BACKGROUND OF THE INVENTION

THIS invention relates to a vacuum arc thruster and to a method of operating the same.

A vacuum arc thruster (VAT) is a small space propulsion system that produces plasma jets by means of vacuum arc pulses between two electrodes separated by an insulator. The schematic shown in Figure 1 depicts the basic elements and features of a typical VAT. The action of the vacuum arc forms hot microscopic cathode spots on the cathode surface, which emits vapourised cathode material. This material becomes ionised within the arc region and expands outward as a dense high-speed plasma, achieving velocities as high as 20 km/s. The vacuum arc pulses within the VAT are generated by a power circuit comprised of a network of capacitors and inductors called a pulse-forming network (PFN).

The term "vacuum arc" is a well-known term in the industry and is used to describe a current-driven arc discharge that exists between a pair of anode and cathode electrodes within a vacuum environment. A characteristic feature of the vacuum arc is that the cathode electrode is a source of both electron emission and plasma production. The mechanism for the creation and emission of plasma is achieved through the formation of small arc spots on the cathode surface.

These cathode spots are microscopic in size and are initially formed by intense thermo-field emission at several micro-protrusions on the surface where the electric field is highly concentrated. The high power density present in these areas is sufficient to heat, vapourise and eject cathode material, which collides with the electron cloud to form highly ionised quasi-neutral plasma consisting of single- and multiply-charged ions travelling on the order of 10-20 km/s. The surprisingly large amount of ion momentum (thrusting force) that is generated by the vacuum arc plasma is presently considered to be primarily due to the ion pressure gradient (gas- dynamic expansion) and electron-ion coupling/friction (fast-moving electrons imparting momentum to slower-moving ions).

The VAT falls under the category of a microthruster, which is a propulsion system that gives small satellites (typically 1-100 kg in mass) the ability to perform orbital manoeuvres, drag compensation and station-keeping. These capabilities are highly attractive because they allow a satellite to orient itself at will, perform orbit positioning and greatly extend mission lifetime. The VAT is attractive as a potential microthruster due to its low overall system mass (e.g. <1 kg), flexible and low average power usage (1-100 W), use of relatively low cost materials or manufacturing techniques, the generation of quasi-neutral plasma (no neutraliser unit is required) and the ability to use any electrically-conductive solid material as propellant. The use of relatively safe and inert solid propellant also eliminates the requirement for, and failure modes associated with, propellant tanks, valves and piping. Additionally, intricate and potentially hazardous propellant handling procedures are avoided and VATs pose little to no risk of catastrophic failure to a satellite. However, in practice, the VAT generally only provides modest specific impulse values (300-600 s) and thrust-to-power ratios (5-10pN/W) compared to other plasma thrusters. Additionally, the VAT is still a relatively new propulsion technology compared to many other commercial systems such as Pulsed Plasma Thrusters, which has almost 50 years of development and flight heritage.

The Inventor wishes to address this issue by providing a VAT with improved performance characteristics.

SUMMARY OF THE INVENTION

In accordance with an aspect of the invention there is provided a vacuum arc thruster which includes:

an anode arrangement which includes at least two anode elements;

a cathode;

an insulator which is located between the anode arrangement and the cathode; and

a control arrangement which is operatively connected to the cathode and each of the anode elements and which is configured to switch each anode element between an active state in which the control arrangement utilises the anode element in order to generate a vacuum arc pulse(s) between the said anode element and the cathode, and an inactive state in which the particular anode element is not used for vacuum arc generation.

The anode elements may be distinct from each other. The anode elements may be electrically insulated from each other.

The anode elements are anode electrodes.

The anode elements may be spaced from each other. More specifically, the anode elements may be spaced around the cathode. The anode elements may be proximate/in close proximity to the cathode. The cathode may be elongate. The cathode may have a cylindrical/rod shaped body. The anode elements may extend circumferentially around the cathode, when viewed along a longitudinal axis of the cathode. The anode elements may be radially spaced around the cathode, when viewed along the longitudinal axis of the cathode.

Each anode element may have an arc shaped body.

The control arrangement may be configured to switch the anode elements between their active and inactive states in a pre-determined manner. More specifically, the control arrangement may be configured to switch the anode elements between their active and inactive states in accordance with a predetermined switching program.

The control arrangement may be configured such that during a period in which one anode element is in its active state, at least one of the other anode elements is in its inactive state for at least a portion of the period. In other words, not all the anode elements are in their active states at a particular point in time during operation.

The control arrangement may be configured to activate and deactivate the anode elements in a cyclic manner such that each anode element is activated and deactivated during an operational cycle. An operational cycle may refer to a periodic cycle during which all of the anode elements have been used to generate a vacuum arc pulse(s).

The anode arrangement may include three or more anode elements. The anode arrangement may, for example, include six anode elements. The control arrangement may be configured to activate and deactivate the anode elements such that at any one time during operation, at least one (i.e. one or more) of the anode elements is in their active states. The control arrangement may be configured to activate and deactivate the anode elements in pairs such that at any one time during operation, two anode elements are in their active states. In another example, the control arrangement may be configured to activate and deactivate the anode elements in two or more anode element groups such that at any one time at least one group of anode elements are in their active states. More specifically, the control arrangement may be configured to activate and deactivate the anode elements in two anode element groups such that at any one time at least one group of anode elements are in their active states.

The control arrangement may include a pulse forming circuit/network/arrangement which is configured to generate electrical pulses. The control arrangement may include a switching circuit/network/arrangement which is configured to switch each anode element between its active and inactive states by controlling the transfer/transmittal of the electrical pulses generated by the pulse forming circuit to each of the anode elements.

The control arrangement may be configured such that the time period between the activation of one anode element from its inactive state to its active state and

the successive/subsequent activation of another anode element,

may be equal or less than the time period between two successive electrical pulses generated by the pulse forming circuit/network.

The pulse forming circuit/network/arrangement may be configured to generate electrical pulses with a pulse length of between about 1 millisecond and about 10 milliseconds. The pulse length may be between about 1 millisecond and about 4 milliseconds.

The pulse forming circuit/network/arrangement may be configured to generate electrical pulses having a frequency in the range of about 1 Hz and about 20 Hz. The cathode may be made of a material which includes graphite. More specifically, the cathode may be made of a graphite-based material. The cathode may be made of metal-impregnated graphite. More specifically, the cathode may be made of copper- impregnated graphite. The cathode may be made of pure graphitic carbon or glassy carbon. The cathode may be made of a metal-graphite compound.

In accordance with another aspect of the invention there is provided a method of operating a vacuum arc thruster which includes an at least two anode elements, a cathode and an insulator which is located between the anode elements and the cathode, wherein the method includes:

selectively switching each anode element between an active state in which it is used, together with the cathode, in order to generate a vacuum arc pulse(s), and an inactive state in which the particular anode element is not used for vacuum arc generation. The vacuum arc thruster may be a vacuum arc thruster as described above.

The method may include switching the anode elements between their active and inactive states in a pre-determined manner. The method may include activing and deactivating the anode elements in a cyclic manner such that each anode element is activated and deactivated during an operational cycle.

The method may include switching the anode elements between their active and inactive states in accordance with a predetermined switching program. The method may include switching the anode elements between their active and inactive states in such a manner that during a period in which one anode element is in its active state, at least one of the other anode elements is in its inactive state for at least a portion of the period. The method may include controlling the transfer/transmittal of electrical pulses generated by a pulse forming circuit/network of the vacuum arc thruster to each of the anode elements by either allowing or disallowing the electrical pulses to be transferred/transmitted to a particular anode element, wherein when the transfer/transmittal to a particular anode element is allowed, the anode is in its active state and when the transfer/transmittal to the particular anode element is disallowed the anode is in its inactive state.

The method may include switching the anode elements between their active and inactive states in such a manner that the time period from when one anode element is switched from its inactive state to its active state, to

when another anode element is subsequently switched from its inactive state to its active state,

is equal to or less than the time period between two successive electrical pulses generated by the pulse forming circuit/network.

The method may include generating pulses with a pulse length of between about 1 millisecond and about 10 milliseconds and transferring it to one or more of the anode elements. More specifically, the pulses may have a pulse length of between about 1 millisecond and about 4 milliseconds. The pulses may be generated by using the pulse forming circuit/network of the vacuum arc thruster. The method may include generating the pulses at a frequency in the range of about 1 Hz and about 20 Hz.

In accordance with a further aspect of the invention there is provided a vacuum arc thruster which includes: an anode;

a cathode;

an insulator which is located between the anode and the cathode; and a pulse forming circuit/network/arrangement which is operatively connected to the cathode and the anode, and which is configured to generate electrical pulses with a pulse length of between about 1 millisecond and about 10 milliseconds which, in use, generate/establish a vacuum arc(s) between the anode and cathode.

More specifically, the pulse length may be between about 1 millisecond and about 4 milliseconds.

The pulse forming circuit/network/arrangement may be configured to generate electrical pulses having a frequency in the range of about 1 Hz and about 20 Hz. In accordance with yet another aspect of the invention there is provided a method of operating a vacuum arc thruster which includes an anode, a cathode and an insulator which is located between the anode and the cathode, wherein the method includes: generating electrical pulses with a pulse length of between about 1 millisecond and about 10 milliseconds and transferring them to the anode such that a vacuum arc is generated/established between the anode and cathode.

In accordance with yet a further aspect of the invention there is provided a vacuum arc thruster which includes: an anode;

a cathode which is made of a material which includes graphite;

an insulator which is located between the anode and the cathode; and a pulse forming circuit/network/arrangement which is operatively connected to the cathode and the anode, and which is configured to generate electrical pulses which, in use, generate/establish a vacuum arc(s) between the anode and cathode.

More specifically, the cathode may be made of a graphite-based material. The cathode may be made of metal-impregnated graphite. More specifically, the cathode may be made of copper-impregnated graphite. The cathode may be made of pure graphitic carbon or glassy carbon.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described, by way of example, with reference to the accompanying diagrammatic drawings. In the drawings:

Figure 1 shows a schematic illustration of some basic elements of a typical vacuum arc thruster (VAT);

Figures 2a&beach show a schematic illustration of a cathode and anode arrangement of a VAT in accordance with the invention, which indicates cathode spot(s) and their expected forced motion over the surface at various stages in an anode switching sequence according to (a) triangular switching with three active anodes and (b) cross-shaped motion with three active anode pairs;

Figure 2c shows a photo of the cathode and anode arrangement shown in

Figures 2a&b; Figure 3 shows a photo of a test ring vacuum chamber and high-vacuum pump system; Figure 4 shows a schematic circuit layout of a pulse circuit with typical component specifications; Figure 5 shows a circuit layout of a control arrangement of a VAT in accordance with the invention; Figure 6 shows a process flow chart of an automated LABVIEW data capture control system; Figure 7 shows a graphical illustration of typical waveform traces of captured (a) arc current and (b) arc voltage, when a Bi cathode is used (peaks beyond 1 ms indicate arc termination);

Figure 8 shows a graphical illustration of typical waveform traces of captured (a) arc current and (b) arc voltage, when an Fe cathode is used (peaks beyond 1 ms indicate arc termination);

Figure 9 shows a graphical illustration of normal probability plots for processed results of average arc current, average arc voltage and arc pulse length, where a Bi cathode was used (50 A peak arc current, 2138 ps median pulse length, 75 sampled traces);

Figure 10 shows a graphical illustration of normal probability plots for processed results of average arc current, average arc voltage and arc pulse length, where an Al cathode was used (50 A peak arc current, 233ps median pulse length, 175 sampled traces);

Figure 11 shows histograms of untransformed and Box-Cox transformed pulse length data from Figure 10; Figure 12 shows a graphical illustration of a normal probability plot for processed results of ion-to-arc charge ratio, where an Fe cathode was used (50 A peak arc current, 529 ps median pulse length, 20 samples);

Figure 13 shows (a) a schematic, three-dimensional view of an overall thrust stand, and (b) a schematic, three-dimensional view of an electrostatic calibration system (ESC) with a 5 degree of freedom linear positioning system, of a trust stand; and (c) a photo of an experimental setup inside a vacuum chamber;

Figure 14 shows a schematic layout of a Faraday Cup probe and circuit; Figure 15 shows a photograph and engineering drawings of a Faraday Cup (FC) probe;

Figure 16 shows a thrust vector diagram with its yaw and pitch components; shows a photograph of an ICDD (Ion Current Density Distribution) measuring/capture system with a TARS rig and Faraday cup probe; shows a schematic side view of an ICDD measuring setup with a TARS (Two Axis Rotation System) rig and Faraday cup probe; shows a process flow chart of a TARS stepper motor control system; shows a functional diagram of the ICDD measuring/capture system; shows a surface fit of ICDD test data with various distribution fits shown for comparison (test data shown here is for a baseline VAT operating with a Fe cathode (50 A pk, 2.7 ms, 3 Hz, 7.5 W) and a FC probe distance of z = 230 mm. Twenty samples per pitch and yaw angle were taken. Best fit is a Gaussian distribution of spread factor w = 1.197 +0.032 {R ² = 0.982, RMSE (Root Mean Square Error) = 0.012)); shows problem geometry and variable definitions used for calculating C _T (the thrust correction factor); shows a sectioned view of an ion collector enclosure; shows a graphical representation of the measurement of ion current signals emitted from a baseline VAT, taken at various ion collector bias voltages; shows photos comparing erosion uniformity between short and long pulses on (a) Bi and (b) Al cathodes; shows a graphical representation of erosion rate results; shows graphical representations of ICDD results for baseline VATs operating at various pulse lengths; shows a graphical representation of the growth of peak ion charge ratios along a thruster centreline with pulse length; shows a graphical representation of thrust correction factor results for baseline VATs operating at various pulse lengths; shows a graphical representation of average thrust current results from baseline VATs operating at 50 A peak arc current at various pulse lengths; shows a map of arc operating conditions (peak arc current and arc pulse length) for several published VAT designs, and which indicates approximate areas identifying extreme (Regions A-D) and desirable (Region E) operating limits; shows a graphical representation of average thrust per current results for baseline VATs with an Fe cathode operating at 25 A, 50 A and 100 A peak arc current at various pulse lengths. shows a graphical representation of average thrust per current results for baseline VATs with an Ai cathode operating at 50 A and 100 A peak arc current at various pulse lengths; shows a graphical representation of average thrust per current results for baseline VAT with a Cu cathode operating at 50 A peak arc current at various pulse lengths; shows a graphical representation of average thrust per current results for baseline VAT with a Bi cathode operating at 50 A and 100 A peak arc current at various pulse lengths; shows photographs of cathode erosion for pure carbon graphite rods; shows a graphical representation of thrust measurements for pure carbon graphite materials tested in terms of thrust per arc current T/l and thrust-to-power ratio T/P; shows photographs of cathode erosion for copper-impregnated carbon graphite rods; shows a graphical representation of (a) measured thrust against arc current for baseline VATs and (b) the change in thrust production per input arc current over a thruster lifetime; shows a graphical representation of measured thrust per arc current and thrust-to-power ratios for copper-impregnated carbon graphite cathodes; shows a graphical representation of thrust per arc current behaviour for pure graphite and copper-impregnated carbon graphite compounds; shows a graphical representation of measured erosion rate results for various cathode materials; shows a graphical representation of the relationship between material properties and (long pulsed) erosion rates (average particle size and electrical resistivity of each material is indicated); shows a graphical representation of measured ICDD of cathode material C-3 in a baseline VAT; shows a graphical representation of an anode switching timeline; shows photos of erosion patterns on (a) Al, (b) Fe and (Bi cathodes subjected to discrete anode switching; shows photos of erosion patterns on (a) AF-5 and (b) C-3 graphite cathodes subjected to discrete anode switching; shows a graphical representation of erosion rate results; shows a graphical representation of erosion rate results for different switching times as a function of arc pulse length; and shows a graphical representation of direct thrust measurements for an Fe cathode operating in a long-pulsed mode.

