WO2020117354A2

WO2020117354A2 - Optimized rf-sourced gridded ion thruster and components

Info

Publication number: WO2020117354A2
Application number: PCT/US2019/052089
Authority: WO
Inventors: Umair M. SIDDIQUI
Original assignee: Phase Four, Inc.
Priority date: 2018-09-28
Filing date: 2019-09-20
Publication date: 2020-06-11
Also published as: WO2020117354A3

Abstract

The invention provides an improved gridded ion thruster design having one or more separate plasma generating modules.

Description

OPTIMIZED RF-SOURCED GRIDDED ION THRUSTER AND COMPONENTS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims benefit of U.S. Provisional Application No. 62/738,745 filed September 28, 2018 which is incorporated by reference in its entirety.

FIELD OF THE INVENTION

[0002] This invention generally relates to plasma propulsion systems including, for example, gridded ion thrusters.

STATEMENT OF GOVERNMENT-SPONSORED RESEARCH

[0003] N/A.

BACKGROUND OF THE INVENTION

[0004] Electric propulsion (“EP”) thrusters have gained widespread use in a variety of orbital maneuvering applications including station keeping and orbit transfer/orbit raising. EP thrusters have been developed for a wide range of power and thrust profiles and using a variety of propulsion principles. EP thrusters generate thrust in a two-step process. First, a propellant gas is ionized. Second, the ionized gas is accelerated and ejected from the thruster. Radio- frequency (“RF”) thrusters ionize the propellent using an oscillating electromagnetic field. Ion acceleration may be effected using magnetic or electrostatic fields. The present invention provides improvements in RF propellant ionization that may be applied to EP thrusters and, in particular, gridded ion thrusters.

SUMMARY OF THE INVENTION

[0005] The present invention provides an electrothermal RF plasma production system and thruster design, and associated components, that may be used in terrestrial applications, in large- scale satellite propulsion systems, and/or miniaturized to the mass, volume, and power budget of Cube Satellites (CubeSats) to meet the propulsion needs of the small satellite (~5 to -500 kg) constellations and larger satellites. In some embodiments, thruster designs that incorporate this plasma production system may be simple, scalable, and effective, and may be produced in large quantities using low-cost mass manufacturing techniques. The present designs and elements eliminate the use of erosive electrodes and high voltage electronics which increase the cost, complexity, and/or manufacturing difficulty associated with other plasma production/thruster designs.

[0006] In one aspect, the invention provides a plasma production device comprising:

(a) a substantially cylindrical plasma production chamber having a cylinder body, a first closed end, and a second open end;

(b) a magnet system comprising one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber (i.e., the cylinder body) such that each magnet produces a magnetic field of the same polarity within the plasma production chamber;

(c) a propellant tank and a flow regulator in communication with the plasma production chamber and configured to deliver a gaseous propellant from the propellant tank into the plasma production chamber; and

(d) a radio frequency (RF) antenna external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber;

wherein the plasma production device is configured to ionize and heat substantially all of a plasma by inductive heating.

[0007] In another aspect, the invention provides a plasma production device comprising:

(c) a propellant tank and a flow regulator in communication with the plasma production chamber and configured to deliver a gaseous propellant from the propellant tank into the plasma production chamber; and (d) a radio frequency (RF) antenna external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber;

wherein the plasma production chamber radius (RL) is equal to 1-7 times the skin depth (p_s) of the RF energy.

[0008] In another aspect, the invention provides a plasma production device comprising:

wherein the plasma production chamber radius (RL) is equal to 1.1 - 5.0 times the Larmor orbit radius (pi) of a plasma ion.

[0009] In another aspect, the invention provides a plasma production device comprising:

(a) a substantially cylindrical plasma production chamber having a cylinder body, a first closed end and a second open end;

(b) a magnet system comprising one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber (i.e., the cylinder body) such that each magnet produces a magnetic field of the same polarity within the plasma production chamber; (c) a propellant tank and a flow regulator in communication with the plasma production chamber and configured to deliver a gaseous propellant from the propellant tank into the plasma production chamber; and

(d) a radio frequency (RF) antenna comprising at least a spiral region (e.g., a flat spiral) external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber.

[0010] In some embodiments, the RF antenna comprises a first region that comprises a spiral (e.g., a flat spiral) and a second region that comprises a coil, helix, or half-helix. In some further embodiments the plane of the spiral region is perpendicular or substantially perpendicular to the longitudinal axis of the second region. In other embodiments, the RF antennal is an FSCH antenna, as described herein.

