differences between the 0.48O 2 + 0.52N 2 mix and the baseline propellant conventionally used in neutralizer studies. Figure 6(a) shows the significant difference in the effect of |B| between xenon and air at a low bias of 40 V, for the nominal microwave power and flow rate. There is an approximately four-fold extracted current increase for Xe from I extr = 0.22 A at no applied B-field to a peak 0.85 A, which strongly suggests ECR as the dominant ionization mechanism. This low bias value of V b = 40 V corresponds with other studies exploiting ECR-heating [13], and is below the internal surface bias typically required to trigger alternative mechanisms which could boost the population of high-energy electrons in the plasma, such as secondary electron emission (SEE). SEE is based on the release of electrons due to collisions of energetic plasma species with a plasma-interfacing surface, which is typically only prevalent at a high negative surface bias capable of supporting a large local E-field, such as in the cathodesheath of a DC discharge [30, p 537]. In the case of ioninduced SEE from a negatively-biased surface, a significant level of electron emission is not typically encountered below a threshold bias, such as a minimum 90-100 V for a stainless steel surface in [31]. As a result, a case where SEE is the dominant plasma mechanism is not expected for this configuration at a bias of 40 V. Notably, the ECR-indicative behaviour seen with xenon is not demonstrated for air, with figure 6(a) showing a general suppression of extracted current from an initial 0.06 A to 0.01 A at increased |B| values. Since the heating of electrons via ECR in the antenna-vicinity is expected to occur similarly for both air and xenon, the stark difference in extracted current can likely be attributed to the difference in ionization events resulting from collisions of energetic electrons with neutral particles of both propellants.
In the case of electron-neutral collisions for air, electron energy is lost for dissociation of O 2 and N 2 into their atomic species, which is expected to be prevalent given the significantly lower dissociation energies compared to the ionization energy values (see section 2.2). As well as this, electron energy is lost to a greater variety of excitation modes present in the air molecules, compared to xenon atoms, such as vibrational and rotational modes. For instance, a high degree of atomic oxygen neutrals is expected in the plasma since the 5.11 eV dissociation energy is accessible for a significant portion of electron energies in the tail of a ∼ 3 eV Maxwellian distribution obtained from internal Langmuir probe measurements (see V b = 40 V data in table 2). While this measurement refers to the bulk plasma, it is likely that significantly higher T e occurs in the antenna-vicinity which supports ionization in the case of both air and xenon. If assuming a T e = 15 eV electron energy sufficient for ionization of O, N and Xe, the electron-impact cross-sections are 1.28 × 10 −21 m 2 , 1.10 × 10 −21 m 2 and 1.15 × 10 −20 m 2 respectively [32][33][34]. Given that the collision-frequency is directly proportional to the cross-section, the expected rate of potentially-ionizing collisions in this case is almost an order of magnitude higher for Xe than O and N (for the same v th , n n and n e ). It should be noted that the thermal velocity, with which the collision frequency is also directly proportional, is higher for the lighter O and N neutrals. Given v th ∝ 1/ √ m [24], thermal velocities 2.9 times and 3.1 times higher are expected for O and N respectively relative to Xe (assuming the same neutral temperature). However, the beneficial thermal velocity ratios are significantly smaller than the detrimental ratios of ionization cross-sections, resulting in an overall reduced ionization level for the atmospheric species. These factors provide an explanation for the behaviour shown in figure 6(a), in which a strong correlation is visible between ECR-based electron heating and increasing extracted current, due to increasing ionization, in the case of xenon but not air.
The effect of |B| on I extr at an increased bias of 80 V is shown in figure 6(b). The extracted current values at zero applied magnetic-field are higher for both air and xenon, as predicted by an increased potential drop and therefore ion velocity through the Child-Langmuir sheath at internal cathode surfaces (see equation (1)), yielding an increased collected ion current density and so current available for extraction. However, the ECR-based behaviour is not seen for xenon as in figure 6(a) and instead I extr is broadly constant around 0.6 A with increasing |B|. This implies that ECRheating is no longer the dominant source of high-energy electrons compared with effects due to potential gradients in the cathode plasma, such as the increased SEE from internal surfaces. This is supported by the difference in electron density with xenon between V b = 40 V and 80 V as reported in table 2, which finds n e four times higher for the high-bias case.
