Radial feeding mechanism for a micro-cathode arc thruster

Abstract

A side feeding micro cathode arc thruster (SF-micro-CAT), and an enhanced, circular (axi-symmetric) micro-CAT, each developed for micro-propulsion applications. SF-micro-CAT can include a cuboidal anode, an insulator, and a spring-loaded titanium wire cathode (propellant consumed per pulse) powered by a traditional inductive PPU (power processing unit) circuit. The spring-loaded feeding mechanism allows the cathode to be consumed during operation, providing a continuous supply of propellant. In one embodiment, an arc thruster includes a central anode; a plurality of cathodes, each having a leading end and each extending radially outward from the central anode; an insulator positioned between the central anode and the leading end of each of the cathodes to form a gap therebetween; and one or more feeding mechanisms coupled to said cathodes, where the feeding mechanisms push the leading end of each cathode toward the central anode.

Description

DOCKET NO. 130761-00533 PATENTRADIAL FEEDING MECHANISM FOR A MICRO-CATHODE ARC THRUSTERRELATED APPLICATION

[0001] This application claims benefit of priority of U.S. Provisional Application No. 63 / 634,614, filed April 16, 2024, entitled “Cathode Side-Feeding in Micro-Cathode Arc Thruster;” the entire content of which is relied upon and incorporated herein by reference in its entirety.GOVERNMENT LICENSE RIGHTS

[0002] This invention was made with Government support under Grant / Contract No. FA9550-23-1-0278 awarded by Air Force Office of Scientific Research (AFOSR). The Government has certain rights in this invention.FIELD

[0003] The present disclosure relates generally to a novel propellant feeding mechanismbased micro cathode arc thruster, and more particularly to a side feeding micro cathode arc thruster (SF-pCAT) and a radial arrangement of a SF-micro-CAT (an axi-symmetric microCAT), all developed for micro-propulsion applications.BACKGROUND

[0004] The advancement of small satellite technology has led to an increasing demand for efficient and compact propulsion systems capable of meeting the unique requirements of small spacecraft, such as CubeSats. Among the various propulsion options available, the micro cathode arc thruster (pCAT) has emerged as a promising solution for micro-propulsion applications.

[0005] The compact size and lightweight design of the pCAT make it ideal for small satellites. With low power requirements, typically ranging from 0.1 to 10 watt, pCAT’s can operate effectively within the limited power resources available on these small platforms. They use the cathode material as propellant, which is ablated and ionized during operation, providing a continuous supply of thrust and enhancing efficiency. Additionally, pCAT’s generate thrust in the micronewton range, allowing for precise attitude control and orbital maneuvers that are essential for accurate positioning and stabilization in space. Their relatively simple design reduces manufacturing and maintenance costs, while the technology's scalability enables customization to meet specific mission requirements. Proven in various1130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT missions, [1], [2], [3], [4], pCAT’s have demonstrated reliability and effectiveness, further solidifying their potential for future space exploration.

[0006] Despite their advantages, pCAT’s face several challenges, including concerns related to operational lifetime and efficiency. Due to lack of an efficient propellant (cathode) feeding mechanism, the operational lifetime of pCAT is limited to one million pulses, thus hampering their ability for long missions that require a higher number of pulses [5], Research on pCAT is focused towards developing an efficient way to feed the cathode to enhance its operational lifespan.

[0007] Previously proposed feeding mechanisms have successfully extended the lifespan of these thrusters to a couple of million pulses. Zhuang et al. [6] introduced a co-axial pCAT design that incorporates a spring at the back of the cathode, which continuously pushes the cathode forward, while a shoulder on the insulator prevents the cathode from being pushed too far. Hurley et al. [7] explored the feeding mechanism of a Linear Actuated pCAT, which has a stepper motor to consistently advance the central cathode, ensuring continuous ablation. This linear pCAT achieved thrust levels and thrust-to-power ratios ranging from 3-7 pN and 3-6 pN / W, respectively, with a lifetime of approximately one million pulses.

[0008] To facilitate controlled propellant feeding, Kronhaus et al. [8] developed an inline- screw-feeding vacuum arc thruster (ISF-VAT), which features a mechanism that moves the cathode toward the exit plane using a screw action. This system includes a spiral spring and an amplified piezoelectric actuator, where the spring stores mechanical energy and the actuator operates based on a pulse signal alternating between 0 and 150 V. The ISF-VAT achieved a thrust-to-power ratio of 2.3 pN / W and approximately 7 pN of thrust, with a lifespan of one million pulses.

[0009] Teel et al. [9] investigated ignition mechanisms using a planar design with rigidly fixed electrodes on a ceramic plate, separated by carbon paint, which demonstrated an ability to sustain up to 180,000 pulses. To examine discharge triggering, Zolotuchin et al.

[0010] employed a rectangular planar design with a variable inter-electrode gap for optimization. This thruster achieved over one million pulses and concluded with a modular propellant feeding design proposal.

[0010] Kuhn et.al [5] achieved eight million pulses with a highly reliable vacuum arc thruster. The thruster head of Kuhn includes a complex double anode (ignition anode and auxiliary anode) and a titanium tube cathode configuration without a feeding mechanism.2130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENTWhile the researchers utilized various mechanisms for feeding the cathode propellant to VATs, Kuhn lacked uniform erosion.

[0011] The addition of a feeding system using a stepper motor also results in non-uniform erosion of the cathode, and increased power consumption, weight, and complexity of the thruster’s circuit design. In conventional systems, particularly those utilizing stepper motors as a feeding mechanism, the motion of the cathode and the resulting arc discharge may not be adequately synchronized, leading to certain areas of the cathode experiencing greater ablation (usually the comer regions) than other regions of cathode (usually the center regions). Moreover, in the previous conventional systems, the cathode size remains greater than the cathode spot which also may cause the non-uniform ablation. In addition, previous conventional systems that use stepper motors as feeding mechanisms typically employ a front-feeding configuration, that is the front surface of the anode faces the cathode. In frontfeeding mechanisms, the cathode is moved forward directly into the discharge zone, which can also contribute to the non-uniform ablation.

[0012] In some cases, the actual pCAT weighs less than the stepper motor itself. Stepper motor is required in previous feeding mechanism-based thruster designs to provide precise control over the positioning of the cathode as it ablates during operation. The motor moves the cathode forward incrementally to ensure consistent propellant supply and maintain effective operation. Essentially, it allows for automated and repeatable movement of the cathode towards the discharge area to optimize ablation. Despite their potential to generate a high number of pulses, these thrusters have not reached their full capabilities due to limitations in efficient propellant feeding mechanisms, uncontrolled ablation, and instability of triggerless ignition. Uncontrolled ablation occurs when the rate at which the cathode material is consumed does not match the expected operational parameters of the stepper motor, potentially due to variable discharge conditions. Triggerless ignition is considered unstable primarily due to its reliance on conditions that can be highly variable, such as the arc's initiation point and uniformity in cathode surface conditions. This can lead to inconsistencies in the plasma ignition process. Structurally, it may not present issues, but electronically, variations in voltage and current due to environmental or setup conditions can cause fluctuations that prevent reliable ignition.3130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENTSUMMARY

[0013] A more efficient propellant feeding mechanism is needed, with controlled ablation, and stability in triggerless ignition. The present disclosure presents a Side Feeding MicroCathode Arc Thruster (SF-pCAT) with a novel propellant feeding mechanism having the capability of extending lifetime by at least 200% (experimentally demonstrated for SF- pCAT, theoretically can be much more) when compared with the traditional pCAT. SF- pCAT’s feeding mechanism addresses key challenges like limited lifetime and irregular erosion. In one embodiment, SF-pCAT is made like a sandwich structure of a cuboidal steel anode (50 x 5 x 3mm), Teflon sheet (thickness 0.6 mm), and titanium (Ti) cathode (diameter 1.2 mm) with feeding support. The inter-electrode gap can be determined by an experimental approach, in one instance, where different thrusters with inter-electrode gaps of 3 mm, 2 mm, 1 mm, 0.8 mm, 0.6 mm, and 0.4 mm were tested. Based on arc stability, the thruster with a 0.6 mm inter-electrode gap was found preferable as the optimum inter-electrode gap. Feeding support is installed to maintain the titanium cathode in its position.

[0014] In one embodiment, an arc thruster includes an anode having a longitudinal axis; a cathode extending radially outward, away from the anode, where the cathode has a leading end and a trailing portion defining a longitudinal axis therebetween, where the longitudinal axis of the anode is transverse the longitudinal axis of the cathode; and an insulator positioned between the anode and the leading end of the cathode, forming a gap therebetween.

[0015] The arc thruster can also include a cathode support formed about the insulator and configured to retain the leading end of the cathode in position relative to the anode and insulator. The anode can be cuboidal in shape. In addition, the arc thruster could include a feeding mechanism coupled to the trailing end of the cathode, configured to push the leading end of the cathode toward the anode.

[0016] The arc thruster can also be configured so that an arc discharge is formed between the anode and the leading end of the cathode, across the gap, where the feeding mechanism provides a bias force that biases the leading end of the cathode toward the anode as the leading end of the cathode erodes due to the arc discharge. The feeding mechanism can be a spring configured to provide the bias force that biases the leading end of the cathode to toward the anode, pushing the leading end of the cathode toward the anode during arc thruster operation.4130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT

[0017] In addition, the insulator could comprise Teflon, and could be a thin layer sheet wrapped around at least a portion of a perimeter of the anode, where the thin layer sheet defines the gap, and where the leading end of the cathode is located at an outer perimeter of the insulator, orthogonal to and across the gap from the anode.

[0018] In another embodiment, an arc thruster includes a central anode; a plurality of cathodes, each extending radially outward from the central anode, where each of the plurality of cathodes has a leading end. The arc thruster also includes an insulator positioned between the central anode and the leading end of each of the plurality of cathodes to form a gap therebetween. One or more feeding mechanisms can be coupled to the plurality of cathodes, where the one or more feeding mechanisms push the leading end of each of the plurality of cathodes toward the central anode.

[0019] The central anode could have a solid circular, solid disc or solid cylindrical shape. Each of the plurality of cathodes could be an elongated rod, where the elongated rod is positioned transverse to a longitudinal axis of the central anode. One feeding mechanism can be coupled to each of the plurality of cathodes, where each feeding mechanism is configured to push the leading end of each cathode toward and transversely to the central anode.

[0020] The arc thruster can be configured so that an arc discharge is formed between said central anode and each leading end of each of the plurality of cathodes across the gap, where the each of the one or more feeding mechanisms provide a bias force that biases the leading end of each of the plurality of cathodes further toward the central anode as the leading end of each of the plurality of cathodes erodes due to the arc discharge.

[0021] The arc thruster can also include a housing having a housing center, an outer housing support structure arranged about the housing center, where the central anode is coupled to the housing center and a proximal end of each of the plurality of cathodes are coupled to the outer housing support structure. The outer housing support structure can define an outer perimeter of the housing.

[0022] The plurality of cathodes, each extending radially outward from the central anode, can be configured to be controlled and operated independently or collectively to form respective arc discharges formed between the central anode and each of the leading ends of the plurality of cathodes across the gap. The one or more feeding mechanisms can each include a spring configured to provide a bias force that biases the leading end of each of the plurality of cathodes toward the anode, pushing the leading end of each of the plurality of cathodes toward the central anode during arc thruster operation. The one or more feeding5130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT mechanisms can each include a feeding mechanism housing including a spring and a base, where the spring can be configured to push a respectively associated cathode out of a distal end of the feeding mechanism housing and toward the central anode. The base can be configured to couple a proximal end of the feeding mechanism housing to an outer housing support structure of the arc thruster.

[0023] The insulator could be comprised of Teflon, and could be a thin layer sheet wrapped about a perimeter of the central anode, where the thin layer sheet defines a central anode housing outer side surface, where the leading end of each of the plurality of cathodes faces and is orthogonal to the central anode housing outer side surface.