[0011] In another aspect, the invention provides a plasma production device comprising:

(c) a propellant tank and a flow regulator in communication with the plasma production chamber and configured to deliver a gaseous propellant from the propellant tank into the plasma production chamber;

wherein the RF energy frequency is less than 25% of an electron cyclotron frequency (/_cc) inside the production chamber.

[0012] In any of the foregoing aspects, the plasma production chamber radius (RL) is equal to 1-7 times (e.g., 4-6 times) the skin depth (p_s) of the RF energy. In some embodiments, the skin depth is about 1.0-2.0 mm including about 1.2-1.9 mm, 1.4-1.8 mm, and about 1.0 mm, 1.1 mm, 1.2 mm, 1.3 mm, 1.4 mm, 1.5 mm, 1.6 mm, 1.7 mm, 1.8 mm, 1.9 mm, and 2.0 mm. It is understood that the plasma production device may be configured to produce skin depths that are greater or less than those recited here and may depend upon the size and composition of the plasma production chamber, the specific propellant, the antenna power and configuration, other design features of the plasma production device, and the performance characteristics desired by the user.

[0013] In any of the foregoing aspects, the plasma production chamber radius (RL) is equal to 1.1 - 5.0 times (e.g., 1.1 - 4.0 and 1.1 - 3.0) the Larmor orbit radius (pi) of a plasma ion. In some embodiments, the plasma ion temperature is about 0.1 eV (~ 1100 K) or about 0.08-0.12 eV, 0.09-0.11 eV including about 0.08 eV, 0.09 eV, 0.10 eV, 0.11 eV, 0.12 eV, 0.13 eV. 0.14 eV, or more.

[0014] In any of the foregoing aspects, the antenna is or comprises a coiled antenna.

Optionally, the coiled antenna is right-handed. Optionally, the coiled antenna has 1-50 turns including, for example, at least 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, or 45 turns, or about 1-5, 1- 10, 1-20, 1-30, 1-40, 2-5, 2-10, 2-20, 2-30, 2-40, 2-50, 5-10, 5-20, 5-30, 5-40, or 5-50 turns). In any of the foregoing aspects, the antenna is a flat spiral coil hybrid (“FSCH”) antenna, as described herein. Optionally, the antenna (e.g., a coiled antenna or an FSCH antenna) is configured to cause a constructive interference in magnetic fields produced within the plasma production chamber. Optionally, the antenna (e.g., a coiled antenna or an FSCH antenna) is configured to seed and accelerate electrons on a plurality of (including a substantial majority, or even every) magnetic field lines inside the plasma production chamber. Other antenna designs for use in any of the foregoing aspects include half-helix, helical, and flat spiral antennas.

[0015] In any of the foregoing aspects, the RF energy frequency is less than 25% (e.g., less than 20%, 15%, 10% or 5%) of an electron cyclotron frequency (f_ce) in a substantial majority, majority, or throughout the entirety of the plasma production chamber.

[0016] In any of the foregoing aspects, the magnet system comprises a first radially- disposed magnet toward the first closed end and a second radially-disposed magnet toward the second open end. Optionally, the first radially-disposed magnet produces a first throat region within the plasma production chamber, the second radially-disposed magnet produces a second throat within the plasma production chamber, and the first throat region and the second throat region are separated by a plasma containment region having a lower magnetic field strength than either of the first throat region or the second throat region. In some configurations, the first throat region has substantially the same or a higher magnetic field strength than the second throat region.

[0017] Optionally, the magnet system comprises at least one planar magnet (e.g., 1, 2, 3, 4,

5, 6, or more, or 1-2, 1-3, 1-4, 1-5, 1-6 or more, or 2-3, 2-4, 2-5, 2-6 or more, or 3-4, 3-5, 3-6 or more, or 4-5 or 4-6 or more) disposed before the first radially-disposed magnet (i.e., closer to the first closed end), wherein the at least one planar magnet produces a magnetic field of the same polarity within the plasma production chamber as the one or more radially-disposed magnets, and wherein the magnetic field of the at least one planar magnet is substantially parallel to the longitudinal axis of the plasma production chamber.

[0018] In any of the foregoing aspects, the plasma production device comprises 1-20 radially-disposed magnets (e.g., 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, or 20, or 2-20, 2-10, 2-8, 2-

6, or 2-4, or 4-20, 4-10, 4-8, or 4-6). In some embodiments, the radially-disposed magnets are annular magnets.