DESCRIPTION OF PREFERRED EMBODIMENTS

The invention relates generally to a vacuum arc thruster (VAT) which includes a central cathode electrode and an anode arrangement which includes a plurality of anode (electrode) elements which are circumferentially spaced around the cathode electrode. The anode elements are distinct from one another (or paired) and are operated on an individual basis via a control arrangement. The control arrangement generally includes a pulse forming circuit/network/arrangement (PFN) for generating pulses and a switching circuit/network/arrangement which is configured to allow the pulses generated by the PFN to be transferred/transmitted to the individual anode elements in order to generate a vacuum arc between the particular anode element and the cathode. Reference is now specifically made to Figures 2a-c. These drawings generally illustrate an anode arrangement 12 and a cathode electrode 14 of the VAT 10 in accordance with the invention. The cathode electrode 14 typically has an elongate, circular-cylindrical/rod-shaped body 16. The body 16 is spaced from the anode arrangement 12 via an insulator 18 which is located there between and extends circumferentially around the cathode electrode 14. In this example, the anode arrangement 12 includes six, generally arc-shaped anode (electrode) elements 20.1- 20.6 (hereinafter collectively referred to as reference numeral 20) which are circumferentially spaced around the cathode electrode 14 and mounted/positioned against a radially outer surface of the insulator 18. The anode arrangement 12 can therefore generally be referred to as a six-segment split anode design. A thin conducting film (e.g. graphite film) is applied to the insulator 18. In one example, a thick layer of conducting carbon paint can be used instead of the usual pencil graphite film (see Figure 2c). This helps to ensure good mechanical strength between the anode elements 20 and the thin conducting graphite film. The application of carbon paint also allows a lower contact resistance between the anode elements 20 and conducting film, thereby reducing the rate of film erosion during a vacuum arc thrusting operation. Table 1 below lists the electrical contact resistances typically manufactured at the thruster's various inter-electrode junctions.

Table 1 : Electrical contact resistances

The anode elements 20 are powered and operated by a control arrangement 22 (see Figure 45). The control arrangement 22 includes a pulse forming network/arrangement (PFN) (generally indicated by reference numeral 24) which is configured to generate electrical pulses and a switching circuit/network (generally indicated by reference numeral 26) which is configured to control the transfer/transmittai of pulses generated by the PFN 24 to the individual anode elements 20. In one example, the PFN 24 is configured to generate pulses of between about 1 millisecond and about 10 milliseconds long at a frequency in the range of about 1 Hz and about 20 Hz.

The switching circuit/network 26, in turn, is configured to switch each anode element 20 between an active state in which pulses generated by the PFN 24 are transmitted/transferred to the anode element 20, and an inactive state in which the generated pulses are not transmitted/transferred to the anode element 20. The switching circuit/network 26 is typically configured to switch the anode elements 20 between their active and inactive states in a cyclic manner such that different anode elements 20 are used for vacuum arc generation at different operating times. For example, if three anode elements 20.1-20.3 are used as shown in Figure 2a, then the anode elements 20.1-20.3 are operated in a triangular (or circular) manner in that firstly the one anode element 20.1 is activated (while the other anode elements (20.2, 20.3) remain in their inactive state) for a certain period of time, whereafter one of the other anode elements 20.2 is activated and the anode element 20.1 is deactivated (i.e. switched to its inactive state). Finally, after the anode 20.2 has been in its active state for a certain period of time, then the anode element 20.3 is activated and the anode 20.2. is deactivated. After all three anode elements 20.1-20.3 have been activated then the process is repeated. In other words, the switching circuit/network 26 effectively switches between the different anode elements 20.1-20.3 during operation.

In the example shown in Figure 2b, each anode element 20 is paired with another anode element which is located on a diametrically opposite side of the cathode 14 (pairs: 20.1 , 20.5; 20.2, 20.4; and 20.3, 20.6). Each pair (20.1, 20.5; 20.2, 20.4; and 20.3, 20.6) is then operated in a similar cyclic manner as described above. In other words, a first pair (20.1 , 20.5) is activated, followed by a second pair (20.2, 20.4) and finally the last pair (20.3, 20.6).

In a preferred embodiment, the frequency at which the switching circuit/network 26 switches from the one anode element 20 to the other should be equal to or greater than the frequency of the pulses generated by the PFN 24. In another preferred embodiment, the cathode is made of a material which includes graphite. More specifically, the cathode may be made of a graphite-based material. Preferably, the cathode may be made of the following materials:

pure graphitic carbon (specifically POCO grades EDM-1 , EDM-3, EDM 200 and AF-5;

glassy carbon; and/or

metal-impregnated graphite, such as copper-impregnated graphite (e.g. POCO EDM-C, EDM-C, EDM-C200, etc.).

The invention will now be described further in relation to a number of experiments which were conducted. In order to conduct the experiments, a specific experimental apparatus and test setup was implemented. The specific experimental apparatus and test setup are herein below described, followed by the specific experiments.

Experimental apparatus and test setup a. Vacuum chamber and high-vacuum pump system

All experimentation was performed in a stainless steel ring vacuum chamber with the following internal dimensions: 760 mm diameter x 200 mm height. The chamber is sealed with a semi-hemispherical lid. A mechanical hoist allowed for safe manipulation and access through the lid. Anti-vibration pads and feet on the vacuum chamber and frame provided mechanical isolation of/for the entire structure. VACOM multi-pin and high-voltage (HV) electrical feedthroughs were fitted onto chamber ports to allow power and data signal transfer. A pump system was comprised of a water-cooled oil diffusion pump (Leybold-Heraeus) and a roughing pump (Alcatel 2012A). Pressure readings were taken by a low-vacuum Edwards PK-10 Pirani gauge (atm-10 ^"3 mbar abs.) and a high-vacuum Leybold- Haraeus PM41 Penning Gauge (10 ^"2 - 10 ^"9 Torr). All testing in this work was performed at a baseline pressure of between 1-5 x 10 ^*5 . Reference is in this regard made to Figure 3 which shows a photo of a test ring vacuum chamber and high-vacuum pump system.

Pulsed power circuit

Circuit development and performance

A schematic of the pulsed power circuit is shown in Figure 4. A stack of standard laboratory power sources supplied an adjustable DC voltage V1 of 20-180 V to the circuit. The VATs used in this setup were typically fired at a maximum of 10-50 Hz for short pulses and 1-10 Hz for long pulses in order to not exceed an average arc power of 30 W. Table 2 below summarises the performance capabilities of the VAT pulse circuit.

Parameter Min Max

Supply voltage (V) 20 180

Arc voltage (V) 10 120

Peak arc current (A) 5 100

Avg. arc current (A) 10 50

Pulse length Qi/s) 50 5000

Pulse frequency (Hz) 1 50

Avg. arc power (W) 0.01 30

Table 2: Range of VAT pulse circuit performance parameters

Arc pulse waveforms i. Data capture

Circuit diagnostics included a 100:1 capacitive voltage divider for monitoring voltage across an IGBT (Insulated-Gate Bipolar Transistor) as well as a LEM hall current transducer (> ±160 A, DC-200 kHz bandwidth) for monitoring current through the inductor. The installation locations of these sensors are shown in Figure 4. Converted sensor voltage signals were subsequently sent to two high-speed digital oscilloscopes (ISO- TECH IDS 8064, 60 MHz IGs/s) for real-time monitoring and test data capture of repetitively-fired arc pulses.

Due to the noisy nature of the vacuum arc, two filtering stages were applied to the sets of arc current, arc voltage and ion current data: 1. An analogue first-order low pass RC filter with a cut-off frequency of roughly 0.5 MHz was installed at the arc current transducer's signal output.

2. A digital second-order Butterworth low-pass filter with a cut-off frequency of 6.25 - 62.50 kHz (depending on the sampling rate) was further applied to each current, voltage and ion waveform sample to further smooth noisy arc data and reject electromagnetic interference (EMI) noise bursts present at the start and end of each arc pulse.

An automated data collection and archiving program (see the process flow chart in Figure 6) was developed in LABVIEW to capture and organise data from the oscilloscopes. The sampling rate of waveform data was adjusted from a few hundred milliseconds to several seconds between samples, depending on test conditions. Although sample sizes of 15-30 waveforms were typically used for most test runs, up to 100-300 waveform samples were captured and stored for some erosion rate tests.

Data processing, reduction and analysis

Once the captured raw data was filtered, further waveform processing was performed in MATLAB to convert data into a usable format and extract key parameters for each pulse waveform sample:

1. Peak arc (discharge) current (/ peak), i.e. the maximum arc current at the beginning of the arc pulse.

2. Arc pulse length (t _p ), i.e. the time duration of the arc pulse from initiation to termination. Arc termination is assumed to occur when the arc current decays down to 1% of its initial peak value.

3. Average (or mean) arc (discharge) current (I), i.e. the arc current value averaged over the arc duration (arc pulse length).

4. Mean arc discharge voltage (V), i.e. the arc voltage value averaged over the arc pulse length.

5. lon-to-arc charge ratio (J), i.e. the ratio of the collected ion and arc current over the arc pulse length, i.e. ratio of current-time integrals.

Examples of a typical set of arc current, arc voltage and ion current sampled traces are shown in Figures 7 and 8 respectively. In Figure 7, a Bi cathode was used (50A peak arc current, 2138 ps median pulse length,

75 sampled traces). In Figure 8, a Fe cathode was used (50A peak arc current, 529 ps median pulse length, 20 sampled traces). Current and voltage traces showed considerable fluctuations due to the present limitations of the pulse circuit and arc triggering method to produce and control vacuum arc pulses (explained in further detail below). To address this, statistical treatment of arc waveform data was used to extract meaningful arc properties and quantify the effect of fluctuations on data accuracy.

Statistical analysis of arc waveform sampled traces within a typical test run or test set (such as in Figures 7 or 8) revealed that most parameters could be loosely considered to fit a Normal distribution, that is, a random spread of data (see dataset examples taken at long and short pulses in Figures 9-12 respectively). However, many of the plots do not show a good fit at their extreme values. A particular note is made of the arc pulse length tested at short pulses (Figure 11), which appeared to fit a Normal distribution rather poorly. Further investigation revealed that the arc pulse length distribution could be better fit to a Log-Normal distribution instead (seen under a Box-Cox transformation of pulse length data as shown in the example of Figure 12). A comparison of transformed pulse length data to a Normal distribution (mean μ = 5.5, standard deviation a = 0.8 in this example) using the Mann-Whitney-U test verified that the Log-normal distribution gave a reasonable fit at Pr « 0.78-0.99.

Due to the non-Normal behaviour of the arc pulse length as well as other arc parameters such as the arc voltage in some cases, arc parameters, such as pulse length, were most visibly affected by this characteristic of the vacuum arc and were therefore handled in a statistical.

Based on these findings, all waveform parameters within this study were aggregated and statistically treated in a non-parametric manner (that is, independent of statistical distribution) by using the median of all the parameters. This was considered an overall more conservative and robust method of determining representative or more likely values of arc pulse properties, rather than merely using the mean value. Order statistics were then used to estimate 95% confidence upper and lower bounds for all waveform parameters.

An exception was made for ion-to-arc charge ratio data, which was able to take into account the noisy fluctuations of vacuum arc behaviour. This occurs because any temporal variation in plasma production at the thruster source is detected by the ion detection probe. Thus, the ion-to-arc current ratio, by its own definition, effectively "cancels out" fluctuations in ion production from the final result. This is demonstrated by J's excellent probability plot fit to a Normal distribution in the example of Figure 12. Therefore, ion-to-arc charge ratio data in this study was treated as Normally distributed. Confidence bounds on aggregated sample data were obtained using Student's f-distribution method.

It is important to note that the resulting confidence bounds (uncertainties) calculated for various arc pulse parameters as outlined here are indicative of arc stability for a given set of captured arc pulse data. By propagating these uncertainties over to thruster performance parameters such as T/l, T/P, J, C _T and E _r , the effect of arc stability on the uncertainty within final thruster performance results can be confidently and conveniently expressed.