The significant increase in I extr with magnetic-field strength for xenon at a low bias is also found for a larger orifice diameter D o = 10 mm, as shown in figure 7. In this case, there is an even more evident correlation between ECR-heating and extracted current, based on the growth of the B ECR layer. This is indicated by insets showing the simulated B-field within the cathode at various points throughout the plot, with the ECR-layer defined between B ECR and 1.5B ECR to account for likely losses in the real magnetic-field applied to the plasma. Figure 7 shows: (a) an initial increase in I extr when the ECRlayer first extends inside the cathode volume (first inset from left), (b) a broadly linear current increase as the ECR-layer grows along the antenna length (second inset), and (c) a plateau of I extr when the ECR-layer has extended across the internal diameter and is no longer growing in the antennavicinity (third and fourth insets).
As part of this testing, the cathode was operated at a xenon mass flow rateṁ = 0.07 mg s −1 and bias V b = 37 V matching the nominal conditions of the JAXA µ10 neutralizer given in [20]. It should be noted that key differences exist in the setups. First, the input microwave power is 16 W, compared to 8 W for the µ10, due to the minimum power limit of the microwave generator used in this study and losses in the coaxial line. Second, a distance between the orifice and extracting-anode of 30 mm, compared to 11 mm for the µ10. The doubled P in predicts a significantly higher extracted current for this study, however the increased orifice-anode distance partially acts against this by lowering the potential gradient (in V/m) through the cathode orifice compared with the µ10. The most significant difference is the 4.2 GHz microwave frequency and B ECR = 150.0 mT in the case of the µ10, as opposed to f = 2.45 GHz and B ECR = 87.5 mT for this study. However, Langmuir probe measurements of the internal plasma for both neutralizers show an overdense regime, for instance n e = 7.1 × 10 18 m −3 ≫ n c = 7.4 × 10 16 m −3 (where n c is the cut-off density) from the data in table 2. As a result, the differing frequency should not affect I extr in the assumption of ECR-heating as the dominant ionization mechanism. This is supported by the similarity in extracted current between the nominal I extr = 0.18 A of the µ10 and the maximum I extr = 0.26 A for a matching configuration in this study, as shown in figure 8. The larger current is explained by the increased P in . The insets on the figure show the significantly stronger emission in the orifice-anode region, and more intense internal plasma visible through the orifice, at the higher current values.

Neutral pressure analysis
The neutral density within the prototype volume depends on the inlet propellant mass flow rate. For the case without plasma, this can be estimated using molecular (collisionless) flow theory [35]. This approach is recommended since pressure measurements inside the cathode (see below) of 2.3-5.5 × 10 −2 mbar (2.3-5.5 Pa), for the mass flow rates tested with the nominal D o = 5 mm orifice, suggest a Knudsen number (Kn) in the 0.3-0.8 range, falling within the Kn > 0.01 indicator of a flow in transition to the free-molecular state (rather than in the continuum regime) [36]. The relation between mass flow rate and neutral density is therefore taken as:ṁ where A o is the orifice area and k B is the Boltzmann constant. In this case, the expected mean velocity ⟨v⟩ is based on the thermalized gas temperature T g (in K) and the transmission probability α represents the conductance of flow through the orifice. The following approximation can be used for the conductance of the nominal cathode orifices tested (D o = 5 and 10 mm) [37]: The measured pressure p n is converted to a neutral density, via a room-temperature T g = 293 K: The experimentally-derived neutral density is compared to the theoretical values in figure 9. While equation (5) assumes a background (or exit) neutral density equal to zero, the experimental vacuum chamber background pressure is recorded and used as a correction to the n n value. Close agreement is confirmed between the predicted and measured neutral air density inside the cathode, when factoring in the background chamber pressure. The n n = 5 × 10 18  The predicted neutral density values for standalone performance tests using the 5 mm and 10 mm orifice diameters are reported in table 3, based on equation (5) with a correction for measured chamber background pressure and an assumed T g = 373 K, which is representative of the AMPCAT wall temperature recorded via a thermo-couple during testing. It should be noted that the effective temperature of neutrals in the cathode plasma during operation is likely to be higher than that of the wall, due to charge exchange collisions between ions and neutral particles. However, the complex gas flow simulations typically required for more precise estimation of the neutrals' temperature are beyond the scope of this study. The effective neutral density of the cathode plasma is therefore most probably lower than the values given in table 3. Nevertheless, the free-molecular approach of equation (5) and use of a thermal velocity matching the walls is seen as a reasonable approximation, which shows close agreement with experimental pressure measurements, at least for the case without plasma.