[0019] In some embodiments, the magnets and/or magnet system is adapted and configured to produce a magnetic field inside the plasma production chamber of greater than at least 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, or 400 Gauss, or more in the coaxial direction throughout the length of the plasma production chamber. In some embodiments, the minimum magnetic field strength over the length of the plasma production chamber about 250-400 Gauss, 250-500 Gauss, 300-400 Gauss, or 300-500 Gauss.

[0020] In any of the foregoing aspects, the radially-disposed magnets and/or the planar magnet(s), independently, are electromagnets, permanent magnets, or combinations thereof.

[0021] In any of the foregoing aspects, the RF energy has a frequency of 3-300 MHz.

[0022] In any of the foregoing aspects, the propellant tank and flow regulator are in communication with the plasma production chamber through the first (closed) end and configured to deliver the gaseous propellant along the central longitudinal axis, or an axis parallel thereto. Alternatively, the propellant tank and flow regulator are in communication with the plasma production chamber through the cylinder body and, optionally, deliver the gaseous propellant along an axis perpendicular, substantially perpendicular, or at about 15°, 30°, 45°,

60°, or 75° to the central longitudinal axis.

[0023] In some embodiments, the propellant (e.g., xenon) flow rate is about 0.01 to 2.0 mg/second including, for example, 0.05 - 2.0 mg/sec., 0.05 - 1.0 mg/sec, 0.05 - 0.75 mg/sec., 0.05-0.5 mg/sec, 0.1 - 2.0 mg/sec., 0.1 - 1.0 mg/sec, 0.1 - 0.75 mg/sec., 0.1-0.5 mg/sec„ including about 0.01, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, and 1.0 mg/sec.

The foregoing flow rates are exemplary and not intended to be limiting. It is understood that higher or lower propellant flow rates may be used depending upon the size, power, and other design features of the plasma production device, the specific propellant used, and the

performance characteristics desired by the user.

[0024] In some embodiments, the AC power source provides 25-500 W to the antenna including, for example, about 50-500 W, 50-250 W, or about 25 W, 50 W, 75 W, 100 W, 150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 450 W, and 500 W. In some embodiments, the AC power is less than 150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 450 W, and 500 W. It is understood that higher or lower power may be used depending upon the size, propellant, and other design features of the plasma production device, and the performance characteristics desired by the user.

[0025] In some embodiments, the plasma production chamber is sized, and the plasma production device is adapted and configured to ionize at least about 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95%, or 99% of the propellant into plasma. In some embodiments, the plasma production chamber has a length, from the closed end to the open end, of about 15-100 mm including about 20-75 mm and 25-50 mm, and about 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, 45 mm, 50 mm, 55 mm, 60 mm, 65 mm, 70 mm, 75 mm, 80 mm, 85 mm, 90 mm,

95 mm, 100 mm, It is understood that the plasma production chamber may be shorter or longer and the specific length may vary according to the design features of the plasma production device, and the performance characteristics desired by the user.

[0026] In some embodiments, the plasma production device is configured and adapted such that the plasma production chamber has a radius (RL) that is 2-10 times the skin depth, as described herein, including for example, about 3-9, 4-8, 5-8, and 5-7 times the skin depth and about 2, 3, 4, 5, 6, 7, 8, 9, and 10 times the skin depth.

[0027] In some embodiments, the radius (RL) is about 5-20 mm including about 8-16 mm and about 10-15 mm, and about 6 mm, 8 mm, 10 mm, 12 mm, 14 mm, 16 mm, 18 mm, and 20 mm. It is understood that the plasma production chamber may have a smaller or larger radius and may vary according to the design features of the plasma production device, including the skin depth, and other performance characteristics desired by the user. [0028] In some embodiments, the plasma production device is configured to produce a plasma density of about 10¹¹ - 10¹⁵ particles per cm³ including about 10¹² - 10¹⁴ particles per cm³ and about 10¹¹, 10¹², 10¹³, 10¹⁴, 10¹⁵ particles per cm³.

[0029] In some embodiments of any of the foregoing aspects, the plasma production device is adapted and configured as follows:

(i) Propellant Flow Rate: 0.1-0.5 mg/second (e.g., xenon);

(ii) AC Power: 100-200 W (e.g., about 125 W or 150 W);

(iii) Plasma Production Chamber Length: about 25-50 mm;

(iv) Plasma Production Chamber Radius (RL): 10- 15 mm (e.g., 12 mm); and

(v) Minimum Magnetic Field Strength: 250-350 G (e.g., 300 G).