Direct thrust measurement stand

The stand that was developed for this work is shown in Figure 13 and is based on the torsional pendulum concept used by a number of authors (see Ziemer, I. K. (2001), Performance measurements using a sub-micro Newton resolution thrust stand, in '27th International Electric Propulsion Conference', Vol. IEPC-01- 238, Pasadena, CA). A thruster is fixed on a mounting assembly at one end of a 600 mm long beam, which is centrally pivoted about the vertical axis by two hinges above and below the beam. To reduce weight, the beam is made of aluminium. An adjustable counterweight is installed at the other beam end to ensure the beam undergoes as pure a horizontal rotation as possible. When the thruster fires, the beam undergoes a small rotational displacement.

For this experiment, the beam end displacement was measured by a Philtec D63 fibre optic displacement sensor which remained fixed to the vacuum chamber. The sensor voltage output was sent to a National Instruments 14-bit Data Acquisition Module (Nl USB-6009) for data capture. All displacement data (uncertainty of +1 mV) was sampled at a sample rate of 300 Hz and smoothed with a low-pass filter of 2.5 Hz, which is roughly an order of magnitude larger than the beam's natural frequency. Filtering was done in order to mitigate sensor noise and possible EMI (Electromagnetic Interference) from the thruster. In this way the beam's response was sufficiently captured and suitably processed for displacement analysis.

The displacement response of the thrust stand can be described analytically based on the derivation of the linear displacement response of an under-damped pendulum to a repetitive impulsive force (Wong, A. R., Toftul, A., Polzin, K. a. & Pearson, J. B. (2012), Non-contact thrust stand calibration method for repetitively pulsed electric thrusters)). Converting the response to an angular displacement results in the following equation: x(t) Ibit ^r a

exp {-ω,,ζτ} sin {ω,,δτ} Η ₀ τ

1 ∑=0 Ι, _η ω _η δ

ζ≤ϊη {ω _η ίδ)

+θ{0)βχρ (-ω _η ίζ) + cos (ω„ ΐδ) θ(0) + 2θ(0)ω _η ζ

+ exp (-ω,, ΐζ) sin (ω _η ίδ) ω _η 6 where δ = γ 1 - ²

ί-

/

and 0 r and x(t) are the angular and linear displacement as a function of time t respectively, r _a is the moment arm from the thruster to the pivot hinge, T _bit is the average impulse bit, l _m is the effective rotating system's moment of inertia, ω _η is the natural frequency of the system, ζ is the damping coefficient (ζ < 1), f is the pulsing frequency, N is the total pulse number, x(0) and x(0) are the system's initial displacement and velocity and H ₀ is the Heavyside step function. The equation above is capable of modelling the system's response to an arbitrary number of repetitive pulses, including a single pulse (N = 1).

The average impulse bit and force from the thruster are found using

where F and t are the pulsed thrust and pulse duration, respectively.

The natural frequency of the thrust stand beam is defined as n =

M

where k _eff is the effective stiffness of the system and is the system mass.

During quasi-steady state, the beam displacement follows Hooke's Law such that

F - keffXg where x _s the steady-state displacement response of the beam to a repetitively- pulsed force.

Thus, the pulsed force produced by a thruster can be calculated as follows:

p _

Faraday cup probe

A Faraday Cup (FC) probe with a cup design was developed and built to measure ion current in the plasma jet emitted from the thruster. A schematic of the probe circuit is shown in Figure 14 (see also Figure 15). In this instance, an ion collector is negatively biased to 118V and connected to ground via a terminating resistor. The resistor value (R) was set at 2.48±0.01 ΜΩ for ICDD (Ion Current Density Distribution) measurements. An additional -60V bias plate was installed for further repulsion of plasma electrons.

A digital oscilloscope (ISO-TECH IDS 8064, 60 MHz IGs/s) measured the voltage drop across a shielded terminating resistor in the circuit to measure the ion current signal. The resistance of the oscilloscope in parallel must also be taken into account if a large terminating resistor value is used. Therefore, the true terminating resistance is

^{Rtrue ~} where Ro = 1 ΜΩ is the oscilloscope resistance and R is the terminating resistance.

Hence, the ion current captured by the FC probe l _ip is simply where V _fc is the voltage drop measured by the oscilloscope across the terminating resistor.

Two-axis rotation system

In order to measure the ICDD, a well-known methodology was implemented by capturing ion current signals from a single (or several) Faraday probe(s) at various relative angles to the head of the thruster. More specifically, the thruster was moved relative to a fixed single probe in Polar co-ordinates (see Sekerak, M. (2005), Plasma plume characterization of a vacuum arc thruster, M.S. thesis, California Institute of Technology, Pasedena, CA). ICDD measurements were taken in two dimensions, thereby allowing the symmetry of the VAT plume to be more accurately assessed. Based on knowledge of the plume shape, the direction of the force (also known as thrust vector) being produced by the VAT can be properly determined.

The thrust vector is defined as the force magnitude and direction comprised of the sum total of all directed ion momentum, taking into account all radial and normally-directed force components. For all cases studied here, this is equivalent to the vector sum of the pitch and yaw components of peak measured ion flow. Figure 16 illustrates the thrust vector diagram and its components. The following expressions for the thrust vector (absolute) magnitude C and deviation angle from normal βτ-can be used:

CsinjSr = ^A ² sin ² jS + B ² sin ² j3p

tan ² β _τ - tan ² β _γ + tan ² β _ρ

where A and B are the respective yaw and pitch magnitudes and py and βρ are the respective yaw and pitch deviation angles of peak ion flow measured in their respective planes.

Expanding on Sekerak's (2005) approach and based on the popular use of mechanical stings in aerodynamic wind tunnel testing, a custom-built two-axis rotation system (TARS), based on the methodology described above, was developed. Figures 17 and 18 respectively show a photograph and schematic of the TARS and FC probe that comprises the entire ICDD setup within the chamber. The TARS provides full and combined +90° pitch and yaw motion of a mounted thruster assembly relative to a fixed ion probe in such a way that the point distance between the thruster head centre point and the probe entrance remains constant at all angles of rotation.

A standalone motor control application was developed in Microsoft Visual Studio to provide a convenient means of manually or automatically controlling the orientation of the thruster assembly for data capture (see the process flow chart illustrated in Figure 19). Starting and ending locations can be independently specified as well as the increment of angle rotations. For simplicity of control, angular increments were set to a fixed multiple of a complete 4-stage rotation of each stepper motor, i.e. for yaw, 1 x 4(1.8) = 7.2° or 2 x 4(1.8) = 14.4° and for pitch, 10 x 4(1.8/7.5) = 9.6° or 20 x 4(1.8/7.5) = 19.2°. A functional diagram of the ICDD measurement system is illustrated in Figure 20.

As shown in Figure 18, the ICDD capture system was arranged such that the

Faraday cup probe was located at a fixed distance from the thruster head. A limitation was placed on how large an expected signal could be received so that the voltage drop across the terminating resistor remained no more than 15% of the negative bias of the ion collector. Thus, the probe was placed at least 200 mm away to allow a maximum voltage signal of no more than 18 V.

The probe position used for ICDD tests was nominally set at 230+0.5 mm, which was defined as the distance from the tip of the VAT to the tip of the ion collector housed within the FC probe. Alignment of the probe with respect to the zero position of the thruster was performed manually using a ruler as guide with an estimated pointing angle accuracy of ~ 0.25°.

ICDD data was typically captured over a pitch angle range of +76.8° in increments of 9.6°, and yaw angle range of +86.4° in increments of 7.2° or 14.4°. At each angular position, 10-20 samples for arc current, arc voltage and ion current were captured and processed. Ion charge ratio values were calculated and aggregated into a single representative mean value (with 95% confidence level bounds) for each position. To remove any outliers, Peirce's Criterion was applied to each J data set.

A least squares method was used to find the best type of distribution to surface fit the plume data. For data sets with only one pitch or yaw range captured, a curve fit algorithm was implemented instead. Due to the non-linear nature of the data fit, the Levenberg- Marquardt regression fit solver was used. Test data was normalized for a probe distance z = I = 1 and for an arc current J.dA = 1. This generalized the data such that the distribution fit could be applied for all probe distances and arc current values. Four types of distributions were assessed to fit J test data in each axis in the following manner:

For an Exponential distribution,

For a Cosine distribution,

For a Gaussian distribution,

For a Parabolic distribution,

where k, w, γ1 and γ2 are distribution-specific parameters or spread factors describing the shape of that distribution, φ is the divergence angle (in pitch or yaw) and cp _e is the deviation angle of φ to the normal axis, i.e. centreline of the thruster head.

The thrust correction factor (C _T ) is a measure of what proportion of momentum from ions leaving the vacuum arc thruster contribute to normal thrust. This factor takes into account the plume divergence of the thrust plume and the spatial interference of the anode electrode to the escaping plume. C _T considers the effect that the ICDD and electrode geometry have on normally-directed thrust.

This is because the divergence of the plume and any interference of the electrode surfaces to the ejected ions causes a reduction in thrust. Hence, the larger the value of C _T , the greater the thrust level produced by the VAT. The assumption is made that the average ion charge state and the average ion velocity of the plasma jet plume are spatially uniform. Therefore, only the ion mass flow is considered to affect C _T . Figure 22 defines the Cy problem domain based on the VAT electrode geometry. The resulting generalised expression of C _T for any arbitrary J distribution is as follows:

where

L = Llr _c

f _a = r _a lr _c

J2 _ £2 ₊ 2 ₊ 2 _ _{2fi 2 COs (0i} _ £ ₂₎ dA _\ dA ₂ = † _\ r ₂ d† _\ df2d0 _\ d02 and i, Γ2 are radial vectors along the cathode surface and anode exit surface as shown in Figure 22. The value of C _T was numerically solved using a combination of Adaptive Simpson quadrature and trapezoidal integration (implemented in MATLAB), where inputs of thruster geometry and the ICDD fit parameters were used (for the example in Figure 21 r _c = 6.35mm, mm, f ₂ = 1.58 and L = 0.16). The Monte Carlo simulation technique was used to determine the effect of all uncertainties on C _T and the thrust vector by generating pseudo-random J data (mean value and angle position) that followed the same assumed statistical behaviour of the actual experimental data measured, i.e. a Normal distribution. A total of 251 random test runs were generated and fitted, resulting in a simulated uncertainty of the ICDD spread factor and deviation angles from actual test data measurement uncertainties and test sampling limits. A comparison between simulated and actual uncertainties were made, with the larger of the two values being the final uncertainty for the relevant parameter. The worst-case ICDD spread factor uncertainty was subsequently used to calculate the final uncertainty of C _T . The worst-case combination of pitch and yaw deviation angles (positive or negative) were used to find the final thrust vector deviation angle uncertainty. Thus, for the example shown in Figure 21 , a final result of C _T = 0.637±0.0132 and βΤ = 4.7° ±1.7° was produced. Typical uncertainties for CT in this study were 5% when only one axis was measured and 1-2% when two axes were measured. Uncertainties for βΤ typically ranged from ±1.5° to ±6°.

A suitable ICDD capture technique was developed for this work, where a TARS actuation system was designed, built and tested to provide acceptable range (±90°) and accuracy (≥ +2.2°) for all thruster assembly load cases. Used in conjunction with the FC probe, the ICDD of VAT plasma plumes could be automatically captured and processed with various control systems and data processing techniques. Resulting thrust correction factors were obtained with good accuracy for this work (2-5%). However, thrust vector deviation angle accuracy was moderate (±1.5- 6°) due to the limited accuracy of the TARS' stepper motors (especially the pitch motor) and the limited number of test samples that could be captured.

Ion Collector

The ion collector is simply an electrically conductive metal enclosure that receives the ion flux travelling outward from the thruster, with the goal of determining the total ion current emitted by the VAT.

Design specifications for the ion collector as depicted in Figure 23, are as follows:

• The collector's circular walls and dome were made of 0.9 mm thick aluminium sheeting. Sections were joined together with conductive copper foil and Kapton tape.

• The ion collector was negatively biased to -60 V with a standard DC power supply to repel plasma electrons.

• The ion collector was sized in order to mitigate the possibility of discharges between the thruster and the collector. Thus, the collector walls were designed to be at least 220 mm away from the thruster head, which was located at the centre of the collector cavity.

• BNC cabling and connectors were used to connect various portions of the ion collector and its circuitry.

The ion-to-arc current ratio is roughly 10% for most cathode materials across a wide range of arc currents. Thus, for a peak arc current of 50 A, a total ion current peak of ~ 5 A was expected to be detected by the ion collector. A terminating resistor value of 2.65 ±0.01 Ω was used to ensure a reasonable voltage drop of roughly 10 V across the resistor. Figure 24 shows ion-to-arc current ratio measurements obtained at various bias voltages (from -60 V to +20 V). A bias voltage of -60 V is shown to achieve full repulsion of plasma electrons. To account for the stochastic nature of ion production, forty samples of ion current were taken for each test and aggregated to produce a smoothed result. Since the ion-to-arc current ratio ε was the final parameter desired, the total charge delivered to the VAT and detected by the collector was used to find this value. Erosion rate measurement

Fuel consumption of the VAT is generally defined as the rate at which cathode material is eroded during thruster operation. The most common means of measurement in literature is the cathode weight loss method. In the weight loss method, the difference in cathode mass Am before and after a set period of thruster operation is measured. In addition, the total cumulative amount of pulse charge∑Q that is delivered to the thruster during the test is also recorded. Using both sets of measured values, the cathode erosion rate can be formulated as

The parameter E _r (normally in units of g/C) is a convenient way for comparing the erosion rate of the cathode across different thruster pulsed operating conditions of arc current, pulse length, pulse frequency and average power level.