Tested extraction in magnetic-field with neutral density
Tests are conducted to assess if varying neutral density influences the effect of magnetic-field strength on extracted current, which is introduced in the previous section. Figure 10 shows the impact of mass flow rate and orifice diameter, which both affect the neutral density, for xenon at V b = 40 V. The n n values predicted analytically for the test cases are shown in table 3 and also noted on the figure. A comparison of two reduced-density configurations with the nominal case (D o = 5 mm,ṁ = 0.1 mg s −1 ) shows that an increased I extr is obtained at high |B| if the inlet mass flow rate is maintained. Despite the fact that the reduced-flowṁ = 0.05 mg s −1 configuration is predicted to result in a higher density (2.5 × 10 20 m −3 ) compared with the increased-orifice D o = 10 mm case (1.1 × 10 20 m −3 ), there is a clear decay of the ECR-induced I extr peak at antenna |B| > 140 mT. This is likely due to electron motion being excessively impeded by the magnetic-field, which is seen to dominate over any additional growth of the ECR-layer earlier for theṁ = 0.05 mg s −1 case. Maintaining a flow rate of 0.1 mg s −1 , however, allows sufficient neutral presence in the high-|B| region around the antenna to reach ionization levels equivalent to the nominal case, even if the overall neutral density is reduced due to the larger orifice.
The impact of neutral density with air is shown in figure 11, for which there is a significant difference in extracted current between bias values of 40 V and 120 V. Data for 120 V is shown since this is generally effective at promoting the transition to the higher-I extr mode in the case of air. As highlighted in table 3 There is no significant n n impact observed at V b = 40 V. However, for V b = 120 V, an increasing |B| is found to boost the extracted current for the reduced-density case over the |B| = 0 value, for instance almost doubling from 0.23 A to a peak 0.43 A in figure 11   For all three regions, the test results presented here indicate that magnetic confinement, while generally not effective for increasing the extracted current with air, is beneficial in the case of reduced neutral density within the cathode volume. This suggests magnetic confinement is a viable approach for targeting the further reduced n n values associated with a feasible air-breathing application in which the cathode is directly coupled to a passive intake, given that theṁ = 0.1 mg s −1 tested is already in the expected ballpark for the AETHER platform.

Varying magnetic-field topology design
As well as the nominal (or 'mirror') magnetic-field geometry, two additional cathode configurations are tested to investigate the impact of B-field topology on extracted current performance. These topologies are termed 'angled' and 'tangential' based on their general direction at the intersection with the outer cylindrical surface of the cathode volume, and they are shown in comparison to the nominal B-field in figure 12. These topologies are achieved by interchanging the iron yokes that sandwich the electromagnet coil with aluminium alloy equivalents, partially and fully for the 'angled' and 'tangential' cases respectively, as also indicated in figure 12. Broadly, the progression between the topologies, from 'mirror' to 'tangential,' reduces the B component transverse to the outer cylindrical surface in the antenna vicinity and creates a more axial field in the primary ionization region downstream of the antenna. Similarly to section 3.1, the magnetic-field of the two additional topologies is verified through comparison of magnetometer |B| measurements with simulated values. This is done following the same measurement paths and axes definitions as in figure 4, for a coil current of 2 A. The comparison yields close agreement between |B| measured in the assembled prototypes and the values from simulations, with maximum discrepancies below 10% for both paths.