[0030] In another aspect, the invention provides a thrust-generating device (i.e., a thruster) including, for example, a satellite propulsion system (i.e., a satellite thruster) comprising a plasma production device of any of the foregoing aspects. In some embodiments, the thruster is electrodeless (i.e., lacks electrodes configured or adapted to produce plasma from the propellant).

[0031] In another aspect, the invention provides a flat spiral coil hybrid (“FSCH”) antenna, as described herein. The FSCH comprises a flat spiral portion and a coiled portion, wherein the plane of the flat spiral portion is perpendicular or substantially perpendicular to the longitudinal axis of the coiled portion. The spiral portion begins at a central point and extends outwards. The spiral terminates in a connection to the coil portion. The electrical input into the FSCH antenna is at the beginning of the spiral portion at the central point

[0032] In another aspect, the invention provides a device comprising (i) a cylindrical chamber having a cylinder body, a first closed end, and a second open end and (ii) an FSCH antenna comprising a flat spiral portion and a coiled portion, wherein the plane of the flat spiral portion is perpendicular or substantially perpendicular to the longitudinal axis of the coiled portion, wherein the spiral portion is disposed within, on, or adjacent to the first closed end and/or the coil portion is wound around the cylinder body and, optionally, embedded within the cylinder body or a groove on an outer surface of the cylinder body. The FSCH antenna is configured to cause a constructive interference in magnetic fields produced within cylinder body.

[0033] In some embodiments of the FSCH antenna in any of the foregoing aspects, the antenna is right-handed. In other embodiments, the antenna is left-handed. [0034] In some embodiments of the FSCH antenna in any of the foregoing aspects, the coil portion is a half-helix. Optionally, the coiled portion of the FSCH antenna has 1-50 turns including, for example, at least 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, or 45 turns, or about 1-5, 1- 10, 1-20, 1-30, 1-40, 2-5, 2-10, 2-20, 2-30, 2-40, 2-50, 5-10, 5-20, 5-30, 5-40, or 5-50 turns). Optionally, the spiral portion of the antenna has 1-50 turns including, for example, at least 2, 3,

4, 5, 10, 15, 20, 25, 30, 35, 40, or 45 turns, or about 1-5, 1-10, 1-20, 1-30, 1-40, 2-5, 2-10, 2-20, 2-30, 2-40, 2-50, 5-10, 5-20, 5-30, 5-40, or 5-50 turns).

[0035] In some embodiments of the FSCH antenna in any of the foregoing aspects, the FSCH antenna comprises a flat wire (i.e., forming a flat coil hybrid antenna (“FSCH”)). In other embodiments, the FSCH comprises a round or oval wire.

[0036] In some embodiments of the FSCH antenna in any of the foregoing aspects, the FSCH antenna is operably connected to an electrical power source (e.g., a battery, a solar panel, and grid power). In some embodiments, the electrical power source is an AC power source.

[0037] In another aspect, the invention provides a gridded ion thruster comprising (a) an upstream plasma production device described in any of the foregoing aspects, and (b) a downstream gridded ion discharge chamber. The downstream gridded ion discharge chamber generally comprises (i) a discharge chamber having an upstream (first) open end in

communication with the open of the plasma production chamber (i.e., to receive the plasma produced by the upstream plasma production device), and a downstream (second) open end through which the plasma ions are ejected to the exterior (e.g., outer space) of the thruster; (ii) a negatively-charged grid covering all or a substantial portion of the downstream open end; (iii) a grounded grid covering all or a substantial portion of the downstream open end and disposed downstream of the negatively-charged grid; and (iv) a cathode configured to eject or release electron to the exterior of the thruster. Generally, the grounded grid is external/downstream from the negatively-charged grid.