The total cumulative pulse charge is

where At is the total operating time of the thruster (or test time). Finally, the mass flow rate of the VAT (in kg/s) can also be found by simply multiplying E _r with the average pulse arc current and thruster duty cycle:

m = E _r I (t _p f)

A typical erosion test in this study consisted of the following features:

· Before an erosion test, each thruster and its cathode rod was prepared and reset to "new" thruster conditions.

• Cathode mass measurements were performed with an analytical mass balance (Pioneer PA214, ±0.1 mg resolution) before and after each erosion test.

· All tests were conducted with thrusters initially at room temperature

(roughly 20° C).

• The VAT was sometimes initially fired for 30-200 pulses depending on the cathode material to "burn-in" the thruster and ensure proper initiation of the thruster. This initial amount of released charge contributed a small, insignificant error to the total value of∑Q (< 0.5-1 %).

The VAT was operated continuously for several thousand pulses - sometimes for as much as 100 C of total pulse charge delivered. This ensured that enough material was eroded for good test accuracy and the thruster operated with realistic and steady heating conditions for an extended period of time. Cathode erosion was also limited such that the changing cathode geometry did not affect the overall thruster geometry and operating conditions in a significant manner.

Between 100-300 pulse waveform samples were captured in a single test, appropriately consolidated and weight-averaged to find the total cumulative pulse charge∑Q. Since the present test method made a time- averaged calculation of E _r , only average values of / and t _p were used to find E Thus, only the uncertainties of /, At and Am were considered in the final uncertainty analysis of E _r (typically 2-4% error). The nominal ranges of uncertainty for each parameter in this study is listed in table 3 below.

Parameter Nom. values Uncertainty Effect on E _r uncertainty

Mass loss, A?n (mg) 2-100 +0.1 Strong

Pulse frequency, / (Hz) 2-10 +0.1-0.001 Medium

Total test time, At (s) 250-3000 + 1-5 Weak

Table 3: Range of typical values and uncertainties for f, At and Am in this erosion study and their effect on final E _r uncertainty.

Example 1 : Pulse length experiment

This experiment considered the effect of arc pulse length on VAT performance and behaviour with particular attention given to millisecond-long pulse lengths, an operational condition largely ignored in VAT literature.

Experiment/Test methodology

Thruster prototypes following a baseline VAT design with Al, Fe, Cu and Bi cathode fuel rods/electrodes were used in this experiment. Numerous prototypes were prepared and operated such that each VAT was test fired with a desired median pulse length within the range of 150- 4500 ps long. The pulse length was roughly controlled by modifying and tuning the inductive energy storage pulse circuit/power circuit for each thruster test to achieve the desired arc pulse waveform characteristics (see Figure 4). Peak arc currents of 25, 50 and 100 A were selected for this experiment, where the majority of tests were run at 50 A peak arc current. Thruster firing rates ranged from 1 to 10Hz in order to (a) control average power level and (b) generate sufficient levels of average thrust for accurate thrust measurement. Detailed thrust, 1CDD (Ion Current Density Distribution), ion current and erosion rate measurements were undertaken on each VAT prototype to characterise their behaviour and performance. The typical test procedures, methods and analysis for each measurement type have already been described.

Experimental results and discussion

(a) Erosion tests

Thruster prototypes operating at long pulse lengths (≥ 1000 ps) tended to produce more uniform erosion of a rod face of the cathode, where there was sufficient time for the cathode spots to travel over the surface area to erode it before the arc pulse extinguished. Figure 25 shows examples of erosion patterns on Bi and Al cathodes operating with short and long arc pulse lengths. Long pulses (2-3 ms) showed a very/near uniform erosion of the cathode surface compared to the use of short pulses (250-500 ps) where erosion only took place up to ~ 1 mm from the cathode edge. In the case of Al, erosion was initially restricted along one side of the cathode/cathode rod, but would be expected to eventually erode the entire cathode edge after an extended period of time (as seen with Bi).

Thus, the arc pulse length played a critical role in how the cathode eroded depending on the size of the cathode surface area. Generally stated, a larger-sized cathode (e.g. 6 mm diameter) requires a much longer pulse length than would be required for a smaller cathode (e.g. 3 mm diameter) to achieve uniform erosion (e.g. 500 ps vs. 2 ms).

Table 4 below compares selected erosion rate test results for both short- and long-pulsed operation using a variety of cathode materials run at / = 50 A peak arc current. In each material case (with the exception of Al), operating VATs with longer arc pulse lengths was found to increase the cathode erosion rate due to the greater heat load imposed on the cathode rod.

Pulse type t _p ( /s) P (W) / (Hz) E _r Qig/C) Dlff.

Al Long 1906 15.7 7 31.9 +0.6

+2.2%

Short 156 8.1 50 31.2 ±0.6

Fe Long 2213 5.4 3 75.5 +1.1 +71.6%

Long 2366 0.4 0.25 76.5 +2.0 +73.9%

Short 236 1.6 20 44.0 +1.1

Cu Long 1420 5.5 2 83.5 +2.1

+72.5%

Short 166 3.0 20 48.4 +1.7

Bi Long 2130 0.8 2 1267.4 +3.6

+34.0%

Short 185 0.6 5 945.5 +12.0 Table 4: Comparison of erosion rate results for Al, Fe, Cu and Bi cathode materials

In essence, all materials will eventually experience large increases in erosion rate given sufficient input heat load. The operating point at which this begins to occur will vary depending on the material and electrode size. Al (which has a high thermal conductivity) did not increase in this case simply because the input heat load in this particular test was below the material threshold of excess melting.

Reference is specifically made to the material properties listed in Table 5 below.

Property Al Fe Cu Bi

*

Purity 2N 3N5 2N5 ^* 5N

Atomic mass (AMU) 26.3 55.9 63.5 209

Density (x 10 ³ kg/m ³ ) 2.70 7.87 8.93 9.78

Boiling point (K) 2792 3134 2835 1837

Melting point (K) 933 1810 1358 545

Thermal cond. (VV/mK), molten 218 32 339 7

Thermal cond. (W/mK), room 237 80 401 8

Commercially pure

Table 5: Material properties of Al, Fe, Cu and Bi cathode samples

Cathode materials with a combination of high thermal conductivity and high melting point were noted to generally produce lower erosion rates. However, an exception in the behaviour of Cu was seen, which showed a significant increase in Er (Erosion) compared to Al, whose Er values were highly resilient to increases in pulse length.

An important finding of this erosion study was that the pulse length plays a much greater role than the average power level in determining the cathode erosion rate. Examples include: (1) Fe producing the near- identical erosion rate result (~76 pg/C) during long-pulsed operation irrespective of average power level (0.4 W vs. 5.4 W), and (2) Bi producing a 34% increase in erosion rate with a longer pulse despite operating with a low average power level (≤ 1 W). These results suggest that it is the local heat conditions near the cathode spot emission sites that are mainly responsible for the cathode erosion. Average power levels above a certain value are assumed to only begin taking effect once the overall cathode temperature rises to the point of gross melting (dependant on an individual material's thermo-physical properties). Interestingly, Fe's erosion rate reached an upper asymptotic limit of Er ~ 75 pg/C at approximately 2500-3000 [is pulse length (see

Figure 26).

Figure 26 expands Table 4's results by plotting erosion rate test data over a wide range of median arc pulse lengths (150-3500 s) and peak arc currents (/=15, 25, 50, 100 A) for various cathode materials. As before, cathode erosion rate is generally seen to increase with increasing arc pulse length.

The erosion rate of Al and Cu was shown to be insensitive to the peak arc current in the 50-100 A range, most likely due to the good thermal conduction of these materials. However, a surprising result is that erosion rates for Fe and Bi are higher at 50 A peak arc current than at 15, 25 or 100 A peak arc currents. As expected, a lower peak arc current causes a lower heat load and hence lower melting. Conversely, a high arc current ought to produce a higher heat load and erosion rate. However, the lower erosion rate values at 100 A peak arc current (higher heat load) in the case of Fe and Bi are counter to this argument. One possible explanation is that operating at a higher arc current was sufficient to generate additional cathode spots on the surface of Fe and Bi at the beginning of the pulse. These spots are more likely to spread out and cover more surface area, eventually distributing the arc heat load to a level lower than would be experienced at 50 A and resulting in a lower erosion rate. Complementary evidence for this view is given in the situation of Cu, which showed no change in erosion rate with varying arc current at short pulses (50 and 100 A), suggesting that no change in heat distribution on the Cu cathode surface occurred. In conclusion, the erosion rate is largely influenced by the local heat load, which is a function of not just the peak arc current, but also of the cathode spot distribution, and the interaction of both these factors.

(b) ICDD measurements

Significantly larger ion charge ratio values were observed when baseline VATs were fired at increasingly longer pulses as shown in Figure 27. In general, a considerably greater increase in charge emitted was found to occur in front of the thruster than at its outer radial edges, where the largest increases (up to 200% or more) were seen of Al's and Fe's J values along the thrust centreline. The behaviour of increasing ion charge ratios also appeared to be consistent for / = 50 and 100 A (at least in the case of Fe). However, there was a limit to this effect for Bi, which showed virtually no change in ion charge ratio values beyond a pulse length of 1500 ps. The slightly higher J values at a very short pulse of 132 ε compared to 506 \is in Fe is likely due to the higher average charge state of the ions being produced under the shorter pulse length condition.

The large increases in collected ion charge per given input arc charge during long-pulsed operation is a surprising result. Conventional understanding of vacuum arc behaviour and operation says that ion production rate should be linear to arc charge. As such, there ought be no change in the magnitude of the ion charge ratio collected regardless of delivered arc charge (integral of arc current with respect to arc pulse length). Indeed, a comparison of Fe's ICDD results at short pulses for both 50 A and 100 A peak arc currents yielded similar levels of peak ion charge ratio along the thruster centreline (ICDD profile shapes of 50 A and 100 A are slightly different because a greater number of cathode spots are present at higher arc currents, which creates a more uniform spread of plasma flux (Gaussian distribution) compared to the Exponential distribution typically generated under low arc current operation).

There are three possible causes for the increase in measured ion signals:

1. A higher ion charge state can give the appearance of higher ion charge ratio when detected by the FC probe. However, this is unlikely to be the case here because of Anders's (1998) observed decrease of average ion charge state with pulse length (Anders, A. (1998), Ion charge state distributions of pulsed vacuum arcs-interpretation of their temporal development, IEEE Transactions on Plasma Science 26(1), 1 18-1 19). In fact, operating at millisecond-long pulse lengths may have actually decreased the average ion charge state even further than had been previously thought due to increased charge exchange collisions with lesser-charged ions and neutrals.

2. Charged macro particles may have been captured by the FC probe and contributed to the total charge signal. Operating for long pulses gives sufficient time (roughly 500 με) for these macro particles to travel across the test setup drift length (230 mm) and potentially enter the FC probe. However, macro particles are mostly ejected at large angles to the normal. This would have caused an increase in collected charge at wide pitch and yaw angles, which was not observed here. In fact, the largest increases in ion signal are observed directly in front of the thruster. Thus, macro particles are also ruled out as a cause for the increase in ion signal.

3. The final remaining possibility is the generation of additional ions in the near cathode spot region(s) or in front of the VAT. This can occur as a result of increased charge exchange (CEX) collisions between ions and neutrals (or even small MP's) to produce a surplus of (lower-charged) ions within the plasma flux. The highest growth rate of J seen along the thruster centreline suggests that most of the CEX takes place within the centrally-located region of the plasma jet.

With reference to published estimates and measurements of ion and total erosion rates under "standard conditions" as shown in Table 6 below , it can be seen that at least 30-50% of eroded material is available for additional ionisation. Thus, reported increases in ion production rates at longer pulses are within possible limits of available cathode material.

Erosion rate, E _r (j/g/C)

Type Description Al Fe Bi

This work

Exp Total mass loss, Am (mg) {5.7 ±0.1) (43.7 ±0.1) (51.9 ±0.1)* 50 A pk, 150-2000 j s 31.2 +0.6 56.6 ±0.6 1267.4 ±3.6 ^*

Exp ^a 100 A, 250 /is 28 48

Exp ^b 200 A, 0.52 s 73

Calc ^c Ion erosion only 19 26 21 1

* Results for Bi were obtained from an additional erosion rate test (Q = 41 C) due to a measurement error in the lifetime test.

a Brown & Shiraishi (1990)

b Kimblin ( 1973)

c Urn et al. (2010)

Table 6: Comparison of measured and predicted erosion rates of baseline VATs with published literature

Brown & Shiraishi (1990) refer to Brown, I. & Shiraishi, H. (1990), Cathode erosion rates in vacuum-arc discharges, IEEE Transactions on Plasma Science 18(1), 170-171. Kimblin (1973) refers to Kimblin, C. (1973), Erosion and ionization in the cathode spot regions of vacuum arcs. Journal of Applied Physics 44{7), 3074-3081. Finally Lun et al. (2010) refers to Lun, J., Dobson, R. T. & Steyn, W. H. (2010), Determining vacuum-arc thruster performance using a cathode-spot model. Journal of Propulsion and Power 26(4), 663- 672.

Using data from Figure 27, a plot of peak ion charge ratios emitted along the thruster centreline with respect to the arc pulse length reveals different growth rates of J depending on the cathode material, shown in Figure 28. In Figure 28, the growth of peak ion charge ratios along a thruster is plotted against pulse length for Al, Fe and Bi cathodes (Peak ICDD test date taken from Figures 27(a)-(c) where peak / = 50 A).

All materials show similar near-linear increases in peak J up to 1-1.5 ms, but then diverge at different rates as the pulse length is extended further.

Least-squares fit trend lines through test data in Figure 28 indicate that Al has a quadratically increasing peak J with t _p , Fe maintains a linear increase in peak J and Bi has a quadratically-decreasing J with t _p (trend line parameters are listed in Table 7 below).