[0024] The arc thruster could further include a hollow housing having a top side, bottom side, a longitudinal axis between the top side and the bottom side, and at least one housing wall extending about the longitudinal axis and between the top side and the bottom side to form an interior space. The central anode could be positioned in the interior space along and about the longitudinal axis of the hollow housing, where the one or more feeding mechanisms are each coupled to the at least one housing wall. The hollow housing could have a disc or cylindrical shape, where the central anode could be circular in cross-section, and the at least one housing wall can be concentric about the central anode. In addition, the one or more feeding mechanisms can each continuously push the plurality of cathodes to the central anode during cathode ablation.

[0025] These and other objects of the disclosure, as well as many of the intended advantages thereof, will become more readily apparent when reference is made to the following description, taken in conjunction with the accompanying drawings. This summary is not intended to identify all essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter. It is to be understood that both the foregoing general description and the following detailed description are exemplary and are intended to provide an overview or framework to understand the nature and character of the disclosure.BRIEF DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

[0026] The accompanying drawings are incorporated in and constitute a part of this specification. It is to be understood that the drawings illustrate only some examples of the disclosure and other examples or combinations of various examples that are not specifically6130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT illustrated in the Figures may still fall within the scope of this disclosure. Examples will now be described with additional detail through the use of the drawings, in which:

[0027] FIG. 1A illustrates an isometric view of an axi-symmetric, radial feeding arrangement of a SF-pCAT having eight electrodes for better performance and efficiency;

[0028] FIG. IB illustrates an axi-symmetric pCAT attached to a 1U (10cm) CubeSat, providing that the thruster can be scaled down or scaled up based on mission, showing plasma ionization process generating ions and electrons, which are then accelerated in a leftward direction, with the CubeSat experiencing thrust in a rightward direction, propelling the CubeSat in space;

[0029] FIG. 2A illustrates a side view of a SF-pCAT, detailing the formation of plasma and showing the cathode spot;

[0030] FIG. 2B illustrates a perspective view of a SF-pCAT featuring a spring-based feeding mechanism for propellant;

[0031] FIG. 3 illustrates a setup involving a vacuum arc circuit (i.e., an inductive energy storage circuit to generate the vacuum arc plasma; a Faraday cup circuit for analyzing charged particle flux in the plasma; and a Langmuir probe set for obtaining the plasma parameters, and the Time-of-Flight (ToF) set up to study the ion velocity, where the Time-of-Flight (ToF) setup comprises two grids spaced 16.5 cm and 25.5 cm away from the thruster, and where the peak current spike over the grid was used for computing the averaged titanium ion velocity;

[0032] FIG. 4A illustrates FEMM simulation for a permanent ring magnet used for SF- pCAT, showing the magnetic flux density;

[0033] FIG. 4B illustrates magnetic flux density as a function of distance from a center of the magnet, where the location of the thruster and center of the magnet is shown;

[0034] FIG. 4C illustrates FEMM simulation for a permanent ring magnet of dimensions ID 9.5 mm, OD 19.05 mm, and a thickness of 6mm, used for axi-symmetric pCAT showing the magnetic flux density;

[0035] FIG. 4D illustrates magnetic flux density as a function of distance from the center of magnet, where the center of the magnet is shown;

[0036] FIG. 5A illustrates discharge current observed as a function of Power Providing Unit (PPU) Voltage under different configurations: without magnetic field, and with 0.2 T, 0.25 T, 0.3 T, and 0.5 T magnetic field;

[0037] FIG. 5B illustrates instantaneous discharge power (w / pulse) as a function of time (s) observed at 21 V PPU Voltage;7130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT

[0038] FIG. 6A illustrates discharge current observed with axi-symmetric pCAT as a function of PPU voltage with and without magnetic field;

[0039] FIG. 6B illustrates instantaneous discharge power (w / pulse) as a function of time (s) observed at 35V PPU voltage;

[0040] FIG. 7A illustrates ion / arc current measured by obtaining potential drop over a 100 □ resistor using a Faraday cup, in the presence and absence of 0.5 T magnetic field for SF- pCAT;

[0041] FIG. 7B illustrates ion by arc current percent as a function of PPU voltage measured in the presence and absence of magnetic field for axi-symmetric pCAT;

[0042] FIG. 8 illustrates average ion velocity as a function of PPU voltage in the presence and absence of a magnetic field (MF) measured using Time-of-Flight (ToF) analysis, where PW stands for pulse width of the PPU circuit, noting higher PW resulted in greater discharge current;

[0043] FIG. 9 illustrates average ion velocity as a function of PPU voltage in the presence and absence of a magnetic field (MF) measured using the Time-of-Flight (ToF) analysis, where the ion velocities at different frequencies are also shown;

[0044] FIG. 10 illustrates current (on the primary axis) and plasma (on the secondary axis) density axial distribution using Langmuir probe;

[0045] FIG. 11 A illustrates a weight-wise erosion rate measured as a function of time;

[0046] FIG. 1 IB illustrates length-wise erosion rate varying with time, where the total change in cathode length was about 10 mm, and where the arc and ablation characteristics were fairly stable during the operation of the thruster;

[0047] FIG. 11C illustrates the weight of the cathode measured as a function of time (Hr), where the difference in weight is marked in the plot;

[0048] FIG. 12 illustrates charge state obtained from computed ion velocity using the E x B probe for SF-pCAT with 0.5T magnetic field;

[0049] FIG. 13A-13C illustrate OES measurements for SF-pCAT at 21V (FIG. 13 A), 25V (FIG. 13B), and 29V (FIG. 13C) in the vacuum environment for titanium plasma;

[0050] FIG. 14A-14C illustrates OES measurements for axi-symmetric pCAT at 21 V (FIG. 14 A), 25 V (FIG. 14B), and 29V (FIG. 14C);

[0051] FIG. 15 illustrates electron temperature calculated from the Ti+2 ions as a function of PPU voltage;8130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT

[0052] FIG. 16A illustrates an SEM image of a control sample of the cathode at 250x magnification;

[0053] FIG. 16B illustrates 350x magnification (with highlighted mark), where the control sample is imaged, where the cathode sample presented is a cut section, and where the spots in the sample show micro granular structures of carbon spots on the titanium material;

[0054] FIG. 17A illustrates an SEM image of the treated Ti sample exposed to plasma for more than a million pulses at 350x;

[0055] FIG. 17B illustrates a Ti treated sample at 500x magnification, where the highlighted circle is believed to be a region of primary deposition;

[0056] FIG. 18 illustrates an EDS analysis of an unexposed sample, where elemental composition was considered at the marked location, and where the figure also includes quantitative numbers of the elements present on the unexposed titanium rod;

[0057] FIG. 19 illustrates an EDS analysis of an exposed sample, where the sample is exposed to plasma for more than 1 million pulses, where elemental composition was considered at the marked location, spot, and where the figure also includes quantitative numbers of the elements present on the exposed titanium rod;

[0058] FIG. 20 illustrates direct thrust measurements performed with an axi-symmetric pCAT, showing thrust as a function of PPU voltage;

[0059] FIG. 21 illustrates axi-symmetric pCAT lifetime results of impedance vs. number of pulses observed;

[0060] FIG. 22A-22B illustrate average thrust to power ratio (T / P) (FIG. 22A), and specific impulse as a function of PPU voltage (FIG. 22B); and

[0061] FIG. 23 illustrates propulsive efficiency calculated as a function of PPU Voltage.DETAILED DESCRIPTION

[0062] In describing the illustrative, non-limiting embodiments illustrated in the drawings, specific terminology will be resorted to for the sake of clarity. However, the disclosure is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes all technical equivalents that operate in similar manner to accomplish a similar purpose. Several embodiments are described for illustrative purposes, it being understood that the description and claims are not limited to the illustrated embodiments and9130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT other embodiments not specifically shown in the drawings may also be within the scope of this disclosure.

[0063] Turning to FIGS. 1 A and IB, a radial, axi-symmetric version of SF-pCAT, namely axi-symmetric pCAT 200 embodiment is illustrated, and presents advantages over a simpler sandwich structure of FIGS. 2A, 2B. FIG. 1A illustrates an isometric view of an axi- symmetric, radial feeding arrangement of a SF-pCAT assembly 200 having one or more (here shown as eight) electrode for better performance and efficiency. FIG. IB illustrates an axi- symmetric pCAT 200 attached to a 1U (10cm) CubeSat 210, providing that the thruster (here, axi-symmetric pCAT 200) can be scaled down or scaled up based on mission, showing plasma ionization process 220 generating ions and electrons, which are then accelerated in a leftward direction (relative to FIG. IB), with the CubeSat 210 experiencing thrust 230 in a rightward direction (relative to FIG. IB), propelling the CubeSat 210 in space.

[0064] Turning to FIGS. 2A and 2B, the present disclosure presents a Side Feeding MicroCathode Arc Thruster (SF-pCAT) assembly 100. The SF-pCAT assembly 100 includes an anode 110, an insulator 120, and a wire cathode 130. In one embodiment, the assembly 100 further includes a spring feeding mechanism 140 that spring-loads the wire cathode 130 (propellant consumed per pulse). The SF-pCAT 100 can be powered by a traditional inductive Power Providing Unit (PPU) circuit. A spring-loaded feeding mechanism 140 allows the cathode 130 to be consumed during operation, providing a continuous supply of propellant. A longitudinal axis of the cathode 130 is transverse (preferably 90°) relative to a longitudinal axis of the anode 110. Thus, the cathode is orthogonal to the front face of the anode, so that the cathode is side-feeding. In side-feeding, the propellant is supplied from the side, allowing for different distribution of forces and a more complete ablation of the cathode.

[0065] FIG. 2A illustrates a side view of a SF-pCAT 100, detailing formation of plasma 170 and showing a cathode spot 180. FIG. 2B illustrates a perspective view of a SF-pCAT 100, featuring the spring-based feeding mechanism 140 for propellant. As shown, a spring can be expandably positioned inside of a spring housing. In the embodiment shown, the spring housing can be a hollow member such as an elongated tube. A plunger has a first inner side that faces the spring and an opposite second outer side that contacts the cathode 130. The plunger is slidably received in the spring housing. The spring is compressed inside the spring housing and biased outward to press against the inner side of the plunger. That in turn results in the outer side of the plunger pressing the cathode 130 toward the support 150 as the cathode10130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT130 is ablated. The spring housing can be situated on or connected to a support or a pCAT housing.

[0066] The SF-pCAT 100, in the FIGS. 2A, 2B embodiment, is made like a sandwich structure that includes a steel anode 110 (which is a steel plate), insulator 120, and support 150. The support 150 keeps the titanium cathode 130 and the anode 110 in position with respect to each other. In operation, the cathode 130 is fed at the end of a thruster (here, SF- pCAT 100) and plasma 170 is formed at the interface of the insulator 120 and the cathode 130. To address the limitation of space debris and irregular erosion, the thruster uses a small titanium wire 130 of a diameter of 1.2 mm. As the surface area of the cathode 130 is configured to be sufficiently small, so that there is no chance of irregular erosion of the electrode as it erodes completely without leaving any space debris. Accordingly, in the axi- symmetric design of the present disclosure, the cross-section of the cathode is configured to be substantially the same size as the cathode spot, here approximately a 1.2mm titanium wire, which makes the ablation uniform. The size of the cathode spot can vary based on the operating parameters of the thruster, with an approximate size range of 10 pm to 100 pm, and the cathode wire can vary to have the same size as the cathode spot, or be slightly larger or smaller than the cathode spot (for example, within 5% or 10% smaller or larger). A small cathode wire is used here to maximize the utilization of the cathode without leaving any waste or leftover fragments in space. This approach minimizes the risk of generating space debris caused by pieces of the cathode left after the operation. However, prior systems may not have adopted smaller cathode wires due to concerns regarding their durability, operational lifetime, and efficiency. A smaller wire might not withstand the wear and tear associated with prolonged usage or could lead to less effective arc formation, limiting propulsion performance. Balancing these factors is crucial to ensure reliable thruster functioning while addressing space debris concerns with an efficient feeding mechanism.