[0038] In another aspect, the invention provides a gridded ion thruster comprising (a) a plurality (e.g., two, three, four, five, or more) of upstream plasma production devices described in any of the foregoing aspects, and (b) a downstream gridded ion discharge chamber. The downstream gridded ion discharge chamber generally comprises (i) a discharge chamber having an upstream end in communication with each of the plasma production chambers (i.e., to receive the plasma produced by the plurality of upstream plasma production devices), and a downstream (second) open end through which the plasma ions are ejected to the exterior (e.g., outer space) of the thruster; (ii) a negatively-charged grid covering all or a substantial portion of the downstream open end; (iii) a grounded grid covering all or a substantial portion of the downstream open end and disposed downstream of the negatively-charged grid; and (iv) a cathode configured to eject or release electron to the exterior of the thruster. Generally, the grounded grid is

external/downstream from the negatively-charged grid. In some embodiments, the plurality of upstream plasma production devices may be independently operated including, for example, independently fired (i.e., such that all, fewer than all, or only a single plasma production device is operational at any given time) and/or independently powered or modulated (i.e., such that all operational plasma production devices are operating at the some power and/or plasma output or different powers and/or plasma outputs). In some embodiments, all plasma production devices are substantially identical in power and design. In other embodiments, one or more of the plasma production devices have different power outputs and/or designs. For example, in one embodiment, the gridded ion thruster contains a single main upstream plasma production device capable of operating at a first maximum power and one, two, three, four, or more secondary upstream plasma production devices capable operating independently at a second maximum power which is less than the first maximum power.

[0039] In other aspects, the invention provides a gridded ion thruster in which the cathode, the negatively-charged grid, and the grounded grid are operatively attached directly to the plasma production chamber of the plasma production device, thereby negating the need for a separate discharge chamber. The plasma production device that forms the basis of this gridded ion thruster may be configured as described in any of the foregoing aspects. For example, the gridded ion thruster of this aspect comprises: (a) a substantially cylindrical plasma production chamber having a closed end and an open end; (b) one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber such that each magnet produces a magnetic field of the same polarity within the plasma production chamber; (c) a propellant tank and a flow regulator in communication with the plasma production chamber through the first end and configured to deliver a gaseous propellant along the central longitudinal axis of the plasma production chamber; (d) a radio frequency (RF) antenna external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber; and (e) an electrode comprising a negatively-charged grid and a neutral grid covering the open end, and a cathode; wherein the plasma production device is configured to ionize and heat substantially all of a plasma by inductive heating.

[0040] By“AC power source” is meant an upstream component that provides alternating current to a downstream component. An AC power source may directly provide alternating current or may be the combination of a direct current (DC) power source and a DC-to-AC converter such as an inverter, and optionally a power amplifier. Optionally, the AC power source may be coupled to the antenna via a passive electrical circuit called a“matching network.”

[0041] By“HF band” or“high frequency band” is meant the range of radio frequency (RF) or electromagnetic radiation waves having a frequency of 3-30 MHz.

[0042] By“ion” is meant the positively-charged plasma ions formed from the neutral propellant gas, as distinguished from the negatively-charged electrons.

[0043] By“plasma” is meant an ionized state of matter generated from a neutral propellant gas that primarily consists of free negatively-charged electrons and positively-charged ions, wherein, the density of charged particles, n_e is greater than 0.5% of the density of total particles ht (charged and neutral) in the system, or n_c/nx > 0.005.

[0044] By“plasma liner” is meant the physical chamber in which the propellant is ionized to form plasma. In some embodiments, the plasma liner is cylindrical having a cylinder body, a closed end and an open end. Propellant may be introduced into the plasma liner through an aperture or nozzle in the closed end. Alternatively, the propellant may be introduced to the cylinder body (i.e., the side wall), as described herein. Typically, propellant will be introduced through the cylinder body at or near the closed end (i.e., within the upstream 5%, 10%, 15%, 20% or 25% of the cylinder body). The open end serves as an exit for the plasma which, in conjunction with the associated magnetic field described herein forms a nozzle for directing the plasma out of the plasma liner. The plasma liner may be constructed from, or lined with, any suitable material that is resistant to plasma-induced corrosion and/or erosion. Suitable plasma liner materials include, for example, various ceramics; such as alumina, boron nitride, aluminum nitride, and Macor®; glasses such as borosilicate, quartz, and Pyrex®; and refractory metals such as graphite, tungsten, carbon, tantalum, and molybdenum. [0045] By“plume” is meant the area immediately outside of the open end of the plasma liner and is formed by the ejection of plasma ions and electrons from within the plasma liner.

The“plume” may refer to the plume of the thruster generally, in thruster applications, or the plume of the plasma liner component of the thruster, specifically, from which the plasma ions are ejected.