Fit type Fit equation Coefficients RSME

a b C

Al Quad. J = ar^ + btp + c 4.383 x l 0~ ⁸ 7.041 x 10 ^" -5 0.153 0.000

Fe Linear J = bt _p + c 14.75 x 10 ^" -5 0.058 0.010

BI Quad. J = αη, + btp + c - 1.619 i0~ ⁸ 9.826 x 10 ^" -5 0.134 0.008

Table 7: Trend fit specifications for peak ion charge ratios J (pC/Cj against median pulse length t _p (ps) as shown in Figure 28.

One interpretation of this behaviour is that all materials initially experience exponentially increasing ion flux production rates with increasing arc pulse length. However, the material's thermal properties ultimately limit the level and rate of flux growth by increased melting and gradual increase of MP(macroparticle) presence in the plasma jet. At some point, increased heating and melting at ever-longer pulses is sufficient to completely halt the growth of ion flux and possibly reduce it to lower levels (as seen with

Bi).

Table 8 below lists the resulting ICDD parameters against pulse length for Al, Fe and Bi cathodes.

characteristics ICDD parameters

/ (A) / (Hz) tp (//S) Dist. Spread C _T

Al 50 10 309 Exp 5.596 0.948 0.590

50 6 1027 Gauss 1.453 0.969 0.723

50 6 2161 Gauss 1.154 0.985 0.619

100 10 1 150 Gauss 1.139 0.937 0.613

Fe 50 10 132 Exp 6.300 0.961 0.571

50 10 506 Exp 6.636 0.934 0.564

50 10 1416 Gauss 1.431 0.977 0.717

50 3 2802 Gauss 1.197 0.982 0.637

120 1 387 Gauss 1.232 0.966 0.651

100 10 2075 Gauss 1.191 0.977 0.635

Bi 50 2 358 Gauss 1.065 0.986 0.579

50 2 1448 Gauss 1.154 0.992 0.619

50 1 3421 Gauss 0.926 0.969 0.505

50 10 4541 Gauss 0.986 0.978 0.538

100 10 3282 Gauss 0.879 0.985 0.477

Table 8: Test parameters and results (distribution type, spread, goodness- of-fit (R ² ), thrust correction factor) for ICDD measurements at various arc pulse lengths. Data from Figure 27 is included.

Results indicate that operating at longer pulse lengths causes the ICDD to transition from an Exponential distribution to a Gaussian distribution. This occurs because there is a greater amount of time for the cathode spots to traverse the cathode surface and uniformly emit plasma instead of being locally restricted to the cathode edge. Thus, in the case of arc currents as low as 50 A peak, operating with long pulse lengths improves the average momentum transfer of ions in the normal direction by influencing the ICDD. A plot of thrust correction factors shows a more detailed picture of its relation to arc pulse length. For example, Figure 29 reveals what appears to be an optimum C _T region occurring in the tp = 1000-1500 s range for all materials tested at / = 50 A peak (as high as 0.72 for Al and Fe, spread ω -1.4). This may have to do with the ICDD shape transition from an Exponential to a widely-spread Gaussian distribution. As the pulse length increases further, the ICDD becomes narrower, resulting in a lower C _T value until the cathode is saturated with cathode spots, approximating a cathode surface with uniform emission of ions (e.g. see Bi results). Testing Fe at higher arc currents (/ = 100 A peak) as indicated in Figure

29 showed that a higher C _T value can occur at short pulses. This is attributed to the increased number and distribution of cathode spots that tends to produce a Gaussian-shaped ICDD. However, this condition appears to keep C _T relatively constant at 0.64-0.65 throughout the arc pulse length range.

No significant changes in C _T were seen for Bi operating at / = 100 A. This is most likely due to Bi already having a large number of cathode spots present in either case of / = 50 A or 100 A. The lower C _T value in Al at / = 100 A remains unexplained. It may have to do with a poorer-shaped Gaussian distribution fit (R ² = 0.937) compared to the rest of the ICDD data set (typ. R ² = 0.97-0.99) or it may provide further evidence that operating the VATs at / = 50 A is a special case as was initially observed in the erosion rate data of Figure 26.

The behaviour of the thrust correction factor also indicates some material dependence. Although all materials exhibit similar C _T values under an Exponential distribution, operating at longer arc pulses resulted in some material differences. Both Fe and Al continue to follow similar behaviour in CT, whilst Bi produces lower increases of C _T and then further decreases in the 3-5 ms pulse length range. Thus, Bi at 3-5 ms represents a special case where two effects are doubly reducing the value of C _T . The first is the growth restriction of ion production rate as seen in Figure 28 and the second is the narrowing of the ICDD. Both effects can be attributed to the extraneous release of MP's, which impedes the ion flux.

(c) Ion Current

Measurements of ion-to-arc current ratios for baseline VATs operating in both short and long pulses under the same single test setup are shown in Table 9 below. Increases of 10.4-16.6% in £ were seen across all materials tested, with greater increases for materials with a higher thermal conductivity and boiling point. This result further verifies that operating VATs at longer arc pulse lengths increases the rate of ion production.

Pulse type tp Q s) {Hz} e (%) DifT.

Al Long 1610 10 8.86 ±0.28

+16.6%

Short 117 6 7.60 ±0.22

Fe Long 2156 6 9.25 ±0.12

+12.7%

Short 228 5 8.21 ±0.12

Bi Long 2492 2 6.17 ±0.11

+10.4%

Short 256 5 5.59 ±0.15 Table 9: Comparison of averaged ion-to-arc current ratio results for Al, Fe and Bi cathode materials in a baseline VAT design operating with long and short pulses. Peak arc current is / = 50 A lon-to-arc current values for Al and Bi are somewhat lower (32-45%) than that measured by Anders (Anders, A., Oks, E., Yushkov, G. & Savkin, K. (2005), Measurements of the total ion flux from vacuum arc cathode spots, IEEE Transactions on Plasma Science 33(5), 1532- 1536) and Kimblin (1973), whilst Fe shows excellent agreement (3%) with literature.

(d) Thrust tests

To further investigate the effect that long pulses have on VAT behaviour and performance, thrust measurements were conducted on baseline VATs over a wide range of pulse lengths and cathode materials (Al, Fe, Cu and

Bi). Figure 30 presents consolidated thrust data for all cathode materials taken from multiple thrust datasets measured over a period of several months. More specifically, Figure 30 shows average thrust per current results for baseline VATs using Al, Fe, Cu and Bi cathodes operating at 50 A peak arc current at various pulse lengths. All thrust data illustrated in

Figure 30 is shown for VATs firing up to no more than a total cumulative arc pulse charge of ~80 C. Error bars have been omitted for visual clarity.

The data shows an increasing trend in thrust production rates (represented here as the ratio of pulsed thrust per average arc current or T/l) with increasing median pulse lengths across all materials tested at / = 50 A peak. Average thrust per arc current values at tp = 2000 ps were shown to be 11.0-24.9% higher (depending on the cathode material) compared to T/l values measured at tp = 500 ps. These thrust results run counter to conventional understanding of VATs, which assumes that the thrust production rate should remain constant and relatively independent of arc current levels and pulse duration (within Region E indicated in Figure 31). Region E has previously been an untested region of VAT operation. The cause of the enhanced thrust production effect is not immediately clear. The observed rise in T/l against tp across different materials operating at the same arc current level suggests that the number of cathode spots present on the surface does not play a significant role here. The arc currents used in this study are also considered too low for appreciable spot interaction (e.g. due to self-magnetic fields) to take place.

Increases in T/l could be explained by both the measured ~10% increase in total ion current and -10% increase in C _T when operating VATs with long arc pulses - giving a ~20% total increase in thrust. However, the significant increases in J values observed in the ICDD tests (up to 100- 200% increases along a thruster centreline) do not fit this explanation.

Additional thrust tests may provide more insight into the mechanism of enhanced thrust production. For instance, detailed thrust results for Fe presented in Figure 32 show that long-pulsed thrust tests running at 25 A and 100 A peak arc current produced differences in thrust production behaviour compared to the 50 A peak tests. More specifically, Figure 32 illustrates average thruster per current results for baseline VAT with Fe cathode operating at 50 A peak arc current at various pulse lengths. A linear fit (for visual purposes) through 50 A data shows an increase in average thrust production with increasing pulse length from 216 pN/A at 500 ps to 262 pH/A at 2000 ps (21.3% increase).

Whilst 77/ values for Fe running at / = 25 and 100 A peak appeared to also follow an increasing trend with pulse length, both datasets were below the 50 A average trend line. This observation suggests that, at least for the case of Fe, operating the baseline VAT at / = 50 A peak represents a special case of VAT operation - a trend consistent with erosion and ICDD results. Indeed, test observations showing that the baseline Fe VAT delivers both its largest increase in thrust production (21.3% incr. in T/l to 262 μΝ/Α, tp = 2000 με) as well as its largest increase in erosion rate (71.6% incr. in E _r to 75.5 pg/C, tp = 2213 με) when operating at / = 50 A and ~2 ms long arc pulses, suggesting a correlation between the two effects.

Thrust tests results on the other cathode materials show some agreement with this argument. Reference is in this regard made to Figures 33-35. Figure 33 illustrates average thrust per current results for baseline VAT with an Al cathode operating at 50 A and 100 A peak arc current at various pulse lengths. A linear fit through 50 A data shows an increase in average thrust production with increasing pulse length from 141 μΝ/Α at 500 ps to 172 pN/A at 2000 ps (22.0% increase). Figure 34 illustrates average thrust per current results for baseline VAT with a Cu cathode operating at 50 A peak arc current at various pulse lengths. A linear fit through 50 A data shows an increase in average thrust production with increasing pulse length from 197 N/A at 500 ps to 246 pN/A at 2000 jus (24.9% increase). Figure 35 illustrates average thrust per current results for baseline VAT with a Bi cathode operating at 50 A and 100 A peak arc current at various pulse lengths. A linear fit through 50 A data shows an increase in average thrust production with increasing pulse length from 364 pN/A at 500 ps to 404 p /A at 2000 ps (11.0% increase). More specifically, Al showed no observable difference in T/l values for / = 50 and 100 A peak, whilst Bi at / = 100 A peak produced lower T/l values compared to 50 A. This behaviour of Bi could be attributed to the presence of additional neutrals or MP's in the plasma plume when operating the VAT at such a high cathode heat load, thus reducing the ion flux. This issue would be absent in Al, which has a higher capacity to absorb the heat load at high arc currents. Thus, a connection exists between the thermal load present during millisecond-long arc pulses and the production of ions (and thrust).

It should be noted that the thermal load at which the enhanced thrust effect becomes most significant is also governed by the size or surface area of the cathode being used. The broader implication is that long- pulsed VATs utilising cathodes of a certain size will be required to operate with a specific set of arc pulse characteristics (arc current level and pulse length) to experience the maximum effect of this enhanced thrust production mode. In this study, the maximum observed thrust benefit was attained within an operating region of / = 50 A peak arc current, tp = 2000- 4000 με on a cathode rod of 6.35 mm diameter.

(e) Proposed mechanism for enhanced ion and thrust production rates

Vacuum arcs emit significant amounts of neutral particles. This occurs not only from currently-active cathode spot emission sites, but also from previously-formed sites or craters long after the cathode spot has moved to a different location. This is because these sites are still sufficiently hot from the intense local heating by the vacuum arc to evaporate neutral particles. When the vacuum arc pulse exists up to a certain duration, there may be sufficient time for these excess neutrals to leave the surface, subsequently collide with and become ionised by surrounding plasma emitted from new spot emission sites. The result is an increase in the amount of ions available to provide additional plasma jet momentum. Since all cathode materials emit neutrals, this could explain why all cathode materials tested experienced an improvement in thrust production regardless of their vacuum arc plasma properties.

Increased CEX between ions of high and low charge states may also occur during longer arc pulses. This has the effect of lowering both the average ion charge state and energy of the plasma. Unfortunately, the degree of additional CEX that might be occurring cannot easily be measured with the present method of testing. This is because changes in the average charge state of ions cannot be detected by the PC probe and ion collector since the total charge of the plume remains preserved during capture. It is only the contribution of additional charge by CEX between ions and zero-charge neutrals (introducing "new" momentum-contributing particles into the plasma) that is being detected by the probes.

There are likely to be limits to which thrust production is enhanced under long-pulsed VAT operation. For example, operating at very long pulses (e.g. ≥5-10 ms) could result in an excess of neutrals and MP's due to increased heating of the cathode, potentially reducing ion production as suggested by the arrested growth of peak J in Bi ICDD data (see Figure 28). Excess neutrals may also significantly reduce the average ion energy such that the net momentum of the ions is reduced rather than enhanced. The effect that operating VATs at long arc pulses lengths has on average ion velocity remains unknown at this stage. Finally excessive cathode heating can lead to accelerated growth of the erosion rate, which is detrimental to the VAT's specific impulse.

(f) Overall performance

An overall view of the typical specific impulse performance of baseline VATs operating with long pulses is given in Table 10 below. For comparison, VATs operating with short pulses are also provided. Average erosion rate data was taken from Table 4, whilst average T/l data was obtained by interpolating against the average linear trend lines of Figures 32-35. Specific impulse values for each thruster are calculated using the following equation:

where I is the arc discharge current and g is gravitational acceleration. The total erosion rate Er is defined here (and commonly in vacuum arc science) as the fraction of net mass eroded Am per sum total of arc pulse charges fired by the thruster∑Q and is normally depicted in units of pg/C.

For example, in the case of Al(t _p = 156 ps), / _sp = (133.3/31.2)/9.81 x 10 ³ =436 s. t _p (//S) Til f/i.\ ^; /A) ^f E _f (/ig/C) hp (s) Diff.

AJ 156 133.3 31.2 436

+24.5%

1906 170.0 31.9 543

I½ 236 207.3 44.0 4SQ

-24.4%

2213 268.6 363

Cn 166 185.5 48.4 391

-29.2%

1420 226.9 83.5 277

Bi 185 355.0 945.5 38

-13.2%

2130 407.5 1267.4 33

Estimated by linear interpolation

Table 10: Comparison of thruster performance for selected baseline VAT designs for Al, Fe, Cu and Bi cathodes operating with short and long pulses. Peak arc current at / = 50 A.