[0067] The feeding mechanism 140 is a spring-based mechanism that pushes the electrode 130 upwards as it erodes. The plasma 170 is formed at the interface of the Teflon insulator 120 and the cathode 130, shown as a cathode spot 180, which is represented by a cloud in FIG. 2A. Prior systems may have relied on higher surface areas to enhance plasma formation and thrust generation, as well as to ensure longer operational lifetimes. Without the implementation of a feeding mechanism and utilizing only a single cathode, achieving a lifetime of at least 2-3 million pulses during operation would be a significant challenge. Additionally, incorporating a feeding mechanism could introduce design complexities that11130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT prior systems may have sought to avoid. There was also concern that employing smaller cathodes might lead to inefficiencies in plasma generation or overall propulsion performance, prompting designers to opt for larger electrodes to ensure adequate thrust and longevity.

[0068] In one example embodiment, as shown, the anode 110 can be any suitable shape, such as cuboidal. In addition, the spring-loaded cathode 130 can be titanium, the insulator 120 can be Teflon (e.g., a sheet of thickness 0.6mm), and the support 150 can be 3D printed. The anode 110, the insulator 120, and the support 150 can each be can be a flat thin plate. The support 150 has a support top surface, a support bottom surface, and a support leading or front face or front surface. The insualtor 120 has an insulator top surface, an insulator bottom surface that contacts the support top surface, and an insulator leading or front face or front surface. The anode 110 has an anode top surface, an anode bottom surface that contacts the insulator top surface, and an anode leading or front face or front surface. The distal anode end, distal insulator end, and distal support end can be substantially aligned with each other, and the anode front face, insulator front face, and support front face can be substantially aligned with each other and can be substantially flush or linear. As best shown in FIG. 2A, the anode 110, insulator 120, and support 150 can be elongated such as rectangular in shape, with a respective anode longitudinal axis, insulator longitduainal axis, support longitudinal axis, anode proximal end, insulator proximal end, support proximal end, and an anode distal end, insulator distal end, and support distal end. The anode, insulator and / or support proximal end can be coupled to a housing, such as by a fastener that extends through the anode, insluator and / or support proximal end into a housing structure. When we refer to a system or structure as "axi- symmetric," it means that it exhibits symmetry around a central axis which is typically the central line around which the entire structure is organized. Axi-symmetry is important because it ensures uniform distribution of forces and effective flow dynamics simplifying the design and analysis processes, making it easier to predict performance and behavior under various conditions. Regarding the potential application of the side-feeding mechanism in asymmetric devices, it can indeed be adapted for use in such systems, though special design considerations necessary to effectively balance the forces involved. While asymmetric devices can benefit from axi-symmetric pCAT by providing better operational characteristics due to their more effective distribution of forces, leading to improved performance and efficiency. In particular, with respect to FIG. 2A, the accerlation and thrust are provided in a symmetrical manner so that, for example, the CubSat is balanced, and in one embodiment the device 200 is symmetrical about the central axis that is normal to the surface 112 of the anode 110 and at the center of the12130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT anode 110 (i.e., into the page of FIG. 1 A). In the example embodiment, the plasma is emitted in a circular manner in a single direction rearward with respect to the Cub Sat.

[0069] The cathode 130 is also elongated and has a cathode longitudinal axis, cathode proximal end, cathode distal end, and cathode leading or front face or front surface. The cathode 130 is side-feeding, namely the cathode longidudinal axis is substantially orthogonal to the anode, insluator and / or support longitudinal axis, such that the cathode front face is substantially orthogonal to the anode front face, insulator front face, and / or support front face. Thus, the cathode front face faces the anode, insulator and / or support bottom surface. The cathode distal end and cathode front face is closest to and adjacent to the support distal end, and can touch the support for example the support bottom surface at the support distal end. The spring mechanism 140 pushes the cathode 130 in a feed direction toward the support 150, parallel to the cathode longitudinal axis. Side-feeding allows for better management of the cathode material, as it can be designed to completely ablate the cathode without any issues due to better distribution of forces. Moreover, the side feeding allows the cathode to be eroded uniformly unlike in conventional thrusters.

[0070] In the SF-pCAT 100, an ion-to-arc current fraction of about 0.025 was detected and an initial pulse count of 1.34M was achieved, demonstrating the effectiveness of the feeding mechanism 140. An average erosion rate of 4 pg / C was measured and a total change in cathode 130 length of 10 mm indicates successful implementation of the spring-loaded side feeding mechanism 140. E x B probe analysis assessed ion charge states while optical Emission Spectroscopy revealed the emissions from plasma 170.

[0071] The SF-pCAT 100 can utilize any suitable arcing, such as for example a well- known phenomenon of triggerless arcing

[0011] ,

[0012] , for its initial discharge. This approach eliminates the need for an external trigger to initiate the arc discharge between the cathode 130 and anode 110, instead relying on the natural backscattering of ablated carbon paint to sustain the arc. In pCATs, plasma is generated by the vaporization of the cathode, which occurs due to the high electric field produced during arc discharge at higher voltages. There are two primary methods for creating this initial arc discharge. One is the triggerless arcing which utilizes a conductive layer, often carbon paint, placed between the anode and cathode to facilitate the initial arc. Second is the external trigger method which relies on an external trigger to initiate the arc. However, using an external trigger can introduce several disadvantages. It adds complexity to the thruster's design, requiring additional circuitry, which can increase the weight and overall system complexity. Consequently, while external13130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT triggering can be effective, it may negatively impact the compactness and efficiency of the pCAT.

[0072] When the cathode 130 material is vaporized due to the intense heat generated during operation, some of the ablated particles can scatter back onto the insulator 120 surface. This backscattering creates a conductive path that allows the arc to continue without the need for an external ignition source. As detailed above, to address the limitation of irregular erosion, the thruster was designed with a small titanium wire of diameter 1.2mm as the cathode 130. The reduced surface area of the cathode 130 leads to complete ablation of the material. The ablation process does not happen all at once; rather, it occurs gradually over time. The backscatter occurs when particles that were originally emitted from the cathode surface collide with ions or other particles in the plasma, causing them to rebound or change direction rather than escaping completely. The spring-based feeding mechanism 140 pushes the electrode upwards as it erodes. The cathode spot 180 is formed at the interface of the insulator 120 and the cathode 130. Accordingly, the novel side feeding mechanism 100 of FIGS. 2A and 2B enhances micro-propulsion system efficiency and performance for CubeSats.

[0073] The novel propellant feeding mechanism 140 of SF-pCAT 100 has the capability of extending lifetime by at least 200% (experimentally demonstrated for SF- pCAT, theoretically can be much more) when compared with the traditional pCAT. The feeding mechanism 140 of the SF-pCAT 100 addresses key challenges like limited lifetime and irregular erosion. In one embodiment, SF-pCAT 100 is made like a sandwich structure of a cuboidal steel anode (50 x 5 x 3mm) 110, Teflon sheet insulator (thickness 0.6 mm) 120, and titanium (Ti) cathode (diameter 1.2 mm) 130 with feeding support 150. The inter-electrode gap can be determined by an experimental approach, in one instance, where different thrusters with inter-electrode gaps of 3 mm, 2 mm, 1 mm, 0.8 mm, 0.6 mm, and 0.4 mm were tested. Based on arc stability, the thruster with a 0.6 mm inter-electrode gap was found preferable as the optimum inter-electrode gap. Feeding support is installed to maintain the titanium cathode in its position.

[0074] Returning to the embodiment of FIGS. 1 A, IB, a plurality (here, eight) radially mounted cathodes 130 are provided, allowing the axi-symmetric pCAT 200 to generate thrust in all directions. The inclusion of multiple electrodes allows for a substantial increase in pCAT lifetime when compared to a single cathode configuration, such as in SF-pCAT 100. While the embodiment of FIGS. 1A and IB includes eight radially mounted cathodes 130,14130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT other cathode 130 numbers are contemplated, along with arrangements that are not necessarily axi-symmetric.

[0075] The preferred circular arrangement of the axi-symmetric pCAT 200 not only contributes to the system's robustness, but also enhances its versatility, as each directional (radially directed) electrode can be controlled independently or operated collectively. In the embodiment of FIGS. 1A and IB, the axi-symmetric pCAT 200 thruster has a single solid central anode 110. The central anode 110 can be relatively flat and circular, with a plate or disc shape, with an anode central transverse axis, and having an outer diameter of 4 mm. The central anode 110 has an anode forward facing side 112, anode rearward facing side, and anode outer side surface.

[0076] A ceramic insulator 120 coaxially surrounds the central anode 110 and can have a ring shape with a width of 1.6mm to provide an outer diameter of 5.6 mm and an interelectrode gap (between the outer perimeter of the central anode 110 and the cathode leading surface) of 1.6 mm, though other suitable dimensions can be utilized. The insulator inner surface touches the anode outer side surface.

[0077] In the embodiment of FIGS. 1A and IB, the cathode is side-feeding, wherein the cathode longitudinal axis of each cathode 130 is transverse (preferably 90°) relative to the outer side surface of the anode 110, and the cathode front surface faces the anode side outer surface. Each cathode 130 can touch the ceramic insulator 120, and each is supported by a spring mechanism 140 that ensures consistent cathode 130 positioning, by the spring mechanism 140 pressing the cathode 130 inward toward the central anode 110 and insulator ring 120. The eight spring mechanisms 140 are each interconnected and anchored to a metal support or base 240 at a bottom, depicted as a ring or disc in FIGS. 1 A and IB. As further shown, the anode front face contacts the insulator outer surface toward the insulator front surface 122, and anode front surface 112. The insulator front surface 122 can be flush with the anode front surface 112 or the anode front surface 112 can be recessed or extend outward with respect to the insulator front surface 122. As shown, the anode projects out from the insulator. That is, the anode front surface projects out from the insulator front surface, which takes advantage of the acceleration due to the electric field. This arrangement facilitates better plasma interaction and enhances the acceleration of the ions produced.

[0078] In this embodiment, each cathode 103 remains unchanged from the embodiment of FIGS. 2A and 2B (each cathode 130 is a titanium wire with 1.2 mm diameter, with other dimensions contemplated). Each electrode 130 is equipped with a coupling mechanism and15130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT an electrical connection such as a cathode electrical connection 250. The cathode coupling mechanism can be, for example, a fastener that couples the spring feeding mechanism 140 to the base 240. The cathode electrical connection 250 enables each cathode 130 to be controlled either individually or simultaneously, providing flexibility in operation. Also provided is an anode electrical connection for the axi-symmetric pCAT 200, that controls the anode 110. The electrical connection for the anode can be, for example, at the back of the axi-symmetric pCAT. The cathode spots 180, illustrated by a circle at a distal end of each cathode 130, formed at a tip of the ceramic insulator 120, in FIG. 1A, indicates where plasma 220 is expelled through the application of an electric field, as discussed above. The cathode spots 180 are at the cathode distal end at the insulator side surface at the side closest to the front insulator surface 122 and anode front surface 112. Visually it is observed that the arc follows the path of lower resistance among all eight electrodes of the axi-symmetric pCAT 200.

[0079] Thus, the central anode 110 and the insulator 110 are at a fixed position at the center of the base 240, and can be fixed to the base 240 or to a separate housing or support. The spring feeding mechanisms 140 are each coupled to the base 240 and are biased inward to press the cathode wires 130 inward toward the insulator 120.