Tested extraction with field strength and topology
The extracted current with air at a 40 V bias is recorded for the three B-field topologies, over mass flow rates of 0.1 mg s −1 and 0.15 mg s −1 as well as an input microwave power range of 24-70 W, which is shown in figure 13. All the results are obtained for the nominal orifice diameter of 5 mm. The topologies are compared using the maximum simulated |B| along the downstream antenna surface, which reveals a significant degree of consistency between the I extr trends of the three configurations. For instance, all topologies show a general decrease in extracted current with minimal applied B-field at P in ⩾ 48 W and the near-total suppression of I extr to below 0.02 A at antenna |B| > 80 mT. However, it is noteworthy that a peak in I extr is present in all four test cases, occurring consistently around an antenna |B| ∼ 50 mT. These three regions are highlighted qualitatively by the dashed lines in figure 13. While the 'interim peak' is most prominent for the 'mirror' B, it occurs for multiple topologies in each test case and is particularly evident for all three B-field shapes at P in = 48 W (both flow rates). Given the peak occurs at |B| significantly lower than B ECR = 87.5 mT, the behaviour cannot be attributed to an ECR-based heating mechanism.
The ion properties in the cathode plasma can be used to suggest a possible explanation for the peaks, based on the Langmuir probe measurements detailed in section 2.5. It is important to check that the probe measurement position correlates with the bulk plasma region, rather than being located within the extents of the Child-Langmuir sheath (see equation (1)). This is because ions within the sheath are predicted to fall through a significant potential drop imposed by the relatively-negative bias of the cathode wall. To verify this, the sheath thickness d can be found by numerically integrating: where d is normalised by the Debye length λ D as: and the plasma potential through the sheath (ϕ) and at the sheath edge (ϕ 0 ) are normalised by the electron temperature: For the internal Langmuir probe measurement with air at V b = 40 V, the plasma potential is found as 21.9 V above that of the cathode wall, i.e. ϕ 0 − ϕ = 21.9 V. Using T e = 2.66 eV and n e = 1.38 × 10 18 m −3 (from table 2), an evaluation of equation (8) results in ξ = 2.8, and given λ D = 0.0103 mm, the Child-Langmuir sheath thickness is found as d = 0.029 mm. Therefore, the Langmuir probe measurement at 8 mm from the internal wall can be reasonably assumed to represent the bulk plasma properties. Now, estimating the ion temperature as T i ≈ T e /10, which is common in the electric propulsion literature [38], yields T i ≈ 0.3 eV (table 2). This can be used to evaluate the ion Larmor radius at a magnetic-field strength of 50 mT, using the mean ion thermal velocity as the velocity perpendicular to the magnetic-field: v ⊥ ≈ v th = √ 8eT i /π m [24]. Factoring an oxygen ion mass M = 16 amu (14 amu gives similar results for N), results in r L = 7.1 mm at |B| = 50 mT. This corresponds well with the cathode internal radius of 16.5 mm, suggesting that the peak in extracted current occurs when ions become effectively confined within the cathode volume (with an appropriate margin to the wall). This reduces ion mobility towards the internal surfaces to a beneficial degree, thus increasing global plasma confinement and so boosting ionization. At low |B|, the Larmor radius is excessively large to affect ion transport towards the wall. At increased |B|, the current likely falls off due to excessive impedance of electron extraction through the orifice. This behaviour is similar to that observed for theṁ = 0.05 mg s −1 curve in figure 10 where, despite efficient ECR-based electron heating and significantly higher ionization with xenon, the extracted current noticeably reduces beyond a certain value of magnetic-field strength. However, it should be noted that a high degree of collisionality within the plasma would prevent a significant influence of the