In most cases, operating the baseline VATs with long arc pulse lengths did not guarantee an improvement in the specific impulse efficiency of the thruster. Although long-pulsed VATs generated appreciably higher thrust per arc current values (11.0-24.0%), their erosion rates were also significantly higher (typ. 34.0-73.0%) compared to short-pulsed VATs.. The net result is that despite the thrust improvement, the long-pulsed VATs were found to have 13.2-29.2% lower l _sp values. An exception is made of Al, which was able to maintain a stable erosion rate for both short and long arc pulse lengths. This meant that the baseline Al VAT was able to achieve a 24.5% increase in specific impulse (543 s) when operated with long pulses. This result is important because it shows that a greater erosion rate is not a prerequisite for a higher thrust production rate, i.e. the additional ion flux originates from neutrals that could already be present during "standard" VAT operating conditions (short pulses). This implies that any means of reducing the excess erosion rate due to the increased thermal load on the cathode surface could potentially allow a long-pulsed VAT to accomplish gains in both thrust production and specific impulse.

(g) Comments on surface contaminants and gas absorption

Studies by Yushkov & Anders (1998) (Yushkov, G. & Anders, a. (1998), Effect of the pulse repetition rate on the composition and ion charge-state distribution of pulsed vacuum arcs, IEEE Transactions on Plasma Science26{2), 220-226) found that the pulse repetition rate can affect the composition and ion CSDs of metallic vacuum arc plasmas. By operating at "standard" vacuum arc conditions (50-300 A, 250 ps) and low pulse frequencies (e.g. < 1-5 Hz), the plasma composition was found to tend towards a lower average ion charge state because of the absorption of residual gases and formation of oxide monolayers by the cathode surface between pulses. Vacuum levels were also shown to influence the formation time of monolayers, with poorer vacuums generating monolayers at shorter times. Vacuum test pressures used place monolayer formation time on the order of 0.3-0.5 s, i.e. 2-3 Hz for this work, which was close to the operating conditions experienced in a number of long-pulsed VAT thrust tests. Thus, surface contaminants could possibly result in lower average ion charge states, which may not be evident at higher vacuum levels (e.g. 10 ^"7 Torr). However, a comparison of several long-pulsed ICDD and thrust datasets operating either in this transitional pulse frequency region or at higher frequencies (e.g. 10 Hz) failed to show any detectable differences in ion production or thrust from one another, or showed behaviour contrary to what was expected of surface contamination effects. Additionally, lower average ion charge states would have resulted in a shift of ICDD data across all capture angles, which was not observed here. Thus, despite operating at low pulse frequencies, the performance of long-pulsed vacuum arcs did not appear to be significantly affected by the possible presence of residual gases and surface contaminants in this work.

Summary of pulse length experiment

This experiment has presented experimental performance data of long-pulsed VATs operating in a different manner to that seen in traditional short-pulsed VATs. New erosion rate, ICDD and thrust data on baseline VATs operating in the 150-4500 ps range of pulse lengths was obtained, extending available literature on the performance and behaviour of cathode materials under different pulse conditions. The previously untested VAT operating region was found to cause enhanced rates of ion and thrust production during millisecond-long arc pulse lengths, challenging conventional understanding of VAT operation and vacuum arc behaviour. In agreement with literature, cathode erosion rates were found to increase (significantly, in the case of Fe, Cu and Bi) with longer pulse lengths due to the increased cathode heat load. The experiment also showed that the erosion rate was largely governed by local heating of the cathode (pulse length) rather than average heat distribution (average arc power). The number of cathode spots present on the surface was also surmised to influence the cathode erosion rate in a way that higher arc currents (>100 A) can sometimes lead to a lower erosion rate due to better spot distribution and motion. ICDD measurements showed significant increases in captured ion charge of up 200% along the thruster centreline when operating with long arc pulses, indicating enhanced ion production. However, total ion current measurements found only up to a 16.6% increase during long-pulsed operation.

The previously assumed "standard" thrust correction factor range of 0.64 by Polk et al. (2008) (Polk, I., Sekerak, M., Ziemer, Schein, J. & Anders, A. (2008), A theoretical analysis of vacuum arc thruster and vacuum arc ion thruster performance, IEEE Transactions on Plasma Science36{5), 2167-2179) serves only as a rough guideline in the design of VATs . In reality the value of C _T was found to rely on a host of factors, such as the cathode material, the arc pulse length and the arc current.

Improvements in average thrust per arc current ranged from 1 1.0-24.9% depending on the cathodes material at I = 50 A peak. The significant increases in erosion rate for many of the cathode materials due to the increased thermal load present during long arc pulses was sufficient to overcome the thrust production gains and actually reduce the l _S p by as much as 29.2%. However, the performance of Al shows that / _sp gains are possible if the thermal load can be successfully managed. A region of maximum specific impulse operation likely exists for each cathode of a certain size (thermal capacity), material composition and arc pulse characteristics (current, pulse shape, length). The particular example found here was the use of arc pulses consisting of I = 50 A peak and tp « 2000 με, which was found to be a distinct test case across all types of measurements on the baseline VAT design, where the common denominator was a cathode of diameter 6.35 mm.

Example 2: Graphite-based cathode experiment

This experiment examines the novel use of carbon graphite compounds as cathode fuels for VATs. An assessment of erosion behaviour, ion current production and thruster performance was made on various carbon cathodes installed on the baseline VAT design.

Material list Several carbon-based cathode material candidates were explored, covering a variety of physical properties, micro structure and composition. Table 1 1 below lists the various grades and properties of the 6 (6.35 mm dia. x 50 mm long) carbon rods tested in this experiment. These rods were mostly sourced from suppliers of EDM- grade electrodes (EDM refers to Electric Discharge Machining), which are prepared specifically for arc-related industrial applications. In particular, POCO electrodes were chosen for their highly isotropic nature and lower porosity (< 0.1 m) over traditional graphites. Graphite compounds were also initially explored by testing copper- impregnated graphite compounds, which are comprised of a homogeneous mixture of copper and graphite micro-particles (estimated 15% Cu by volume according to the final sample material's density). Finally, glassy (or vitreous carbon) exhibits unique structural and thermophysical features compared to graphite, with noticeable features such as extreme hardness, zero porosity, impermeability to liquids and gases as well as being composed of nano-sized structures (fullerene).

Name & grade Supplier Avg. particle size Density Electrical resistivity

(pm) (g/cm ³ ) (μΩχηι)

Pure carbon

GC (G series} ^* HTW < 0.01 1.42 114

AF-5 POCO 1 1.80 1727

EDM-3 POCO 5 1.81 1372

EDM-200 POCO 10 1.82 1219

Copper-impregnated graphite ¹

TTK-4C Toyo Tanso 4 2.90 254

EDM-C3 POCO 5 3.05 305

EDM-C200 POCO 10 3.00 178

Glassy carbon

* Estimated 15% Cu by volume

Table 11: List of grades and properties of carbon rod materials tested in this study (data obtained from suppliers' websites). Carbon materials are grouped according to their composition, namely that of (1) pure carbon and (2) copper-impregnated graphite compounds. Materials are arranged in order of increasing average particle size.

Operating conditions and performance tests

Arc pulses of 50 A peak were exclusively applied to all carbon VAT tests. This was mostly because of ensuring restricted thermal loading on the cathode as well as a limitation of the pulse circuit components, which experienced difficulty in generating higher peak arc currents due to the higher resistance of carbon graphite cathodes.

Various VAT performance tests were conducted on each carbon or graphite cathode sample, capturing detailed measurements of thrust, erosion rate, total ion current and plume distribution (C-3 only). Thrust and most erosion tests were combined in a single test run, where the VATs were initially fired for up to approximately∑Q = 20 C with 10 short pulse measurements (≤ 500 ps) and then up to∑Q = 60-100 C with 20- 30 long pulse measurements (~2 ms). This was done to assess if any change in thrust production against arc pulse length was present. Visual inspection of cathode erosion behaviour on each sample was also performed.

Results and discussion a) Pure carbon graphite cathodes Figure 36 displays erosion patterns for pure carbon graphite sample cathodes resulting from the combined thrust and erosion tests (GC, AF-5, EDM-3, EDM-5). The erosion pattern on all graphite cathodes were observed to consist of deep craters (on the order of 0.5-1 mm) concentrated at the triggering edge of the cathode rod and tended not to extend further than roughly 1 mm from the insulator inner edge. The eroded surface roughness of GC was different to that of the other graphite cathodes. Apart from being largely restricted to the rod edge, its eroded surface was considerably finer, most likely due to the nano-sized structures and superior hardness of GC. Carbon cathode erosion behaviour was in stark contrast to the more uniform and distributed erosion of metal cathodes. This can be explained by considering the following:

Firstly, temperature has a unique effect on the resistivity of carbon graphite, which behaves in a manner opposite to metals, i.e. graphite becomes more electrically conductive the hotter it gets. The result is that cathode spots are discouraged from moving away from their locations and tend to "burrow" themselves into the bulk cathode body.

Secondly, spot motion is also discouraged by the typically low thermal conductivity levels (30-45 W/mK ¹ ) locally experienced by graphite material heated up by the high temperature cathode spots. This means that surface conditions for subsequent cathode spot generation are most suitable close to the previously extinguished hot crater site and least suitable far away on the colder bulk body surface.

Thirdly, graphite does not melt, but instead sublimates. In metals, the molten state of freshly-made craters causes the surrounding metal to flow, spread out and blend back into the bulk cathode surface. This material behaviour is absent in graphite.

Finally, the formation of deep craters widens the gap between the cathode and insulator, further isolating the central core of the cathode body from stable vacuum arc processes.

Figure 37 displays thrust measurements for the pure carbon materials tested in terms of thrust per arc current T/l and thrust-to-power ratio T/P for typically 6000 pulses. For much of the test, thrust production of GC and AF-5 remained relatively constant at 380 pN/A with a few intermittent "spikes" of high and low values. This was in contrast to EDM-3 and EDM-200, which showed a decline of thrust per current levels (450 μΝ/Α to 300 μΝ/Α) as the total number of pulses increased. Additionally, EDM-3 results were more erratic and EDM-200 thrust production showed a gradual increase near the end of its test (80-110 C). Thrust- to-power levels were initially very high (up to 36 μΝ W for GC, ~ 16 μΝ/W for the rest of the group) and showed a rapid decline to 5-8 μΝΛ/V at the end of the test run. In contrast to metallic cathodes, no discernible changes in carbon's thrust production was observed between short- and long-pulsed operation. However, this difference could be partially obscured by the effect of the fast-receding cathode. Nevertheless, these results support the view that increased thrust production at long pulses is due to greater amounts of CEX between ions and neutrals reducing the average ion charge state. This is because C ions from a pulse vacuum arc were previously measured in literature to be almost entirely singly charged, i.e. Z = 1 (Yushkov & Anders 1998, Brown 1994). Thus, further lowering of Z using longer arc pulses is not possible in this case, with the expected result that thrust production remains constant regardless of arc pulse length.

The negative effects of deep crater erosion on the emission of plasma flux and arc voltage was evident in Figure 37, where thrust production of EDM-3 and EDM-200 underwent a decline over time as the cathode spot became more receded into the cathode body. This effect is further exasperated by the low density of graphite rods. Eventually, a relatively stable thrust value was approached, likely due to the depth limit of the craters being reached. Intermittent bursts of high thrust values can be explained by the cathode spots travelling back to the top of the cathode surface and generating more plasma, before eroding part of the surface away and quickly receding into deep craters again. Erosion uniformity is obviously affected by the size of the cathode. For example, a smaller cathode would experience better erosion characteristics since the erosion "zone" would occur over much large portion of the cathode surface. However, cathode recession would also occur at a higher rate, not to mention increased thermal loading on the smaller cathode body. Copper-impregnated graphite

Figure 38 displays erosion patterns on copper-impregnated graphite cathodes resulting from the combined thrust and erosion tests. Erosion behaviour of copper-impregnated materials exhibited a blend of metal and graphite erosion characteristics. Although each material developed a large shallow crater (3-4 mm in length and 1-2 mm in breadth) on one side of the cathode, spot coverage was seen over the entire surface area with significantly greater uniformity than that of the pure carbon samples. The surface of C-3 possessed fine erosion structures likely due to its smaller particle sizes (compared to C-200) and lower porosity (compared to TTK-4C). The inclusion of Cu micro-particles was therefore shown to improve the thermal characteristics of the cathode compound such that spot coverage was visibly increased, leading to better erosion characteristics.

It is speculated that melting of copper micro-particles within copper-graphite compounds by the heating action of the cathode spot(s) may help to bind surrounding carbon particles together, mitigating thermal shock and rod cracking. The fact that the bulk cathode body is comprised entirely of microscopically-sized particles may also assist in limiting the emission of large macroparticles. Figure 40 displays measured thrust results for copper-impregnated graphite compounds also in terms of T/l and TIP. As with pure cathodes, no discernible changes in thrust production were observed between short- and long-pulsed operating regimes. However, thrust production values and behaviour were different compared to pure carbon cathodes, following similar thrust trends overtime to pure metal cathodes (see Figure 39). For example, thrust production of TTK-4C remained almost steady at an average value of 267 μΝ/Α, which was more than 40% lower than average thrust production values of GC and AF-5. Although TTK-4C's thrust-to-power declined in a similar manner to pure graphite cathodes (8 μΝ/VV to 4 μΝ/W, especially after∑Q = 60 C), thrust-to-power ratios for C-3 and C-200 remained relatively stable at roughly 6 μΝ W, a behaviour not seen in the pure carbon graphite cathodes.