[0080] In FIG. IB, the pCAT 200 is fixedly coupled at the rear of the CubeSat 210 (the left side in the embodiment of FIG. IB), for example, the base 240 can be coupled to the CubeSat housing. In addition, the anode front surface 112 faces rearward (to the left in the embodiment of FIG. IB), so that the ionized particles are accelerated rearward (to the left in the embodiment of FIG. IB), creating forward thrust (to the right in the embodiment of FIG. IB). It is further noted that all of the particles from all of the cathodes (eight in the embodiment of FIG. 1A) are accelerated in the same direction (here, rearward), and the force of the thrust can be adjusted by simultaneously activating one or more of the cathodes. Additional pCAT systems 200 can be fixedly coupled to other sides of the CubeSat 210 to create thrust in other directions.

[0081] The axi-symmetric pCAT 200 offers several advantages over traditional feedingbased vacuum arc thrusters. Axi-symmetric pCAT 200 has multiple radially mounted cathodes 130, which significantly enhance thrust 230 and allow thrust generation in all directions, thus improving maneuverability. Additionally, this configuration contributes to increased operational lifetime, as the simultaneous use of multiple electrodes can optimize consumption of cathode material, leading to more efficient propellant use. Independent control of each electrode (cathode 130) provides flexibility in thrust management, essential16130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT for precise attitude adjustments in satellite operation. Furthermore, the robust structural design of the axi-symmetric pCAT 200 enhances stability and resistance to varying operational conditions, ensuring reliability for long-duration missions.

[0082] As detailed below, the SF-pCAT 100 and axi-symmetric pCAT 200 are characterized using a combination of non-invasive and invasive diagnostic tools to assess performance, operational efficiency, and lifespan. Faraday cup experiments were conducted to measure total ion and electron currents within the vacuum arc plasma. Langmuir probes were used to analyze plasma parameters, including electron density and plasma potential. Time-of-Flight (ToF) measurements help investigate distribution of ion velocities, contributing to a better understanding of ion dynamics. Erosion rate analysis was carried out to assess consumption of cathode material, while indirect and direct thrust measurements evaluate the thruster's propulsion capabilities. Furthermore, cathode imaging and material composition were analyzed using Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) to study deposition during thruster operation. The E x B probe is used to access ion dynamics within the plasma as confirmed by Optical Emission Spectroscopy (OES). By using these diagnostic tools, thorough characterization of the pCATs of the present disclosure can be obtained, while acquiring deeper insights into operational behavior and effectiveness of the feeding mechanism.SETUP AND PLASMA DIAGNOSTICS

[0083] To investigate the performance of the SF-pCAT 100, the thruster was placed in a cylindrical stainless-steel vacuum chamber that typically maintains a pressure range of 10'5Torr. Experiments, including the Faraday cup, Langmuir probe, and erosion rate assessments, were performed to analyze the SF-pCAT 100 with and without magnetic field. The magnetic field enhances the performance and efficiency of the thruster by increasing the rate of ionization. Detailed experimental setup and circuit diagrams are shown in FIG. 3.

[0084] FIG. 3 illustrates a setup involving a vacuum arc circuit 310 (i.e., an inductive energy storage circuit to generate vacuum arc plasma; a Faraday cup circuit 320 for analyzing charged particle flux in the plasma; a Langmuir probe set circuit 330 for obtaining plasma parameters, and a Time-of-Flight (ToF) circuit 340 set up to study ion velocity, where the Time-of-Flight (ToF) setup circuit 340 comprises two grids 342, 344 spaced 16.5 cm and 25.517130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT cm away from the thruster 110, and where a peak current spike over the grid was used for computing the averaged titanium ion velocity.Optimization of Magnetic Field

[0085] A well-designed magnetic field can significantly improve the ionization rate, plasma density, and overall thrust efficiency of the thruster

[0013] ,

[0014] , So, magnetic field simulations were performed using Finite Element Method Magnetics (FEMM) for axially magnetized Neodymium N42 permanent ring magnets. For simplicity, in these embodiments, both the SF-pCAT and axi-symmetric pCAT use N42 permanent ring magnets. The simulations aimed to optimize cathode spot rotation and achieve uniform cathode erosion at the cathode-insulator interface. The study employed a 2D axi-symmetric magnetostatics model, which is particularly suitable for analyzing ring-shaped magnets and their surrounding magnetic fields. The magnetic flux density plot, shown in FIGS. 4 A and 4C illustrate the magnetic field distribution in free space at various distances from the magnet, with warmer colors representing higher magnetic fields and cooler colors indicating lower magnetic fields. Additionally, a correlation between the axial magnetic flux density and the distance from a center of the thruster is depicted in FIGS. 4B and 4D. The graph is crucial for determining optimal positioning of the thruster relative to the magnet. The thruster is strategically positioned at a distance from the center of the magnet so that the plasma plume can experience a maximum magnetic field of 0.5T for the SF-pCAT. This magnetic field efficiently bends and directs the plasma in the -J * B direction, thereby enhancing ionization rate and increasing both the plasma density and ion velocity.

[0086] Accordingly, FIG. 4A illustrates FEMM simulation for a permanent ring magnet used for SF-pCAT, showing the magnetic flux density. FIG. 4B illustrates magnetic flux density as a function of distance from a center of the magnet, where location of the thruster and center of the magnet is shown. FIG. 4C illustrates FEMM simulation for a permanent ring magnet of dimensions ID 9.5 mm, OD 19.05 mm, and a thickness of 6mm, used for an axi-symmetric pCAT showing the magnetic flux density. FIG. 4D illustrates magnetic flux density as a function of distance from the center of magnet, where the center of the magnet is shown.

[0087] The magnet location in the case of axi-symmetric pCAT directly influences plasma dynamics, ionization rates, and the magnetic field strength. By strategically positioning the magnet at an optimal distance, the magnetic field can effectively control the flow of charged18130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT particles, ensuring that the plasma plume is concentrated toward the center of the thruster

[0015] .Initial Diagnostics

[0088] The experimental setup for the SF-pCAT thruster involved several key components to measure arc current, ion current, and ion velocity. The discharge current was measured using a Pearson 110A Rogowski coil

[0016] and observed over a Tektronix TDS 2004C oscilloscope

[0017] , The values observed in the oscilloscope (for all the experiments) were averaged over 128 values and experiments were repeated three times with measurement accuracy greater than 95%. A Faraday cup, with a biased voltage of -85 V and an area of 0.12 m2, was precisely aligned with the center of the thruster to ensure accurate ion current measurements. The current was calculated using Ohm’s law based on the potential drop across a 100 Q resistor. Additionally, a Langmuir probe was constructed using a titanium wire with a thickness of 1 mm and a length of 2 mm exposed to the plasma, while the remaining wire was shielded with non-porous alumina ceramic to minimize interference. For measuring ion velocities, a Time-of-Flight (ToF) method was employed, which utilized two negatively biased grids positioned at a known distance from the thruster, both set to -85V to eliminate any electric field between them. This comprehensive diagnostic approach aimed to obtain detailed ion velocity profiles. All primary diagnostic methods were conducted with and without the application of a magnetic field, with results presented in subsequent sections.Erosion Rate

[0089] Following the initial diagnostics, experiments were done to measure erosion rate, providing a deeper understanding of temporal dynamics of cathode ablation during the operation of the SF-pCAT. Erosion rate is determined by accurately measuring the weight of the propellant (titanium cathode) before and after the experiment. Mass measurements were performed using a Mettler Toledo scale

[0018] ,

[0019] , with an accuracy of lOOpg. Additionally, the scale was tared to maintain the accuracy of the measurements. Simultaneously, the length of the titanium wire is monitored pre- and post-experiment. During the experiments, the SF- pCAT was operated for approximately 108,000 pulses while maintaining stable arc current conditions.Optical Emission Spectroscopy and E x B Probe

[0090] Additionally, the E * B probe, also referred to as a Wien filter

[0020] ,

[0021] , was used to measure the velocity and charge state of the ions in the plasma. The principle behind the probe is based on the drift of ions due to Lorentz force. This diagnostic has a balancing electric19130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT field (E) and magnetic field (B) in the perpendicular direction to filter the ions based on their velocities. The E x B probe is designed in such a way that only the ions with the correct velocity will pass through the narrow passages by deflecting other ions. This makes the E*B probe act as a charged particle energy analyzer, monochromator, or mass spectrometer. In other words, an E*B probe is a band-pass ion filter that selects ions based on their velocities through the application of crossed electric and magnetic fields. To support the arguments, Optical Emission Spectroscopy (OES) was employed to analyze the elemental composition of the plasma generated by the source, measuring the photon intensities emitted by various species within the plasma to create a detailed profile of the elements present and their ionization states. Conducted at different Power Providing Unit (PPU) voltages — specifically at 21V, 25V, and 29V — OES allows for the observation of variations in plasma emissions without the influence of a magnetic field, with analyses performed using the NIST database to correlate plasma composition with thruster performance. Detailed procedure for OES and E x B has been mentioned in ref. [12 / 16], Together, the analysis provided by the E * B probe and OES offers a detailed understanding of the plasma characteristics and ion dynamics within the thruster.Cathode Material Analysis

[0091] Furthermore, Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) were used to investigate structural and compositional characteristics of the cathode material. SEM provides high-resolution imaging of the cathode's surface, revealing topographical and microstructural features after plasma exposure. EDS uses X-ray emission to evaluate the elemental and material composition. The preparation of the cathode samples involved creating small cut sections for both control and treated samples. These samples were then loaded into the vacuum chamber of the SEM for imaging. Later, the EDS detector (Everhart Thornley) was installed in the SEM to perform elemental analysis.Direct Thrust Measurements

[0092] As previously mentioned, a torsional thrust stand designed and developed at the George Washington University’s MpNL was used to measure the thrust generated by the source, capable of detecting forces in the micro-newton to milli-newton range. A detailed description of the thrust stand can be found in

[0022] , Given the size of the source, it is supported by an arm mounted to the thrust stand. The thrust is measured indirectly by attaching a thin, lightweight Teflon plate to the movable thrust arm positioned in front of the thruster. When20130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT the thruster operates in a vacuum chamber at a pressure of 4 x 10-4Torr, the plasma exhaust from the thruster exerts a force on the Teflon plate, causing the arm to rotate around its axis of rotation. The DMS sensor was utilized to detect minute changes in distance, operating within the micrometre range, which was essential for capturing the subtle deflections caused by the thrust generated by the thruster. To ensure accurate thrust measurements, a calibration process is conducted prior to the experiments. This involves applying known voltages to the electrostatic combs and measuring the corresponding forces generated, allowing for the establishment of a voltage-to-force calibration curve. During the experiment data collection phase, the thrust measurements are taken in a systematic manner: the thruster is turned off for 30 seconds, then activated for 30 seconds (data is collected from a DMS sensor using a separate software), and finally turned off again for another 30 seconds. This alternating pattern allows for the comparison of thrust data during active and inactive periods, ensuring that the measurements are reliable and that any potential noise or fluctuations can be accounted for in the analysis done using in house build python code. The performance characteristics like the thrust to power ratio, power requirements, erosion rate, specific impulse, impulse bit of the axi-symmetric pCAT were measured.RESULTS

[0093] In this section, the results of the experimental analysis conducted on the SF-pCAT and axi-symmetric pCAT, as detailed above, are presented. Findings from these experiments reveal more about key performance parameters, including thrust, specific impulse, plasma plume characteristics, and erosion rates. Notably, the optimal magnetic field significantly enhanced the overall plasma parameters and plume characteristics. Additionally, material analysis was performed to investigate deposition on the cathode after extended operation of the thruster. The results contribute to a deeper understanding of the behavior of the feeding mechanism based pCAT.Vacuum Arc

[0094] The arc current of SF-pCAT, with and without magnetic field, concerning the Power Providing Unit (PPU) voltage at 21V and 750 ps pulse width is shown in FIG. 5A. The arc current demonstrates an increasing trend with both the PPU voltage and the magnetic field. Higher PPU voltage and magnetic field strength enhance the ionization rate, allowing for a more rapid stripping of ions and electrons from the cathode due to the higher energy available for ionization. Additionally, the magnetic field contributes to uniform erosion and21130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT can increase collision frequency, further boosting ionization. It is known that arc current rises with an increase in PPU voltage, and the SF-pCAT exhibits similar behavior to the traditional pCAT. Notably, the arc current increased by 75% when a magnetic field of 0.5 T was applied at a PPU voltage of 21V. This increase in arc current is evident when comparing the values at 0.5 T with those recorded without a magnetic field. Based on the obtained arc current from FIG. 5, a magnetic field strength of 0.5 T was determined to be the optimal value and was used in subsequent experiments.