[0046] By“propellant” is meant a neutral gas that is capable of being ionized into plasma. Typical propellants suitable for use in this invention include the noble gases including, for example, helium, neon, argon, krypton, xenon, and radon; molecules such as water, iodine, nitrogen (N2), oxygen (O2), air, methane (CFB), and various hydrocarbon compounds; and alkali metals such as cesium, sodium, and potassium. Mixed noble gases and other gases may be used as a propellant.

[0047] By“VHF band” or“very high frequency band” is meant the range of radio frequency (RF) or electromagnetic radiation waves having a frequency of 30-300 MHz. including, for example the band at about 100-300 MHz, 150-300 MHz, 200-300 MHz, 100-250 MHz, 150-250 MHz, and 100-200 MHz.

DESCRIPTION OF DRAWINGS

[0048] FIG. l is a schematic diagram of a gridded ion thruster (GIT) illustrating the design principles and major components.

[0049] FIG. 2 is schematic diagram of a plasma production device illustrating the principles of the plasma liner, RF antenna, and injection of a neutral propellant gas.

[0050] FIG. 3 is a CST simulation output showing the magnetic field strength and direction induced in a xenon plasma by the coiled antenna described herein.

[0051] FIG. 4 is a scatter plot showing the measured plume density -temperature product (y- axis) versus the square of the input power (x-axis) for three different propellant (xenon) flow rates in the plasma production/thruster device described herein.

[0052] FIG. 5 A is a 2D projection of CST-modeled axial induced magnetic fields inside a plasma as driven by the A6 antenna design described herein. FIG. 5B is a cross-sectional illustration of the magnetic field strength versus radius (?) shown in FIG. 5A at Z = 7 mm. [0053] FIG. 6A is a 2D projection of CST-modeled axial induced magnetic fields inside a plasma as driven by the A2 antenna design described herein. FIG. 6B is a cross-sectional illustration of the magnetic field strength versus radius (A) shown in FIG. 6A at Z = 7 mm.

[0054] FIG. 7 is a series of graphs showing the performance testing results of plasma production devices using antenna A2 (squares) and antenna A6 (circles) as measured in the exhaust plume by a Langmuir probe, each as a function of antenna RF power. FIG. 7A shows plume temperature. FIG. 7B shows plume density. FIG. 7C shows relative current density.

FIG. 7D shows relative current density per Watt of input power.

[0055] FIG. 8 is a series of graphs demonstrating the kinetic energy fluctuation of an electron as a function of initial electron velocity /kinetic energy (FIG. 8A) and for different RF driving frequencies (FIG. 8B). The area between the dark horizontal lines corresponds to the optimum energy range of an electron to ionize a neutral xenon atom (40-60 eV).

[0056] FIG. 9 is a three-dimensional graph showing the relative likelihood of neutral propellant gas ionization as a function of initial electron kinetic energy and RF frequency.

[0057] FIG. 10A is a schematic diagram of an integrated thruster design, in cross-section, that embodies the principles described herein. FIG. 10B is a schematic diagram of an integrated thruster design, in cross-section, having a flat spiral coil hybrid antenna. FIG. IOC is a schematic diagram of an integrated thruster design, in cross-section, having both a flat spiral coil hybrid antenna and a magnet system comprising a planar magnet and radially-disposed magnets.

[0058] FIG. 11 A is a graph showing one configuration of magnetic field strength across the longitudinal length of the plasma liner described in FIG. 10 in which the magnetic field strength increases toward the open end of the plasma liner/plasma production chamber, thereby forming a defined“throat” section 288, before decreasing towards and through the open end. FIG. 1 IB is a graph showing another configuration of magnetic field strength across the longitudinal length of the plasma liner described in FIG. 10 in which the magnetic field strength is continuously decreasing (or at least does not increase) from the closed end to the open end. Throat section 288 represents a reduction in the rate of change (reduction) in the magnetic field strength along the longitudinal axis from the closed end to the open end.

[0059] FIG. 12A is a schematic diagram of a gridded ion thruster (GIT) combining the principles and elements of the plasma production device described herein into a single plasma production apparatus (PPA) design in which the plasma liner functions as the GIT discharge chamber.

[0060] FIG. 12B is a schematic diagram of an alternative single PPA GIT design in which the PPA is positioned upstream of the GIT discharge chamber.

[0061] FIG. 13 is a schematic diagram of a multiple PPA integrated GIT design.