Another difference in thrust behaviour between pure and copper-impregnated graphite cathodes was observed with samples C-3 and C-200, which both initially generated low thrust values close to 200 μΝ/Α. Over time, both materials showed a gradual increase in thrust production, reaching intermittent values in excess of 400 μΝ/Α. To further illustrate this, Figure 41 compares thrust production over time for both EDM-3 and EDM-200 cathodes and their respective copper- impregnated counterparts (C-3 and C-200). Each material test began with different starting levels of thrust, but appeared to converge to similar thrust production levels by∑Q= 50 C. Thus, it is shown that the presence of Cu does not negatively affect thrust production within carbon graphite cathodes over long- term VAT operation.

The presence of a compound mixture of elements within a cathode might provide synergistic benefits. Recently, Zhirkov et al. (2013) (Zhirkov, L, Eriksson, A. & Rosen, I. (2013), Ion velocities in direct current arc plasma generated from compound cathodes. Journal of Applied Physics 114, 213302) found that the presence of a high cohesive energy material such as C within a Ti-C compound cathode resulted in plasma with higher average and peak ion energies than the native ion energies of the two elements alone and independent of the ion mass. This was explained by plasma quasi-neutrality and higher pressure gradient generated within the plasma. Thus, it is possible that the Cu ions in C-3 and C- 200 are accelerated to higher velocities than seen in pure Cu cathodes (which have lower thrust production compared to pure graphite), allowing C-3 and C-200 to achieve equal or higher final thrust per arc current values over the pure graphite cathodes. Erosion rate

Figure 42 presents erosion results for all graphite samples tested over a range of pulse lengths. It should be noted that all long-pulsed results (≥500 με) presented here (except for C-3) are weight-averaged from carbon thrust tests, which used both short and long pulses. Three distinct groupings of results can be made. The first group are the majority of pure graphite cathodes, which possessed average E _r values close to ~42 pg/C. This shows that the particle size (1-10 pm) within the pure carbon cathodes has a weak influence over the erosion rate. A unique feature of the graphite cathodes was their relatively constant erosion rates over the tested range of pulse lengths. This meant that these cathodes were relatively insensitive to the increased heat load at longer pulse lengths and hence did not generate more MP content because no additional melting of the bulk cathode occurred (Graphite cathodes still produce MP's despite sublimating, most likely resulting from various-sized pieces of cooler solid material being released by the explosive and violent nature of the vacuum arc). The second group is GC's results, which contain the highest set of values of all the carbon cathodes tested here (average of 46.2 pg/C). A small increasing trend of erosion rate with pulse length was observed, a behaviour similar to metals, but opposite to that of the rest of the carbon samples. The third group are the copper-graphite compounds, which delivered the lowest erosion rates in the long-pulse regime (33.4-39.3 pg/CJ. However, these compound cathodes showed increases in erosion rate when operated at short pulses (8.7% increase for TTK-4C and 50.9% increase for C-3). Figure 43 plots various carbon cathode samples in relation to their properties

(average particle size, electrical resistivity) and resulting long-pulsed erosion rates. Data reveals that Er experiences small reductions in both sets of pure and copper-impregnated graphite rods (4 and 12.3% respectively) as the material's electrical conductivity (opposite to resistivity) and average particle size decreases. This result is in agreement with Kandah & Meunier (1996, p. 525)

(Kandah, M. & Meunier, J. (1996), Erosion study on graphite cathodes using pulsed vacuum arcs, IEEE Transactions on Plasma Science 24(2).) who found that factors such as porosity and grain size can influence cathode spot motion and velocity over the cathode surface, where larger pore sizes can result in slower spot velocities, resulting in higher erosion rates.

Further evidence for the effect of micro structure on erosion rate was seen in a comparison between the compositions of C-3 and C-200, where C-3 contained micro-sized particles of Cu and C closer to or smaller than the characteristic cathode spot size normally seen on carbon. The presence of a small-sized cathode surface micro structure may produce the effect of appearing homogeneous to the cathode spot, "fooling" it into behaving as if it were on a conventional "smooth" metallic cathode. This can result in higher spot velocities and hence a lower erosion rate. The higher erosion rate of TTK-4C is suspected to be due to different quality of porosity or particle isotropy between the Toyo

Tanso and POCO samples.

An exception is made of GC, which has a different structural form (fullerene) compared to graphite (polycrystalline). This structural difference can significantly influence the thermal properties of the material. For example, despite its low resistivity and sub-micron structures, GC has a very low thermal conductivity (6.3 W/mK at room temperature) compared to EDM graphites (69-121 W/mK at room temperature; 30-45 W/mK at 2000 K). Coupled with the highly localised erosion seen at the triggered cathode edge (see Figure 36), intense thermal conditions are considered to be the most likely cause of GC's higher erosion rates.

ICDD measurement An ICDD test was done on a copper-graphite compound sample, which produced improved uniform erosion that would make a ICDD fit possible. Test material C-3 was chosen and its ICDD measured as shown in Figure 44 (typically pulse conditions are l=50 A peak, t _p =1.4 ms, f=2 Hz). Test results revealed a Gaussian distribution, but also showed significant scatter in data points, possibly due to the variable properties of each Cu and C ion species. Only J along the yaw axis was measured due to large scatter and shortening of the pulse length during the ICDD test. On average, a high thrust correction value of C _T = 0.757 was obtained, albeit with a large uncertainty of ±0.197. Thus, a graphite-based cathode material was shown to produce a relatively widely-spread plasma plume that resulted in a thrust correction factor only slightly higher than measured for a typical metal cathode under the same pulse length (see Table 8).

Overall performance

A summary of VAT thrust and erosion rate results (long-pulse) provided in Table 12 below reveals that carbon graphite cathodes produced high average thrust per arc current values (267-383 μΝ/Α) and similar or better erosion rates (33.4-49.2 Mg/C) compared to metal cathodes. Thrust-to-power ratios (4.9-12.8 μΝ/W) and thruster efficiencies (1.7-4.8 %) were on the order of or better than that measured for a mid-performance metal like Fe (see also Table 13 below).

Til (μΝ/Α) TIP ( Ν/W) hp (s) η {%)

GC 49.2 372 12.8 771 4.8

AF-5 40.4 383 9.6 966 4.6

EDM-3 42.3 378 6.6 911 2.9

EDM-200 42.1 350 8.0 847 3.3

TTK-4C 39.3 267 7.7 693 2.6

C-3 33.4 327 5.1 998 2.5

C-200 38.1 298 4.9 797 1.9

Fe (/p = 658 _s) 56.6 221 10.5 398 2.0

Table 12: Summarised performance test results for long-pulsed baseline VATs with pure and copper-impregnated graphite cathodes. Thrust per arc current, thrust-to-power ratio and impulse per pulse energy results are weight-averaged against delivered charge per test sample for a total population sample from∑Q = 0 to 80 C. Fe baseline performance as measured and set out in table 13 below is provided for comparison.

Performance metric Al Fe Bi

Thrust per arc current, 77/ (μΝΙΑ) 117 (161) 221 (181) 502 (449)

Thrust-to-power ratio, TIP (pNI W) 3.2 (6.8) 10.5 (8.0) 42.5 (28.8)

Specific impulse, l _S p (s) 382 (584) 398 (385) 40 (217)

Efficiency, ?7 (%} 0.6 (1.9) 2.0 (1-5) 0.8 (3.1)

Table 13: Comparison of weighted-averaged measured and empirically predicted performance results for baseline VAT tests using Al, Fe and Bi cathodes (predicted results in brackets)

Specific impulse values of / _sp = 693-998 s for carbon graphite materials were calculated to be in the order of 50-250% higher than a typical baseline metal cathode as measured in this study. This finding shows that carbon-based cathodes are amongst the highest performing fuels that can be used in a VAT. More importantly material C-3, which delivered the highest l _sp value of any other cathode material in this experiment, also achieved the highest experimentally- verified / _sp value of any VAT fuel reported in prior literature, which the Inventor is aware of.

The small differences in average thrust production between pure graphite materials in Table 12 suggest that plasma production is weakly affected by the cathode material's structural properties. This is expected given that the plasma composition is identical across all cases (that is, only C ions). However, the cathode micro structure appeared to, if briefly, significantly affect the operating arc voltage of the cathode material. For example, compare the initial thrust-to- power ratios between GC and the pure graphite materials in Figure 37. GC, with its nanostructure, showed a very high thrust-to-power ratio (36 μΝ/W) at the beginning of its thrust test, until cathode erosion increased the VAT's interelectrode gap. On the other hand, AF-5, EDM-3 and EDM-200 produced lower (but still good) initial thrust-to-power ratios (~16 μΝ/W). These preliminary results hint that a finer cathode micro structure may help to lower the operating arc voltage and improve thruster power consumption.

In contrast to pure graphite, different grades of graphite compounds produced varying levels of average thrust production. For example, TTK-4C produced only 81.7 % of the thrust generated by C-3, despite having similar average particle sizes. This suggests that some other factor is affecting thrust production. One possibility may be related to the MP production from each material, where TTK- 4C produces a 17.7% higher erosion rate than C-3. These additional MP's may impede the outgoing plasma flux, causing a lower thrust value. Summary of results

The novel use of glassy carbon, graphite and metal-impregnated graphite compounds as cathode fuel for VATs was successfully demonstrated and their performance characteristics measured. Each type of carbon was shown to possess unique cathode performance and erosion behaviour based on its set of thermal, electrical and micro-structural properties.

The erosion behaviour of these carbon graphite cathodes is clearly different to those comprised of pure metals. Deep craters were typically seen in pure carbon and graphite samples, whilst the modest inclusion of a highly-conductive metal to graphite (15% by volume) enabled surface erosion characteristics similar to that of metals. By improving the thermal properties of graphite cathodes and increasing spot motion, erosion rates as low as 33.4 pg/C (material C-3) could be accomplished. The erosion rate of carbon cathodes was generally robust against the arc pulse length and showed general agreement with literature. Surprisingly, E _r trends for copper-impregnated graphite were opposite to that of metals, generating higher E _r at short pulses and lower E _r at long pulses. Interpreting these results in conjunction with previous studies suggests the possibility that operating at even longer pulse lengths (on the order of seconds) may lower cathode erosion rates even further.

Average thrust production from pure carbon graphite cathodes (350-383 pN/A) was significantly higher than predicted by the empirical model (262 μΝ/Α). Reasons for this are not clear at this stage, where measured improvement in the thrust correction factor of 18.3% to give Cr= 0.757 can only account for roughly half of the enhanced levels of thrust production observed. Copper-impregnated graphite cathodes also generated high average thrust production levels (267-327 μΝ/Α), but showed a gradual increase in 77/ over the test duration compared to the gradual thrust decrease seen in pure carbon cathodes (due to deep crater formation). This places metal-graphite compounds at an advantage over pure- carbon graphite cathodes in maintaining good thruster performance over long operating times.

All carbon graphite cathodes generated very high thruster performance, with some producing excellent initial thrust-to-power ratios and specific impulse values amongst the highest seen in VATs (16-36 μΝΛ/V, 700-1000 s). As mentioned, it may be argued that material microstructure and composition played a prominent role in determining cathode performance. Materials comprised of a combination of fine micro structure and possessing high electrical resistivity were generally found to deliver high levels of thrust per arc current and low erosion rates.

Finally, the time-dependence of carbon graphite VAT performance was seen in thrust data, where the arc voltage was noticeably lower, often by more than half, at the beginning of the thrust test and quickly rising as thruster operation progressed. This was likely due to the quick erosion of cathode material away from the triggered edge as well as the formation of deep craters, both of which increased the inter-electrode surface gap between the VAT electrodes. Example 3: Anode switching experiment

Description of anode switching setup

In one example, only the three anode elements 20.1 -20.3 were used and controlled independently to generate vacuum arcs while the other anode elements 20.4.-20.6 are disconnected from the control arrangement 22 (i.e. dead) (see specifically Figures 2a and 3). In another example three anode element pairs (20.1 , 20.5; 20.2, 20.4; and 20.3, 20.6) were controlled independently (see Figure 2b).

In the example illustrated in Figure 2a, a first anode switching pattern was implemented by activating each of the three anode elements 20.1-20.3 spaced equally apart in a repetitive circular sequence. The remaining three anodes 20.4-20.6 were kept inactive (or "dead") and played no role in the vacuum arc other than to restrict plasma from exiting the side of the VAT 10. The "dead" anodes 20.4-20.6 were not connected to the conducting film or PVN 24. This mode of operation was observed to cause the cathode spots to move in a typically triangular fashion. In this regard, reference is specifically made to the black dots and arrows in Figure 2a which represent cathode spot(s) and their expected forced motion over the surface at various stages in the anode switching sequence according to a triangular motion with three active anode elements 20.1 -20.3.

The second anode switching pattern (see Figure 2b) consisted of three connected pairs of anode elements (20.1 , 20.5; 20.2, 20.4; and 20.3, 20.6). This configuration allowed all six anode segments/elements 20 to be controlled with only three anode switching commands. By connecting two oppositely-facing anode segments/elements into a pair, the first segment/element (with conducting film installed) (e.g. 20.1) triggered the beginning of the arc pulse. During the arc, plasma filled the near- cathode region and allowed the second segment/element (with no conducting film installed)(e.g. 20.5) to become electrically active as well. Eventually, the second segment/element 20.5 became favoured as the primary current-carrying anode due to the lower electrical resistance between it and the cathode 14, with the plasma acting as a conducting bridge. Thus, the desired result is to force the arc spot(s) to travel in a crossed-shaped pattern, following each preferred anode segment/element 20 with each cycle. In this example switching times (T^ of 45, 120, and 520 με were chosen when running the DAS technique (see further below) for VATs 10 operating with pulse lengths of 200-2000 [is long. This was done in order to encourage the arc spot(s) to "follow" the active anode 20 within a single arc pulse. The switching circuit/network 26, in this example, is a DAS switch control system (SCS) which comprises of a set of three IGBT transistor switches 28.1-28.3 which are connected to the PVN 22 in order to control its power output to the three anodes 20.1- 20.3. Each switch 28.1-28.3 includes a transistor (Q1 , Q2 and Q3) and is powered by an electrically floating gate driver (G1 , G2 and G3). Commands to each gate driver (G1-G3) are sent from a microcontroller (S1 , S2 and S3) (e.g. an Arduino microcontroller).