[0095] Accordingly, FIG. 5 A illustrates discharge current observed as a function of PPU Voltage under different configurations: without magnetic field; and with 0.2 T, 0.25 T, 0.3 T, and 0.5 T magnetic field. FIG. 5B illustrates instantaneous discharge power (w / pulse) as a function of time (s) observed at 21V PPU Voltage.

[0096] The power requirements for pCATs vary based on mission specifications. For missions that necessitate low power consumption, such as those involving CubeSats, the pCAT can adjust its performance parameters to achieve reduced power usage. Conversely, in missions where maximizing thrust and efficiency is essential, the pCAT can be optimized to operate at higher power levels

[0011] ,

[0012] , In FIG. 5B, at 21V with a pulse width of 750 ps, the discharge power is approximately 12 W per pulse.

[0097] FIG. 6A illustrates discharge current observed with axi-symmetric pCAT as a function of PPU voltage with and without magnetic field. FIG. 6B illustrates instantaneous discharge power (w / pulse) as a function of time (s) observed at 35 V PPU voltage.

[0098] The arc current trend for the axi-symmetric pCAT, as shown in FIG. 6A, reveals a significant increase in comparison to the SF-pCAT under the same operational conditions. Specifically, arc current significantly grew the max of 59% with the application of magnetic field at 35 V PPU Voltage. The introduction of a magnetic field appears to play a crucial role in this enhancement, as it facilitates improved confinement and stability of the plasma, thereby promoting more efficient ionization. This effect is particularly seen at higher PPU voltages, where the magnetic field can effectively influence the behavior of charged particles, leading to a more robust arc. On the other hand, the arc current and arc voltage trend is observed as a function of time in FIG. 6B. The discharge power consumption at 21 V PPU voltage turns out to be 1.74W, which makes it even more reliable for small Sats. The power consumption greatly reduced from 12W / pulse to 1.74W / pulse with the axi-symmetric configuration. The combination of low power consumption and a self-feeding mechanism makes the SF-pCAT an excellent choice for CubeSat propulsion.22130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENTFaraday Cup

[0099] Theoretically, it is suggested ,

[0023] that plasma is predominantly composed of electrons, which carry approximately 90% of the arc current and is crucial for sustaining the arc discharge. However, in an electron-dominant plasma, these electrons do not directly contribute to thrust production due to their extremely low mass. Consequently, only about 10% of the arc current is used for thrust generation. An optimized magnetic field of 0.5 T was used to enhance the total ion current. The increase in ion current can be attributed to a rise in ion velocity (due to the Lorentz force) and an increase in ion charge density (resulting from improved ionization).

[0100] FIG. 7A illustrates ion / arc current measured by obtaining potential drop over a 100 □ resistor using a Faraday cup, in the presence and absence of 0.5 T magnetic field for SF- pCAT. FIG. 7B illustrates ion by arc current percent as a function of PPU voltage measured in the presence and absence of magnetic field for axi-symmetric pCAT.

[0101] Furthermore, for SF-pCAT, in the absence of a magnetic field, the ion current flux appears asymmetric in the positive z-direction, with a greater concentration of ion current towards the negative z-direction. This observation suggests that the cathode spot is focused in the direction of higher ion current density. When a magnetic field is applied, it directs the cathode spot towards the center of the thruster, resulting in a more symmetric ion current density distribution. Additionally, the presence of a magnetic field has been shown to cause the splitting of cathode spots, a phenomenon previously studied by Taploo et al.

[0024] using high-speed imaging. The cuboidal geometry of the SF-pCAT may also contribute to the redistribution of fractional ion flux in all directions. However, ion back flux could be minimized by designing a cylindrical geometry-based SF-pCAT, which would allow for symmetrical arcing. This serves as the motivation behind the design of axi-symmetric pCAT of the present disclosure.

[0102] On the other hand, the results from the axi-symmetric pCAT indicate that the ion current increases with the PPU voltage, reflecting higher levels of ionization. To a surprise, the ion current reaches a saturation point at higher PPU voltages. Additionally, the ion-to-arc current fraction, shown in FIG. 7B, shows a decreasing trend regardless of the presence of a magnetic field. Remarkably, at a PPU voltage of 21V, the ion-to-arc current ratio is 5% without the magnetic field and increases to 10.5% with the influence of magnetic field.

[0103] These findings suggest that the introduction of a magnetic field significantly enhances the efficiency of ionization processes within the thruster, resulting in a larger portion23130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT of the arc current being converted into useful ion current. The increase in the ion-to-arc current ratio indicates that the magnetic field not only stabilizes the arc but also improves the confinement and acceleration of ions, ultimately leading to enhanced thrust performance of the axisymmetric pCAT. Results regarding ion velocity distribution are presented below. Time-of-Flight (ToF)

[0104] Ion velocities are measured using ToF diagnostics with the presence and absence of magnetic field. The ion velocities don’t vary much with an increase in PPU voltage, but there seems to be an increment of ion velocity at 28 V PPU voltage, when compared to the ion velocity at 21 V PPU voltage. An increase from 7.2-7.8 Km / s can be seen as measured by ToF. Interestingly, there is an increase in the ion velocity with the increment in the magnetic field, as shown in FIG. 8.

[0105] FIG. 8 illustrates average ion velocity as a function of PPU voltage in the presence and absence of a magnetic field (MF) measured using Time-of-Flight (ToF) analysis, where PW stands for pulse width of the PPU circuit, noting higher PW results in greater discharge current.

[0106] There is a clear increasing trend of ion velocities with the increase in magnetic field. Additionally, the ion velocities also increase with longer pulse duration due to increment in arc current. However, it is also observed that the ion velocity reaches saturation at 7.8 km / s, without the magnetic field, at 750 PW and 7.5 km / s at 650 PW. This saturation is also observed with a 0.3T magnetic field at both 650 and 750 PW. Notably, there is a potential increase in the ion velocity with a 0.5T magnetic field at 750 PW.

[0107] FIG. 9 illustrates average ion velocity as a function of PPU voltage in the presence and absence of magnetic field (MF) measured using the Time-of-Flight (ToF) analysis, where the ion velocities at different frequencies are also shown.

[0108] The Time-of-Flight (ToF) analysis reveals the velocity profile for the axi-symmetric pCAT. It was observed that there is no significant increase in ion velocities with varying PPU voltages, regardless of the presence or absence of magnetic field, as observed from FIG. 9. A similar trend was noted with the SF-pCAT. The ion velocities were observed to double in the presence of a magnetic field for the axi-symmetric pCAT due to the drift of ions. Furthermore, there was no discernible change in ion velocity with frequency, whether in the presence or absence of a magnetic field. This behavior can be attributed to the sustained arc at a frequency of 5 Hz, which is more stable compared to that at 10 Hz. At 5 Hz, the arc exhibits greater24130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT stability, leading to consistent ion velocities, whereas the 10 Hz frequency results in less sustained arc conditions.Langmuir Probe measurements

[0109] Langmuir probe is used to obtain a single dimension (ID) spatial resolution of SF- pCAT’s plasma parameters. Experimentally, it is seen that the plasma potential, floating potential, and electron temperature don’t change concerning the distance from the thruster. The plasma potential of 47.6 V, floating potential of 9 V, ion saturation current of 4 mA, and electron temperature of 2 eV are observed at the point of discharge. However, the ion saturation current typically decreases as the Langmuir probe is moved away from the thruster. This decrease is due to the current reaching the probe decreasing as the distance increases.

[0110] FIG. 10 illustrates current (on the primary axis) and plasma (on the secondary axis) density axial distribution using Langmuir probe. As shown in FIG. 10, the maximum ion current, charge density, and plasma density were observed as 2 A, 103A / m2, and 3* 1018nr3. The decrease in the plasma parameters is possibly due to the recombination of ion species. The plasma parameters were assumed to be the same for the axi-symmetric pCAT, as the electrode materials are identical with the same titanium plasma.Erosion Rate Analysis

[0111] The erosion rate of a titanium cathode in the SF-pCAT was examined by measuring the change in weight of the cathode during experimentation, which was found to be around 4 pg / C on average. The value, depicted in FIG. 1 IB, was determined by monitoring the weight before and after the experiment. The erosion rate was calculated by averaging eight measurements, showing that the mass of the cathode consumed was initially high but decreased over time due to the re-deposition of carbon paint on the cathode, a phenomenon that will be further explained through material analysis.

[0112] FIG. 11 A illustrates a weight-wise erosion rate measured as a function of time. FIG. 11B illustrates length-wise erosion rate varying with time, where the total change in cathode length was about 10 mm, and where the arc and ablation characteristics were fairly stable during the operation of the thruster. FIG. 11C illustrates the weight of the cathode measured as a function of time (Hr), where the difference in weight is marked in the plot.

[0113] Although the average erosion rate of the SF-pCAT (4 pg / C) is significantly lower than that of traditional pCATs (40 pg / C) [8], the SF-pCAT can still produce a thrust of 3.26 pN (determined indirectly), which is comparable to that of traditional pCATs. Additionally, the change in length of the cathode was monitored as part of the erosion rate data presented25130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT in FIG. 13B. A total of 10mm of length was ablated over 1.134M pulses in 15.75 hours. This change in length demonstrates the motion of the spring mechanism and serves as proof of concept for the spring feeding mechanism.

[0114] On the other hand, the erosion rate of a titanium cathode in axi-symmetric pCAT was investigated like that of the SF-pCAT, and the erosion rate was found to be around 1.8 pg / s on average, as shown in FIG. 11C. Additionally, since the axi-symmetric pCAT has eight electrodes with the arc rotating among them, the erosion is distributed across all electrodes. This design results in a minimized amount of propellant being consumed for each electrode.Wein Filter

[0115] The ion charge state and different ion species present in the plasma are measured using the Wein filter, which separates the ions based on their velocities. The plasma mostly consists of Ti ion species ( Ti+, Ti+2, Ti+3) which is evident that the cathode is made of titanium. The charge state and velocity of different ion species in a titanium plasma are predicted using a Python code built at MpNL (results summarized in Table 1). The code takes into account different mechanisms, like the collisions between ions, and ionization of charged particles, to accurately predict the charge distribution and velocity components of the titanium charged particles. Detailed procedure for analysis can be found in

[0021] Table 1. Charge state and velocity comparison of different ion states and for different metals and compoundsCharge VTi(km / s) VTiO2VTi03VFe(km / s) VAl(km / s)State (km / s) (km / s)0 0 0 0 0 01 15.236104 11.792939 8.794809 14.109695 20.2963752 21.547105 16.677734 12.437738 19.954122 28.7034093 26.389706 20.425969 15.233056 24.438709 35.154354

[0116] FIG. 12 illustrates charge state obtained from computed ion velocity using the E x B probe for SF-pCAT with 0.5T magnetic field.