magnetic-field on the ion motion [38]. Therefore, further investigation of the exact mean free path of ions within the internal plasma is needed for certainty of this proposed explanation of optimum ion confinement within the cathode chamber dimensions. Figure 14 shows the effect of |B| at different topologies for an increased V b = 120 V. This clearly indicates that the applied magnetic-field reduces the extracted current below the |B| = 0 value for the higher-I extr mode. A likely explanation for this behaviour originates from the fact that, at high bias voltages, the DC sheath is the dominant contributor to ionization within the cathode plasma (see section 3.2). A key role is played by SEE, whereby electrons are typically emitted from plasma-interfacing surfaces with low energies ∼1 eV [39] and are accelerated through the sheath into the bulk plasma. The magnetic-field is therefore an obstacle to the motion of these electrons, as per equation (4). This effect increases from minimal in the case of B perpendicular to the surface, for which electrons escape along the field lines, to total in the case of B tangential to the surface, whereby the magnetic component of the Lorentz force steers electron trajectories away from the surface-normal direction [40]. This imposes an increased electron density close to the surface, forming a virtual cathode which lowers the effective electron-accelerating E-field and so reduces SEE flux into the bulk cathode plasma [41]. The virtual cathode is increasingly effective at suppressing SEE yield with increasing |B| for a given non-zero (relatively) negative bias of the surface [40], which agrees with the trend of decreasing I extr with magnetic-field strength clearly visible in figure 14. This behaviour is consistent across the P in andṁ tested, as highlighted by the dashed lines in the figure. Another contributory factor to the decrease in extracted current with |B| is likely the excessively impeded electron motion through the orifice due to the magnetic-field. This motivates the following section, which investigates the reduction of the localised |B| value in the orifice region. 6. Orifice magnetic-field reduction 6

.1. Orifice field design
The impact of reducing the magnetic-field strength at the orifice is analysed with an updated cathode prototype, featuring a coil of 15 turns (enamelled 0.8 mm diameter Cu wire) around a D o = 10 mm orifice. The reduced orifice |B| is applied to the nominal 'mirror' magnetic-field topology. It should be noted that this increased orifice diameter results in a reduced neutral density of 2.4 × 10 20 m −3 within the cathode, 4.4 times lower than for the nominal 5 mm orifice. Data of the larger D o = 10 mm orifice ('mirror' field without the secondary coil) is provided in section 4, for instance see figure 11. The modified prototype configuration of this section is shown in figure 15. The B-field imposed by the orifice coil works against that of the primary 650-turn electromagnet if a negative (opposite) orifice coil current I coil,o is applied, thereby reducing |B| in the orifice. Conversely, applying a positive I coil,o slightly increases the orifice B-field. The added coil is shielded from plasma exposure with a grade 304 stainless steel sleeve to maintain the same plasma-interfacing material as the internal cathode surfaces. The small size of the orifice coil ensures that B in the antenna vicinity is essentially unaffected, given the significantly larger size of the primary coil. During tests, the orifice coil current is varied between 0 A and −7.5 A, with an additional data point at 5 A to check the effect of increasing |B|. The I coil,o sweep is performed at primary coil currents of 0 A, 1 A and 2 A, corresponding to maximum |B| values of 0 mT, 48 mT and 96 mT respectively along the antenna. The effect of the orifice coil in reducing the local B-field is shown in figure 15 for I coil = 2 A. In this case, |B| at the centre of the orifice exit plane is reduced from 11.7 mT to 4.2 mT by applying −7.5 A in the orifice coil.