Instructions (e.g. anode switching times (discussed further below)) may be sent via a PC which is connected to the microcontroller (S1-S3). Optocouplers (U1 , U2 and U3, model H11 L1M-FC) is used to isolate the microcontroller electrically from the SCS. A cache of 9 V batteries (V1 , V2 and V3) are used as floating voltage sources for the optocouplers (U1-U3) and gate drivers (G1-G3). The gate drivers (G1-G3) and IGBT transistor switch 28.1-28.3 components used may be the same model types as for the PVN 24 (see the transistor Q4 and gate driver G4). Current- and voltage-limiting resistors for the optocouplers (U1-U3) and gate drivers (G1-G4) are merely omitted from the schematic in Figure 5 for visual clarity. Battery power for each optocoupler is also omitted for the same reason. It should be noted that the arc voltage being measured here includes the voltage drop across the anode IGBT transistor switches 28.1-28.3. This makes the measured arc voltage conservatively a few volts higher than the potential drop between the anode and cathode electrodes 20, 14.

Due to inherent speed restrictions in the microcontroller, a single command to the anodes to switch states took 20 ps to be executed. A lower anode switching limit of 40 ps was therefore dictated by the current switching control system (SCS) used. To protect the SCS and VAT pulse circuit/VPN, a transitional phase was applied between each anode switching step, where both the prior anode element and the next anode element in the switching sequence were both active for a brief period (T2) of 20 ps before fully transitioning to only the next anode element being active and deactivating the prior anode element in the switching sequence. Therefore, each anode element (or anode element pair) was active on their own for periods of Δ T = 5, 80 and 480 ps.

Figure 45 shows the anode signal switching timeline used for both the triangular and cross-shaped patterns where

T1 = T2+ Δ T +T2

In Figure 45, S1-S3 indicate the three anode signals where T1 is the anode active switching time (45, 120 and 520 ps), T2 is the transition time (20 ps) and ΔΤ is the dedicated anode activation time (5, 80, 480 ps).

The SCS was linked to the VAT pulse circuit trigger signal such that it would only begin switching once the VAT circuit (i.e. the VPN) began powering the VAT 10. The SCS was also configured to disconnect the VAT 10 from the pulse circuit after a short period of time to ensure that arc current did not continue flowing through the VAT longer than desired. For example, after firing arc pulses of 500 ps long, the SCS kept the anode side of the circuit open for 250-500 ps for a total VAT closed-circuit duration of 750-1000 ps.

Test methodology for anode switching setup

Initial tests showed that the cross-shaped anode switching pattern produced better surface coverage and more uniform erosion of the cathode surface. Therefore, the majority of test results presented here made use of the cross-shaped anode switching pattern. The graphite film at the inter-electrode interface was rebuilt anew prior to each VAT test to ensure consistent and repeatable thruster operation. Erosion rate tests were performed for a range of switching times (45, 120, 480 ps), cathode materials (Al, Fe, Bi, AF-5, C-3), arc pulse currents (25, 50 A) and pulse lengths (200-2000 ps) to characterise the effectiveness and limits of the DAS technique. Finally, a thrust test was performed on one of the discrete anode VAT designs to verify that the DAS technique did not negatively interfere with plasma production.

Experimental results (a) Erosion behaviour across different cathode materials

The DAS technique was tested on a variety of cathode materials to assess its effect on erosion behaviour. Figures 46 and 47 present erosion patterns on several cathode samples (Al, Fe, Bi, AF-5 and C-3) operating with DAS (120 ps switching time, crossed pattern). Short pulses (300-400 ps, 5 Hz) were especially used to observe the limits of erosion coverage.

Each material experienced a net eroded mass loss of 2.4-3.9 mg (except Bi, Am =28.5 mg).

Figures 46a-c illustrate erosion patterns on Al (46a), Fe (46b) and Bi (46c) cathodes subjected to discrete anode switching (120 ps switching time, crossed pattern). Levels of erosion are labelled according to severity. A high-contrast image of each cathode provides an approximate visual indication of cathode spot erosion coverage. Pulse characteristics are /=50 A peak and t _p =300-400 ps long.

Figures 47a-c illustrate erosion patterns on AF-5 (47a) and C-3 (47b) graphite cathodes subjected to discrete anode switching (120 ps switching time, crossed pattern). Levels of erosion are labelled according to severity. A high-contrast image of each cathode provides an approximate visual indication of cathode spot erosion coverage. Pulse characteristics are /=50 A peak and t _p =300 ps long. Significant differences in erosion behaviour across the range of cathode materials were observed. The level of spot motion and extent to which the spots spread out over the surface could be attributed to the varying thermal conductivities of the materials studied. For example, Al (high thermal conductivity, Figure 46 (a)) demonstrated very good erosion coverage, whilst Bi and AF-5 (low thermal conductivity, Figure 46(c) and Figure 47(a) respectively) maintained poor coverage with most erosion craters occurring close to the triggered edge. Fe and C-3 (medium-to-low thermal conductivity, Figures 46b and 47b respectively) showed moderate coverage with an untouched central area of the cathode surface. Thus, the material-dependant "stickiness" or mobility of the cathode spots determined to a large degree the effectiveness of the DAS technique to induce spot motion.

The number of cathode spots present on the surface did not appear to affect coverage. For example, although a large number of spots were present in Bi, the majority of craters appeared closely located. In contrast, Al showed good erosion coverage despite only having a single arc spot. It is surmised that the self-magnetic field within the spots was insufficient to cause spot spreading due to the low arc current level used in these tests (/ = 50 A peak). Thus, operating at higher arc currents (e.g. 100-200 A peak) may improve the effectiveness of the DAS technique by forming a greater number of spots and encourage spot spreading on the cathode surface.

(b) Switching limits

A preliminary test/experiment was performed to determine some of the operational limits to which the DAS technique would influence the cathode erosion rate. Conservative VAT tests were run on a Fe cathode with low peak arc currents (25 A), short pulses (~250 ps) and low average power levels (1-2 W). A large range of switching times were tested, ranging from as little as 0.5 pulse per switching operation (120 ps) up to 50 pulses per switching operation. For reference, erosion tests were also performed for VATs with (1) all discrete anodes connected as a common anode and (2) the standard ring anode. The results of the tests are presented in Figure 48. Figure 48 illustrates erosion rate results demonstrating lower limits of operation and switching times of DAS technique applied to baseline VAT design with an Fe cathode. Pulse characteristics are /= 25 A peak, £ _p =200- 330 ps pulse lengths and 1-2W average thruster power. A node triangular switching pattern was used in this case.

Figure 48 shows that the manner in which DAS is implemented is important. Operating at fast switching times of 0.5 to 1 switching operation per arc pulse (120 and 520 ps respectively) showed no improvement to the erosion rate compared to the standard VAT design. Thus, results suggest that DAS is ineffective for VATs operating at low arc currents and short pulses. Furthermore, operating with 5-50 pulses or even no switching for each discrete anode produced worse erosion rates over the standard ring design (16.6-68.8% higher). This occurred because spot motion was restricted to a local area of the cathode surface closest to the active anode segment, increasing local temperatures and (likely) MP (macro-particle) production. Thus, operating with at least one switching operation per pulse is recommended when implementing the DAS technique in VATs.

(c) Effect of DAS with varying arc pulse length As already discussed, the pulse length can have a strong influence on cathode erosion rate during nominal VAT operating conditions. With this in mind, a study of different DAS switching times was applied to a Fe cathode operating with peak arc current I = 50 A for a range of pulse lengths. Figure 49 provides a map of erosion rate results for 45, 120 and 520 ps switching times at short and long pulse lengths. More specifically,

Figure 49 shows erosion rate results for different switching times as a function of arc pulse length. Tests were performed on an Fe cathode running at /=50 A peak. Erosion results for a baseline VAT operating with a standard anode ring, is included for comparison purposes.

Applying the DAS technique at short pulses (≤ 500 ps) did not show any improvement to the erosion rate (DAS results follow the same interpolated line of baseline VAT results). This may be interpreted such that DAS was unable to increase spot motion beyond the spot mobility limit of the cathode material. However, the DAS technique was successful in achieving reductions in the cathode erosion rate when operating with long pulses (1.5-2 ms). As expected, smaller switching times showed greater reductions in Erosion E _r (520 ps→ 5%, 120 ps→ 11%, 45 ps→ 24%, estimated by comparing the interpolated Er results of the baseline VAT at equivalent pulse lengths). Erosion rate data also suggested that the effectiveness of the DAS technique improved as the pulse length increased, successfully distributing the increased heat load on the cathode surface to a level similar to that present during short pulsed operation.

These experimental results support the view that the erosion rate of a cathode depends more on the heat load within the local spot vicinity than that averaged over the cathode surface. A possible and significant consequence of reduced melting and erosion is the mitigated production and release of MP's.

(d) Thrust

Thrust measurements on a Fe cathode operating with DAS (45 ε switching time) is shown in Figure 50. More specifically, direct thrust measurements for Fe cathode operating in long-pulsed mode with and without DAS implementation are illustrated in Figure 50. Baseline thrust data was obtained from Figure 32 with error bars omitted for visual clarity. DAS-enhanced VAT operating conditions were /= 50 A peak, f=6 Hz, 45 με switching time (crossed pattern) run up to a total charge of ∑Q= 92.5 C. The thrust measurements revealed that a DAS-enhanced VAT generated

21.6% higher average levels of thrust production over a baseline VAT operating at the same average pulse length (319 μΝ/Α vs. 262 μΝ/Α at t _p = 1997 MS). This result shows that the thrust-production benefits of long pulsed operation can be sustained and even improved whilst simultaneously mitigating the higher operating heat loads and keeping the erosion rate low (in this test, measured Er = 53.0 ±1.1 g/C). The additional increase in average thrust levels could be explained by the reduced production and presence of MP's, which tend to absorb or impede the ion flux.

In light of the above (1 ) the action of increased spot motion has no observable negative effect on thrust production, and (2) it is the additional ionisation of neutrals, and not necessarily the added heating, melting and erosion of the cathode during long arc pulses, that determines the increased production of thrust.

(e) Overall performance Table 14 below compares specific impulse performance for (1) short- and

(2) long-pulsed baseline VATs as well as for (3) a DAS-enhanced VAT. Average thrust per arc current values for cases (1 ) and (2) were obtained by interpolating against the average linear trend lines of Figure 32, whilst average erosion rate values for case (2) was obtained by linear interpolation of Erosion (E _r ) values in Figure 26. As expected (and discussed earlier), the long-pulsed baseline VAT suffers from a 22.1 % drop in l _sp due to the large increase in E _r when compared to the short- pulsed VAT. However, the DAS-enhanced VAT was successful in achieving a significant overall positive gain in l _sp of 614 s - signifying a 27.9% higher specific impulse compared to the short-pulsed baseline design and 50.0% higher specific impulse over the long-pulsed baseline design.

Fe VAT design Tp (/ S) 17/ (μΝ/Α) E _r ( tg/Q hp (S) Dlff.

Baseline (short) 156 207 ^† 44.0 480

Baseline (long) 1997 262 ^† 71.4 ^* 374 -22.1%

DAS, 45 μβ switch 1997 319 53.0 614 +27.9%

^T Estimated by linear interpolation of Til trend line in Figure 32. * Estimated by linear interpolation of E _r values in Figure 26.

Table 14: Comparison of thruster performance

It is unknown if an upper limit exists for DAS-induced spot motion and its improvement to overall thruster performance. Under general VAT operating conditions, this limitation is expected to depend (in approximate order of influence) on (1) the cathode material's thermal conductivity, (2) the arc pulse length, (3) the DAS' switching time, (4) the arc current level, (5) the number of cathode spots present and (6) the cathode body's average temperature. In contrast, the influence of magnetic fields to steer cathode spots (as widely reported in literature and used in industry) appear to be of sufficient strength to overcome many of the above- mentioned factors. Results of anode switching experiment

The discrete anode switching technique was successfully demonstrated to be a novel and feasible method of controlling the erosion behaviour of a VAT. However, a number of factors limited the effectiveness of DAS implementation. For example, the arc current and anode switching frequency must be sufficiently high to generate appreciable spot motion, and the switching time preferably shorter than the arc pulse duration. The cathode material's thermal conductivity determined to a large degree the amount of erosion coverage or spot mobility present on the cathode surface. Highly conductive materials such as Al demonstrated excellent spot mobility, whilst low conductive materials such as Bi exhibited poor mobility. The relationship between cathode spot mobility and material thermal conductivity, which was not explicitly characterised in VATs until now, has wider implications for ensuring good cathode erosion behaviour in a VAT design. Reductions of up to 24% in erosion rate were achieved when DAS was used at long arc pulses, whilst no improvements were observed during short pulses regardless of switching frequency. This suggested that the material's characteristic spot mobility limit had a dominant influence during short- pulsed operation of the VAT. Thrust tests on the DAS-enhanced Fe VAT confirmed that anode switching or forced spot motion alone does not negatively affect thrust, but can actually improve it by more than 20%. The thrust test also answers a number of questions raised in the pulse length experiment about the nature of increased thrust production of VATs under long-pulsed operation and mitigating the negative effects of the inherently higher thermal load on the cathode erosion rate and overall thruster performance. The DAS technique was able to increase the Fe VAT's specific impulse by up to 27.9 % over the short-pulsed baseline design. In the light of the analysis set out above (including all three experiments), the Inventor believes that the implementing of an anode switching process (described above) in VATs, can lead to the VATs having improved performance characteristics. In addition, the extension of the pulse lengths and the presence of graphite in the cathodes can also contribute to improving the performance characteristics of VATs.