[0117] FIG. 14 shows the results of the E x B probe measuring the charge state and the resulting velocity of the ion species. In the magnetic field-free environment, the plasma comprises TiO2+ions with an average ion velocity of 9 km / s, indicating a lack of ionization at 21 V PPU voltage. To rectify this discrepancy, the experiment was repeated at a higher26130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENTPPU voltages and with a 0.5T magnetic field. The revised results indicate the initial presence of TiO2+ions likely due to the residual air in the chamber at 5xl0'4Torr at the start of the experiment. Subsequently, further ionization occurred, and the plasma consists of predominantly Ti+2with an ion velocity of 40Km / s. This may be the true velocity of the ions with the influence of the magnetic field as demonstrated with the axi-symmetric pCAT described in FIG. 12. These results are supported by the OES detailed below.Optical Emission Spectroscopy

[0118] The OES spectra for SF-pCAT exhibit prominent peaks of Ti+Ti+2, Ti+4, C at different wavelengths, indicating the presence of elements at different ionization states. Most of the emission lines lie within the range of 200-400 nm while the strong emissions are in the 300-400 nm range as shown in FIG. 13A at 21 V. The peaks are annotated by different colors for different ionization states of elements. Most of the eminent peaks persist at higher PPU voltages. Higher intensities could imply a higher concentration of corresponding emissions. The Ti peaks are characteristic of the Ti arc and the C emissions are from the carbon paint applied on the front surface of SF-pCAT. There is a prominent peak of carbon at 335.5 nm with an intensity of 54 a.u, which reveals the deposition of carbon on the cathode. This deposition of carbon acts as a protective layer and the erosion rate is also low for SF-pCAT. FIG. 13B and 13C at 25 and 29V showed similar emission spectra but with different intensities.

[0119] FIG. 13A-13C illustrate OES measurements for SF-pCAT at 21V (FIG. 13A), 25V (FIG. 13B), and 29V (FIG. 13C) in the vacuum environment for titanium plasma. The OES analysis was also performed on the axi-symmetric pCAT under the same operating conditions as the SF-pCAT. The results from this analysis reveal the plasma composition at various PPU voltages. The emission spectra from the axi-symmetric pCAT are consistent with those observed in the SF-pCAT, primarily featuring emissions from titanium in different ionization states (Ti+1, Ti+2, Ti+4) as well as carbon (C) as shown in FIGS. 14A, 14B, 14C. A significant observation is that the predominant titanium emissions originate from the titanium cathode, which is expected and confirms the primary source of ions in the thruster. However, the notable difference in carbon emissions between the two thruster designs is particularly interesting. FIG. 14A-14C illustrates OES measurements for axi-symmetric pCAT at 21V (FIG. 14A), 25V (FIG. 14B), and 29V (FIG. 14C).27130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT

[0120] The intensity of the carbon peak is lower in the axi-symmetric pCAT compared to the SF-pCAT. Additionally, the number of carbon peaks has gradually decreased, indicating a reduction in carbon emissions. This decrease in carbon emissions is particularly evident at higher PPU voltages, where the plasma tends to exhibit a pure titanium composition.

[0121] The trend towards a purer titanium plasma at higher PPU voltages suggests that the axi-symmetric pCAT operates more efficiently under these conditions, resulting in less carbon deposition on the cathode surface. This effectiveness can be attributed to several factors. First, higher voltages provide more energy for electron impact ionization, favoring the production of titanium ions over carbon species. Second, the circular geometry may enhance plasma confinement, reducing interactions with carbon-containing surfaces. Additionally, the higher voltages may shift the electron energy distribution to favor titanium ionization over carbon excitation or ionization.

[0122] The electron temperature based on the emissions of the Ti+2ion transitions is calculated. The emission at 279.9nm corresponding to the transition from3t / 2(3F)4t / , and the emission at 351.6nm from 3< (3F)4 — 3t / 2(3F)4 / 9 are considered for this analysis. These emissions correspond to electron transitions in the Ti+2ion and are observed during spectroscopic measurements obtained under controlled plasma conditions. Assuming local thermodynamic equilibrium, the relative populations of the excited states of the ions can be expressed using the Boltzmann distribution. The ratio of the intensities of the two emission lines can be related through the Boltzmann equation:

[0123] In this equation, g and g2represent the statistical weights of the energy levels while and A2are the respective wavelengths. The energies E and E2are derived from the respective wavelengths of the transitions and KBis the Boltzmann constant, and Teis the electron temperature. A Python script was written for analyzing the electron temperature and is used for calculating the electron temperature as a function of PPU Voltage, depicted in FIG. 15. Detailed analysis is mentioned in

[0015]

[0124] FIG. 15 illustrates electron temperature calculated from the Ti+2 ions as a function of PPU voltage. As the PPU voltage increases, it injects additional energy into the plasma, which accelerates the free electrons to higher speeds, consequently raising their kinetic energy. These high-energy electrons collide more frequently and more intensely with the Ti+2ions, transferring energy that excites the ions to elevated energy states. Under local28130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT thermodynamic equilibrium, the populations of these excited states adhere to the Boltzmann distribution. This means that as the electron temperature rises, a larger fraction of ions occupy higher energy levels. The increased excitation is evident in the altered intensity ratio of the emission lines, as described by the Boltzmann equation. Therefore, the higher voltage results in enhanced collisional excitation of the ions, leading to the observed upward trend in the electron temperature with rising PPU voltage.Cathode Imaging and Composition

[0125] High-resolution microscopic images were captured for the titanium cathode to analyze changes in structural morphology and composition. The images were taken for a cathode sample which was operated for over a million pulses and a sample that has not been exposed to plasma. The comparison between the exposed and unexposed samples allows for a detailed examination of the effects of prolonged plasma exposure on the titanium cathode. The treated sample, which underwent extensive operation, is expected to show significant alterations in its surface morphology, potentially including the deposition of carbon and other structural changes resulting from the plasma environment. In contrast, the control sample, which remained unexposed, serves as a baseline for understanding the natural state of the titanium wire.

[0126] FIG. 16A illustrates an SEM image of a control sample of the cathode at 250x magnification. FIG. 16B illustrates 350x magnification (with highlighted mark), where the control sample is imaged, where the cathode sample presented is a cut section, and where the spots in the sample show micro granular structures of carbon spots on the titanium material.

[0127] FIG. 17A illustrates an SEM image of the treated Ti sample exposed to plasma for more than a million pulses at 350x. FIG. 17B illustrates a Ti treated sample at 500x magnification, where the highlighted circle is believed to be a region of primary deposition.

[0128] The treated sample has a layer of deposition, primarily composed of carbon, which was previously used for triggerless arcing. Over extended periods, this carbon layer redeposits onto the cathode surface, influencing the erosion rate, as discussed above. The thruster has been operated under various conditions, such as PPU voltages, arc currents, pulse widths, and frequencies, which may affect the extent of carbon deposition. The next steps involve studying the material deposition. EDS analysis will be used to determine the elemental composition of the metal surface, which is particularly useful in studying deposition processes where various unknown elements accumulate over time. EDS analysis identifies and29130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT quantifies the elements present on the metal surface, offering in-depth knowledge about the deposition phenomena occurring on the titanium cathode.

[0129] FIG. 18 illustrates an EDS analysis of an unexposed sample, where elemental composition was considered at the marked location, and where the figure also includes quantitative numbers of the elements present on the unexposed titanium rod.

[0130] FIG. 19 illustrates an EDS analysis of an exposed sample, where the sample is exposed to plasma for more than 1 million pulses, where elemental composition was considered at the marked location, spot, and where the figure also includes quantitative numbers of the elements present on the exposed titanium rod.

[0131] EDS confirmed that the sample was made up of titanium with 85.14% weight followed by Carbon, Nitrogen, Scandium, and Silicon with weight percentages of 9.56%, 2.32%, 2.14%, and 0.84% respectively. EDS revealed that the treated sample consisted of major deposition of carbon with 53.96% of weight followed by oxygen, titanium, and silicon with a weight percentage of 22.4%, 15.43%, 5.37% respectively. The highest peak in the graph corresponds to carbon. A similar deposition of carbon on their grid sample was observed by Taploo et. al. [5], Interestingly, the carbon layer that was previously applied on the front surface of the thruster for triggerless arcing gets deposited on the surface of the titanium cathode during vacuum arc discharge. So, this also explains the reason for the low erosion rate in the absence of a magnetic field. As observed from FIG. 1 IB, the first iteration taken for the erosion rate analysis has the highest erosion rate of 195.23 pg, as there is no deposition of carbon. From there on the erosion rate decreases as there is deposition of carbon on the titanium rod. The newly deposited carbon gets ablated causing less erosion of titanium.Thrust Measurements

[0132] In case of the axi-symmetric pCAT, direct thrust measurements were performed with the thruster mounted directly on a beam. Prior to obtaining the thrust results, the thrust stand was carefully balanced to assess any resulting torque that could potentially affect the thrust measurements. This step is crucial, as the forces involved are in the micro-newton range; even the slightest disturbance or residual force may lead to inaccurate data. Once the balancing was completed, the thrust stand was calibrated, and thrust data was collected following a pattern of 30 seconds with the thruster off, 30 seconds with the thruster on, and then 30 seconds with the thruster off again, as previously detailed. The thrust data was recorded as a function of PPU voltage and frequency to analyze trends associated with these parameters.30130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT

[0133] Results are presented in FIG. 20, which illustrates direct thrust measurements performed with an axi-symmetric pCAT, showing thrust as a function of PPU voltage.

[0134] The thrust levels show a clear upward trend with increasing PPU voltages. This can be attributed to the higher amounts of arc current generated at these PPU voltages. As the arc current increases, the arc current enhances the ionization process, leading to a greater production of ions that contribute to thrust generation. Additionally, thrust levels show a linear increase with frequency at lower PPU voltages, indicating a direct relationship between frequency and thrust in this range. However, at higher PPU voltages, the trend shifts to a gradual exponential increase in thrust levels with frequency. This behavior may be due to the fact that increased ionization levels at higher voltages lead to a more robust arc discharge. As frequency increases, rapid cycling of the discharge allows for more efficient ionization and acceleration of ions, resulting in a significant enhancement of thrust. For SF-pCAT, thrust is calculated indirectly, using the ion velocity and erosion rate. At 21 V PPU voltage and 750 ps pulse width, the SF-pCAT generates a thrust of 3.26 pN. This indicates a force of 3.26 pN exerted by the ions within the plasma.Lifetime Assessments

[0135] The lifetime of the axi-symmetric micro-cathode vacuum arc thruster (pCAT) is evaluated by monitoring arc voltage and arc current at regular intervals, specifically every 72,000 pulses. This approach is designed to assess the thruster's performance and reliability over time, particularly as the axi-symmetric pCAT operates at a frequency of 20 Hz throughout the lifetime testing. The impedance, as shown in FIG. 21, calculated by dividing arc voltage by arc current, is used to monitor the thruster's operational health. Variations in impedance, characterized by drops and peaks, indicate deposition of carbon and the degradation of the cathode due to arcing.

[0136] FIG. 21 illustrates axi-symmetric pCAT lifetime results of impedance vs. number of pulses observed.

[0137] Visual inspections after the lifetime tests reveal extensive damage to the ceramic and anode, including significant wear and degradation, as well as burning of the cathode support. This damage is attributed to the harsh operating conditions that pCATs endure during prolonged use. Interestingly, observations indicate that the anode also experiences erosion, leading to the formation of distinct anode spots when operated at a higher frequency. This erosion suggests that the anode is not merely a passive component but actively participates in the arcing process, which may have implications for the overall efficiency and longevity of31130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT the thruster. Moreover, the diameter of the cathode spot appears to be larger than the contact area of the cathode on the ceramic, resulting in a shift of the electric field towards the anode. This phenomenon contributes to the formation of the anode spots, raising questions about the underlying mechanisms driving this behavior. The interaction between the cathode and anode during operation may lead to complex plasma dynamics that influence the observed erosion patterns. Further studies are needed to explore the mechanisms behind the formation of anode spots and their impact on thruster performance.Performance Characteristics

[0138] In this section, the performance characteristics, such as thrust-to-power ratio, specific impulse and operational efficiency are calculated for axi-symmetric pCAT. The thrust-to-power ratio (T / P) at 21V PPU voltage is measured to be 8.21 pN / W, as shown in FIG. 22A. The thrust-to-power ratio trend exhibits a U-shaped pattern concerning PPU voltage, initially showing a decreasing effect at lower voltages before gradually increasing as the PPU voltage rises. At lower voltages, thrust production is less efficient due to insufficient ion acceleration, resulting in a lower thrust-to-power ratio. As the voltage increases, ion acceleration improves, leading to higher thrust efficiency. However, this initial improvement is offset by increased power consumption, causing the ratio to decrease. At higher voltages, the enhanced ion acceleration and generation lead to more efficient thrust production, outweighing the increased power consumption and causing the ratio to rise again.