Tested extraction with modified orifice field strength
The effect of reducing the orifice magnetic-field on the extracted current at V b = 120 V is detailed in figure 16 for flow rates of 0.1 mg s −1 and 0.15 mg s −1 . First, the reduction in orifice |B| with increasingly negative I coil,o is shown in figure 16(a) as labels on the curve corresponding with an antenna |B| = 96 mT, i.e. the case simulated in figure 15. For a 0 mT antenna B where there is no primary coil current, I extr falls sharply with increasing |B|, since the orifice coil is simply imposing a Bfield at the orifice which impedes electron extraction. For zero applied I coil,o , the antenna |B| = 48 mT case in figure 16(a) demonstrates the largest extracted current value of 0.35 A, since this is an optimum level of magnetic-confinement at this reduced-neutral density scenario (given the 10 mm diameter orifice, as shown previously in figure 11). Most notably, for both |B| = 48 mT and |B| = 96 mT cases atṁ = 0.1 mg s −1 , there is a clear I extr increase resulting from a reduction of the orifice magnetic-field, which is highlighted by the linear fits included in figure 16(a). The B relaxation is particularly effective for the |B| = 48 mT case, whereby I extr is increased by 25% from 0.36 A to 0.45 A. These results are in agreement with a similar study in [20] on the µ10 neutralizer operating with xenon (see figure 6 of [20]), where a reduction from the nominal orifice |B| = 22.5 mT to 15 mT yields an extracted current increase from 0.18 A to 0.25 A. The results of [42] also demonstrate a similar trend, whereby an increase in extracted current from a miniature microwave neutralizer is achieved by weakening |B| in the orifice region, rather than through modifications in the magnetic-field topology aiming to guide electrons through the orifice. The beneficial effect on extracted current is also visible at the higher flow rate of figure 16(b), however it is less pronounced than atṁ = 0.1 mg s −1 . This is likely because, as shown in section 4.2, magnetic-confinement with air is more beneficial at the reduced neutral density of the lower mass flow rate. In general, the analysis supports the suggestion that an optimum magnetic confinement with air (at this reduced n n ) is accompanied by a detrimental component of reduced electron mobility through the extraction orifice. Reducing the local orifice |B| therefore allows an increase in the extracted current value.

Conclusion
In conclusion, an AMPCAT is developed in this study, featuring an electromagnet coil that permits a variable magneticfield strength within the cathode volume. Standalone tests compare an 0.48O 2 + 0.52N 2 air mixture to xenon for a prototype design targeting ECR in the vicinity of a 2.45 GHz antenna immersed into the plasma. For the ECR-targeted configuration: • The extracted current profile with xenon suggests ECRbased heating, with an approximately four-fold increase from 0.22 A to 0.85 A. The current increase correlates well with the predicted growth of the ECR-strength magneticfield layer across the internal volume. • Conversely for air, an applied B-field does not result in such a clear current increase, which is likely due to the significant differences in ionization from electron-neutral impacts between the molecular and noble gas propellants. Magnetic confinement is however beneficial to extracted current with air at reduced neutral density values, for instance a |B| = 36 mT field at the antenna supporting I extr > 0.4 A at n n = 2.4 × 10 20 m −3 .
An analysis is conducted to explore the effect of varying magnetic-field strength and topology within the cathode. This demonstrates: • At low bias voltage, an optimum extracted current with air around |B| ∼ 50 mT at the antenna. A possible explanation relates to an optimally-constrained ion Larmor radius, however high collisionality in the internal cathode plasma would prevent significant ion magnetization. Further investigation is therefore needed to support this suggestion. • At an increased bias voltage, where the cathode operates in the higher-current mode, an applied magnetic-field consistently reduces the extracted current. This is likely because |B| > 0 acts to suppress the motion of SEE electrons into the bulk plasma.
Finally, the effect of a reduced magnetic-field strength at the orifice is analysed using a secondary electromagnet coil. This data shows: • An improvement in extracted current values of up to 25% resulting from a decrease in orifice magnetic-field strength from 11.7 to 4.2 mT. Such an increase in current is recorded for both |B| = 48 mT and 96 mT magnetic-field strengths at the antenna. This suggests that electron extraction is impeded by an excessively high B at the orifice and motivates magnetic circuit design towards relaxing the field strength in this region.
It should be noted that the air discharge may contain a population of negative ions that contribute to the negative current extracted, unlike a xenon plasma which contains only positive ions. While the experimental results in this study do not suggest any significant presence of negative ions, an investigation into the ratio of electron current to negative ion current with air will be pursued as a future work. While this paper focuses on magnetic-field effects, future AMPCAT studies will investigate continuous operation of the cathode with air at elevated extracted current levels, targeting the mitigation of possible erosion or performance-loss mechanisms that may be associated with operation at higher bias voltages.