[0139] FIGS. 22A-22B illustrate average thrust to power ratio (T / P) (FIG. 22 A), and specific impulse as a function of PPU voltage (FIG. 22B).

[0140] In addition to the thrust-to-power ratio, specific impulse shows a positive correlation with increasing PPU voltage, as shown in FIG. 22B. The specific impulse increases from about 2350 seconds at 21 V to approximately 2700 seconds at 35 V, suggesting that the thruster becomes more efficient in using propellant mass to generate thrust at higher voltages. This higher specific impulse allows for longer mission durations with a given amount of propellant. Overall, the positive correlation between these metrics and PPU voltage implies that increasing the voltage can enhance the thruster's performance. However, it is essential to recognize that this trend may not persist indefinitely; at higher voltages, the system may encounter limitations in ability to efficiently convert additional energy into thrust, resulting in a diminished effect of voltage on both metrics.

[0141] The propulsive efficiency of the axi-symmetric pCAT is calculated by dividing the output thrust by the power input, as shown in FIG. 23. The propulsive efficiency at 21V PPU32130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT voltage is recorded at 48%. However, as PPU voltage increases, propulsive efficiency decreases to 38.2% at 35 V. Notably, the propulsive efficiency reaches its lowest point at 28V, where it drops to around 31.6%.

[0142] FIG. 23 illustrates axi-symmetric pCAT propulsive efficiency calculated as a function of PPU Voltage.

[0143] This behavior indicates that at lower voltages, the thruster effectively converts input power into thrust, likely due to optimal ionization and energy transfer conditions. As the voltage rises beyond this point, efficiency diminishes, potentially due to increased losses in the plasma, such as resistance between the electrodes or a reduction in ionization efficiency.

[0144] In space propulsion, delta-v calculations are crucial for understanding the performance of thruster systems, especially for small satellites like CubeSats. Delta-v determines a spacecraft's capability to alter its trajectory or altitude, making Delta-v a critical parameter for various mission phases, including insertion into orbit, rendezvous, and transfer maneuvers. In practical operation, the thruster functions with a mass flow rate of 5 / 10-4g / s during arcing

[0016] ,

[0017] , This operational mass flow rate is typically around 300 times higher than the average erosion rate of 1 ,8pg / s. The thruster is operated in a pulsed mode with a total of 10 million pulses, each lasting 620 ps. This results in a cumulative arcing time of 6200 seconds.

[0145] To calculate the delta-v for a 1U CubeSat with a mass of 1 kg, we use rocket equation, which is given by:where Av = Change in velocity (m / s) Ve= Exhaust Velocity of ions (m / s) m0= Initial mass (Kg) nif= Final Mass (Kg)

[0146] Given the results at 21V PPU voltage, the exhaust velocity of the ions is measured to be 20 km / s (or 20,000 m / s). Considering the operational mass flow rate of 5 / 104g / s, the initial and final mass of the CubeSat can be determined. After performing necessary calculations, the delta-v is determined to be 60 m / s.CONCLUSION

[0147] Existing traditional pCATs exhibit various designs, each with unique capabilities; however, a common limitation across these designs is the lack of a propellant feeding33130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT mechanism, which can significantly impact their lifespan. As detailed above, this disclosure introduces a novel propellant feeding mechanism aimed at increasing the lifetime of pCATs, establishing a foundation for enhancing the efficiency and longevity of these thrusters. This disclosure presents, two pCATs with efficient feeding mechanisms: the SF-pCAT and the axi-symmetric pCAT. The plasma parameters and performance characteristics of both thrusters are detailed and compared above.

[0148] The optimum operating conditions for the SF-pCAT were observed at a 21V PPU voltage and a 750 ps pulse width. The ion current density and plasma density were measured at 103A / m2and 3 x 1018m3, respectively, with a maximum ion-by-arc current ratio of 3.2%. This indicates that a significant amount of arc current was used for thrust generation. In contrast, the axi-symmetric pCAT demonstrated improved performance metrics, with ion velocities measured at 15 km / s in the absence of a magnetic field, which doubled to 30 km / s due to the drift of ions in a magnetic field.

[0149] The application of a 0.5T magnetic field resulted in a 75% increase in discharge current, a 52.6% increase in ion current, and a 62.77% increase in ion velocity for the SF- pCAT. However, a loss of 0.04A in ion current was measured when the Faraday cup was positioned at 90 degrees and 270 degrees relative to the thruster head, attributed to the splattering of ions at lower PPU voltages leading to non-uniform ion emission. In contrast, the axi-symmetric design effectively resolved the ion divergence issue observed in the SF- pCAT, resulting in more consistent ion emission. The back-flux of 4mA was detected by simulating a real -world satellite scenario at the back of the SF-pCAT, which served as motivation for the development of the axi-symmetric pCAT. Experimentally, the erosion rate of the SF-pCAT was determined to be 4 pg / C. The E x B probe designed at MPNL was used to find the charge state of the ion plasma as a function of expected velocity. Emissions from the Wein filter primarily consisted of Ti+1, Ti+2, and C emissions, verified with SEM analysis data. The velocity of the titanium ions was estimated to be 40 km / s when measured with the E x B probe in the presence of the magnetic field. The carbon deposition on the cathode formed a protective and conductive layer, potentially contributing to the low erosion rate.

[0150] An ion contribution of 5% from arc current was observed without the influence of a magnetic field, while the drift of the magnetic field increased this value to 10.5% in the axi- symmetric pCAT. This indicates that a greater amount of the ion current is extracted, making the axi-symmetric pCAT design more robust and minimizing ion current losses. As the ion current and percentage of ions increased in the axi-symmetric pCAT, thrust levels rose to 3534130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT pN at 21 V PPU voltage and 5Hz frequency, further increasing to 168 pN at 35V PPU voltage and 20Hz frequency. The thrust-to-power (T / P) ratio of the axi-symmetric pCAT was measured at 8.21 pN / W, with a power consumption of 1.7W, meaning that for every watt of electrical power consumed by the thruster, the axi-symmetric pCAT generates a thrust of 8.21 pN. The specific impulse of the axi-symmetric pCAT was recorded at 2322 seconds, indicating its efficiency in converting propellant into thrust. An impulse bit of 85.5 mN s refers to the total change in momentum delivered by the thruster in a single pulse. Additionally, the axi-symmetric pCAT ablated 1.61 pg of titanium cathode per second, achieving a propulsive efficiency of about 48.25% which is obtained by dividing the output thrust power by the input power. Additionally, extensive lifetime experiments and delta-v calculations were performed, culminating in a total of 13M pulses and achieving a delta-v of 60m / s. The axi-symmetric pCAT maintains optimal functionality even after 13M+ pulses and can continue arcing until the propellant is fully exhausted. This makes the axi-symmetric pCAT a choice for performing other operations in space.

[0151] In summary, while both the SF-pCAT and the axi-symmetric pCAT demonstrate advancements in pCAT technology, the axi-symmetric pCAT design shows superior performance in terms of ion velocity, thrust generation, and overall efficiency, addressing characteristics observed in the SF-pCAT.

[0152] The The disclosure, particularly the axi-symmetric pCAT, addresses several issues encountered in the prior art. The SF-pCAT utilizes a spring-based feeding mechanism rather than a stepper motor or any other electrical devices, which reduces overall weight. The stepper motor often adds significant mass to thruster designs, and by eliminating it, both the SF- pCAT and axi-symmetric pCAT achieves a more lightweight configuration that is especially advantageous for small satellite applications. The design eliminates the need for a stepper motor. Instead of relying on a motor to push the cathode forward continuously, the SF-pCAT and axi-symmetric pCAT uses a mechanical spring as its feeding mechanism. The spring provides a simple and lightweight solution that continually pushes the cathode into position as it erodes without the added complexity and power demands of a motor, and provides enhanced ablation efficiency and uniform erosion, and provides a reliable and streamlined solution, though in certain embodiments a stepper motor can be utilized.

[0153] In addition, the system uses a triggerless arc ignition process, to initiate the arc, which is more reliable. By ensuring that the cathode's surface area is smaller, the present device allows for uniform ablation, mitigating issues of irregular erosion that were prevalent35130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT in prior art mechanisms. Controlled ablation refers to the ability to manage the rate and uniformity of material removal from the cathode as it operates, unlike the uncontrolled ablation seen in traditional setups using stepper motors, where the erosion pattern can be inconsistent and unpredictable. The strategic configuration of the SF-pCAT and axi- symmetric pCAT, including the optimization of the inter-electrode gap and the maintenance of the cathode position through the feeding mechanism, further contributes to successful ignition and consistent operation.

[0154] The spring-based feeding mechanism in the cathode system allows for more controlled ablation by enabling the cathode to move upward as it is ablated, creating and maintaining no gap between the cathode tip and the ceramic support (i.e., the cathode tip contacts the ceramic support). This dynamic adjustment occurs naturally as the spring responds to changes in the cathode's length, ensuring optimal positioning without manual intervention. In contrast, stepper motors push the cathode forward based on pre-programmed instructions, regardless of the actual ablation state, which can lead to uneven material loss. Consequently, the spring mechanism promotes a more responsive and efficient and controlled ablation process. The cathode must remain pressed against the ceramic support to ensure consistent arc generation. It is essential to maintain an optimum inter-electrode gap between the anode and cathode; this gap is determined experimentally by testing various configurations. In this design, the inter-electrode gap corresponds to the width of the ceramic insulator, allowing for stable and effective operation of the thruster.

[0155] Accordingly, the present device provides a specific configuration and arrangement of components, particularly the cathode being positioned around the anode and the implementation of the feeding mechanism. The unique arrangement of multiple cathodes relative to the anode, the way the cathode is fed by a spring into the discharge zone optimizes plasma generation and stability. Additionally, the adoption of a smaller cathode wire represents a significant innovation; which is effectively utilized alongside the distinct feeding and support mechanisms to achieve controlled and uniform ablation over extended use. Most importantly, this innovative design has allowed us to achieve a remarkable lifetime of over 13 million pulses, a milestone that previous systems failed to reach.

[0156] It is noted that the drawings may illustrate, and the description and claims may use geometric or relational terms, such as side, top, bottom, rear, forward, front, rearward, axial, elongated, parallel, orthogonal, circular, symmetric, axi-symmetric, end, center, perimeter, radial, surface, distal, proximal, end. These terms are not intended to limit the disclosure and,36130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT in general, are used for convenience to facilitate the description based on the examples shown in the Figures. In addition, the geometric or relational terms may not be exact. For instance, surfaces may not be exactly perpendicular or parallel to one another because of, for example, roughness of surfaces, tolerances allowed in manufacturing, etc., but may still be considered to be perpendicular or parallel.

[0157] The foregoing description and drawings should be considered as illustrative only of the principles of the disclosure, which may be configured in a variety of shapes and sizes and is not intended to be limited by the embodiment herein described. Numerous applications of the disclosure will readily occur to those skilled in the art. Therefore, it is not desired to limit the disclosure to the specific examples disclosed or the exact construction and operation shown and described. Rather, all suitable modifications and equivalents may be resorted to, falling within the scope of the disclosure. For example, while the thruster is described and shown for use with a CubeSat, any suitable housing or application can be provided.

[0158] The following patents and documents cited herein are incorporated herein in their entirety by reference: [1] Y. Song, Y. R. Lee, J.-P. Park, and S.-Y. Park, “CANYVAL-X: Operational Scenario and Strategy,” in 2018 SpaceOps Conference, Marseille, France: American Institute of Aeronautics and Astronautics, May 2018. doi: 10.2514 / 6.2018-2636; [2] J. Schoolcraft, A. T. Klesh, and T. Werne, “MarCO: Interplanetary Mission Development On a CubeSat Scale,” in SpaceOps 2016 Conference, Daejeon, Korea: American Institute of Aeronautics and Astronautics, May 2016. doi: 10.2514 / 6.2016-2491; [3] R. L. Staehle et al., “Interplanetary CubeSats: Opening the Solar System to a Broad Community at Lower Cost”; [4] A. Freeman, “Exploring our solar system with CubeSats and SmallSats: the dawn of a new era,” CEAS Space J, vol. 12, no. 4, pp. 491-502, Dec. 2020, doi: 10.1007 / sl2567-020- 00298-5; [5] M. kuhn and J. Schein, “Development of a High-Reliability Vacuum Arc Thruster System,” Aerospace Research Central, vol. 38, no. 5, doi: https: / / doi.org / 10.2514 / LB38202; [6] T. Zhuang, A. Shashurin, G. Teel, D. chiul, and M. Keidar, “Co-axial Micro-Cathode Arc Thruster (CA-uCAT) and Performance Characterization,” Aerospace Research Central, Nov. 2012, [Online], Available: https: / / doi.Org / 10.2514 / 6.2011-5884; [7] S. Hurley, “Advancements to the Micro-Cathode Arc Thruster: Linear Actuator, Ablative Anode, and Modular Designs,” The George Washington University, Washington DC, 2018. [Online], Available: https: / / scholarspace.library.gwu.edu / concem / gw_etds / pc289j271 pp: 28-34; [8] I.Kronhaus, M. Laterza, and Y. Maor, “Inline screw feeding vacuum arc thruster,” Review of37130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENTScientific Instruments, vol. 88, no. 4, p. 043505, Apr. 2017, doi: 10.1063 / 1.4979706; [9] G. Teel, A. Shashurin, X. Fang, and M. Keidar, “Discharge ignition in the micro-cathode arc thruster,” Journal of Applied Physics, vol. 121, no. 2, 01 2017, doi: https: / / doi.Org / 10.1063 / l.4974004;

[0010] D. B. Zolotukhin, S. R. P. Bandaru, K. P. Daniels, I. I. Beilis, and M. Keidar, “Demonstration of electric micropropulsion multimodality,” Sci. Adv., vol. 8, no. 36, p. eadc9850, Sep. 2022, doi: 10.1126 / sciadv.adc9850;

[0011] A. Anders, I. G. Brown, R. A. MacGill, and M. R. Dickinson, “'Triggerless’ triggering of vacuum arcs,” J. Phys. D: Appl. Phys., vol. 31, no. 5, pp. 584-587, Mar. 1998, doi: 10.1088 / 0022- 3727 / 31 / 5 / 015;

[0012] A. Anders, J. Schein, and N. Qi, “Pulsed vacuum-arc ion source operated with a ‘triggerless’ arc initiation method,” Review of Scientific Instruments, vol. 71, no. 2, pp. 827-829, Feb. 2000, doi: 10.1063 / 1.1150305;

[0013] M. Keidar et al., “Magnetically enhanced vacuum arc thruster,” Plasma Sources Sci. Technol., vol. 14, no. 4, pp. 661-669, Nov. 2005, doi: 10.1088 / 0963-0252 / 14 / 4 / 004;

[0014] M. Keidar and schein Jochen, “Modeling of a magnetically enhanced vacuum arc thruster,” AIAA;

[0015] A. Anders and G. Yu. Yushkov, “Ion flux from vacuum arc cathode spots in the absence and presence of a magnetic field,” Journal of Applied Physics, vol. 91, no. 8, pp. 4824-4832, Apr. 2002, doi: 10.1063 / 1.1459619;

[0016] “Pearson Electronics 110A Current Sensor.” [Online], Available: 39. https: / / pearsonelectronics.com / pdf / 110A.pdf;

[0017] “TDS2004 Digital Storage Oscilloscopes.” [Online], Available: 40. https: / / download.tek.com / manual / 07117900Q.pdf;

[0018] S. Hurley, “Advancements to the Micro-Cathode Arc Thruster: Linear Actuator, Ablative Anode, and Modular Designs,” Theis, The George Washington University, Washington DC, 2018. [Online], Available: https: / / www.proquest.com / docview / 2090893154 pp: 53-55;

[0019] S. R. P. Bandaru, “23.Multi-Stage Micro-Cathode Arc Thrusters,” Thesis, The George Washington University, 2023. [Online], Available: https: / / www.proquest.com / docview / 2801875353?pq-origsite=primo pp: 45-64;

[0020] D. Gerst, D. Renaud, S. Mazouffre, P. Chabert, and A. Aanesland, “E*B probe investigation of the PEGASES thruster ion beam in Xe and SF6,” in 33rd International Electric Propulsion Conference, The George Washington University, Washington, D.C., USA, 2013, p. 11;

[0021] E. M. Oks et al., “Elevated ion charge states in vacuum arc plasmas in a magnetic field,” Applied Physics Letters, vol. 67, no. 2, pp. 200-202, Jul. 1995, doi: 10.1063 / 1.114666;

[0022] “Lifetime Investigations of Micro-Cathode and Matrix Arc Thrusters.pdf. ”pp: 22-45;

[0023] M. Keidar and B. Isak, Plasma Engineering: Applications from Aerospace to Bio- and Nanotechnology. Elsevier / AP pp: l-14;

[0024] A. Taploo et al., “Characterization of a circular38130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT arc electron source for a self-neutralizing air-breathing plasma thruster,” J Electr Propuls, vol.2, no. 1, p. 21, Oct. 2023, doi: 10.1007 / s44205-023-00058-7 pp: 135-142.39130761 .00533 / 153764690v.1

Claims

DOCKET NO. 130761-00533 PATENTWhat is claimed is:

1. A vacuum arc thruster, comprising: a central anode; a plurality of cathodes, each extending radially outward from said central anode, each of said plurality of cathodes having a leading end; an insulator positioned between said central anode and the leading end of each of said plurality of cathodes to form a gap therebetween; and one or more feeding mechanisms coupled to said plurality of cathodes, said one or more feeding mechanisms pushing the leading end of each of said plurality of cathodes toward said central anode.

2. The arc thruster of claim 1, wherein said central anode has a solid circular, solid disc or solid cylindrical shape.

3. The arc thruster of claim 1 or 2, wherein each said plurality of cathodes comprise an elongated rod, where said elongated rod is positioned transverse to a longitudinal axis of said central anode.

4. The arc thruster of any one of claims 1-3, where one feeding mechanism is coupled to each of said plurality of cathodes, each feeding mechanism configured to push the leading end of each cathode toward and transversely to said central anode.

5. The arc thruster of any one of claims 1-4, configured so that an arc discharge is formed between said central anode and each leading end of each of the plurality of cathodes across said gap, where the one or more feeding mechanisms each provide a bias force that biases the leading end of each of said plurality of cathodes further toward said central anode as the leading end of each of said plurality of cathodes erodes due to the arc discharge.

6. The arc thruster of any one of claims 1-5, further comprising a housing having a housing center an outer housing support structure arranged about said housing center, where said central anode is coupled to the housing center and a proximal end of each of said plurality of cathodes are coupled to said outer housing support structure, the outer housing support structure defining an outer perimeter of said housing.40130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT7. The arc thruster of any one of claims 1-6, wherein the plurality of cathodes, each extending radially outward from said central anode, are configured to be controlled and operated independently or collectively to form respective arc discharges formed between said central anode and each of the leading ends of the plurality of cathodes across the gap.

8. The arc thruster of any one of claims 1-7, wherein said one or more feeding mechanisms each comprise a spring configured to provide a bias force that biases the leading end of each of said plurality of cathodes toward the anode, pushing the leading end of each of said plurality of cathodes toward the central anode during arc thruster operation.

9. The arc thruster of any one of claims 1-8, wherein said one or more feeding mechanisms each comprise a feeding mechanism housing including a spring and a base, said spring configured to push a respectively associated cathode out of a distal end of the feeding mechanism housing and toward said central anode, and said base configured to couple a proximal end of the feeding mechanism housing to an outer housing support structure of the arc thruster. .

10. The arc thruster of any one of claims 1-9, wherein said insulator comprises Teflon.

11. The arc thruster of any one of claims 1-10, wherein said insulator comprises a thin layer sheet wrapped about a perimeter of the central anode, said thin layer sheet defining a central anode housing outer side surface, where the leading end of each of said plurality of cathodes faces and is orthogonal to the central anode housing outer side surface.

12. The arc thruster of any one of claims 1-11, further comprising; a hollow housing having a top side, bottom side, a longitudinal axis between the top side and the bottom side, and at least one housing wall extending about the longitudinal axis and between the top side and the bottom side to form an interior space; said central anode positioned in the interior space along and about the longitudinal axis of the hollow housing, where said one or more feeding mechanisms are each coupled to the at least one housing wall; where said hollow housing has a disc or cylindrical shape, said central anode is circular in cross-section, and said at least one housing wall is concentric about said central anode; and where said one or more feeding mechanisms each continuously push said plurality of cathodes to said central anode during cathode ablation.41130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT13. The arc thruster of any one of claims 1-12, wherein each said plurality of cathodes is configured to completely ablate.

14. The arc thruster of any one of claims 1-13, wherein said arc thruster is axi-symmetric.

15. The arc thruster of any one of claims 1-14, wherein said plurality of cathodes are symmetrically arranged about said central anode and generate a symmetrical thrust.

16. The arc thruster of any one of claims 1-15, wherein said central anode is a flat disc having a circular cross-section.

17. An arc thruster, comprising: an anode having a longitudinal axis; a cathode extending radially outward, away from the anode, the cathode having a leading end and a trailing portion defining a longitudinal axis therebetween, where the longitudinal axis of the anode is transverse the longitudinal axis of the cathode; and an insulator positioned between the anode and the leading end of the cathode, forming a gap therebetween.

18. The arc thruster of claim 17, further comprising a cathode support formed about said insulator and configured to retain the leading end of the cathode in position relative to the anode and insulator.

19. The arc thruster of claim 17 or 18, wherein the anode is cuboidal in shape.

20. The arc thruster of any one of claims 17-19, further comprising a feeding mechanism coupled to the trailing end of the cathode, configured to push the leading end of the cathode toward the anode.

21. The arc thruster of any one of claims 17-20, configured so that an arc discharge is formed between the anode and the leading end of the cathode across the gap, where the feeding mechanism provides a bias force that biases the leading end of the cathode further toward the anode as the leading end of the cathode erodes due to the arc discharge.

22. The arc thruster of any one of claims 17-21, wherein the feeding mechanism comprises a spring configured to provide a bias force that biases the leading end of the cathode to toward the anode, pushing the leading end of the cathode toward the anode during arc thruster operation.42130761 .00533 / 153764690v.1DOCKET NO. 130761-00533 PATENT23. The arc thruster of any one of claims 17-22, wherein said insulator comprises Teflon, or any insulator material.

24. The arc thruster of any one of claims 17-23, wherein the insulator comprises a thin layer sheet wrapped about at least a portion of a perimeter of the anode, said thin layer sheet defining the gap, where the leading end of the cathode is located at an outer perimeter of the insulator, orthogonal to and across the gap from the anode.

25. An arc thruster, comprising: an anode having an anode leading end with an anode front surface; an elongated cathode extending orthogonally outward from the anode, the cathode having a cathode leading end with a cathode front surface; and an insulator positioned between the anode front surface and the cathode front surface, and a discharge plasma is formed by the anode leading end and the cathode leading end.43130761 .00533 / 153764690v.1

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