DETAILED DESCRIPTION

[0062] The present invention provides an RF propellant ionization design that may be applied electric propulsion thrusters and gridded ion thrusters, in particular. The principles of this invention are described in the context of gridded ion thrusters but may be adapted to a variety of other thruster designs.

[0063] Gridded Ion Thruster Design

[0064] FIG. l is a simplified schematic diagram of a gridded ion thruster (GIT) showing the main features to illustrate the design and operational principles. Generally, a GIT 100 comprises a discharge chamber 110. Discharge chamber 110 may be cylindrical, ovoid, cubic, or cuboidal, for example, and generally has a closed end 111 and an open end 112. A neutral propellant gas 120 is introduced into discharge chamber 110 at or towards closed end 111 from propellant tank 125 via propellant injector 126. It is understood that propellant 120 may be introduced along any plane or axis of discharge chamber 110 that is convenient. FIG. 1 illustrates that propellant 120 is introduced along the longitudinal axis of discharge chamber 110 but, for example, propellant 120 may be introduced substantially perpendicular to the longitudinal axis of discharge chamber 110, if desired.

[0065] Neutral propellent 120 is ionized into positive ions 121 and electrons 122 to form a plasma within discharge chamber 110. The plasma may be generated within chamber 10 or created outside and introduced into discharge chamber 110. It is understood that any suitable plasma generation system may be used in GIT 100 including, for example, electron

bombardment, RF excitation, and/or microwave excitation.

[0066] FIG. 1 illustrates that neutral propellant 120 is introduced into discharge chamber 110 from propellant tank 125 via propellant injector 126. FIG. 1 illustrates a radio frequency (RF) system for plasma generation in which discharge chamber 110 is surrounded, at least in part, by antenna 30 through which an alternating current is driven. The alternating current may be supplied from an alternating current power source 135 (e.g., grid power) for example in certain terrestrial application, or from solar panels and/or DC batteries for other terrestrial and space (on-orbit) applications. It is well-known that DC current may be converted to AC through various means including, for example, an inverter, and if necessary, a power amplifier.

Optionally, the AC power source is connected to antenna 120 through a series of electrical elements including, for example, an active or passive RF matching network. FIG. 1 illustrates antenna 130 as a coiled antenna for simplicity and to illustrate the principles of this invention. The coiled antenna is not limiting on the types of antennas that may be used in the various aspects of the invention.

[0067] Discharge chamber 110 is further comprises one or more magnets 160 configured to maintain positive ions 121 within the body of discharge chamber 110 and reduce or prevent positive ions 21 from impacting on the inner wall of discharge chamber 110.

[0068] GIT 100 provides thrust using an electrode-based design powered by high voltage power source 145. Discharge chamber 110 has at least two high voltage electric grids at or towards open end 112; a negative grid 140 (anode) and a neutral grid 150 (ground), wherein negative grid 140 is disposed closer to the site of plasma generation and neutral grid 150 is external/downstream from negative grid 140. Positive ions 121, once formed, are accelerated towards negative grid 140 and ejected from chamber 110 by passing through negative grid holes 141 and neutral grid holes 151, thereby generating thrust. Neutral grid 150 reduces or eliminates the tendency of ejected positive ions 121 from reversing direction and impacting negative grid 140.

[0069] GIT 100 develops a net negative charge as position ions 121 are ejected. Electrons 122 impact the inner wall of chamber 110. Accordingly, GIT 100 also comprises high voltage cathode 170 which serves to disperse electrons to space and, therefore, maintain charge neutrality.

[0070] The negative grid 140 (anode) may be fabricated from a conductive material(s), usually metal(s), in order to complete the electrical circuit necessary to accelerate the positively- charged propellant ions. Typical anodes are fabricated from stainless steel, steel, iron, molybdenum, copper, and the like. [0071] The present invention provides improvements to GIT performance by improving design aspects around plasma generation. By more efficiently generating plasma from the neutral propellant gas, GIT performance may be improved, and lifespan may be extended.

[0072] Plasma Production Apparatus

[0073] The improved GIT designs described herein are based on improvements to the plasma production apparatus which will be first described. The application of the improved plasma production apparatus to a GIT is then described.

[0074] FIG. 2 is a schematic diagram of the core components of the plasma production apparatus 200 and associated components. A neutral propellant gas 220 is injected into plasma liner 210 along the longitudinal axis of the (e.g., cylindrical) chamber from the closed end 211 in the direction of the open end 212. The plasma liner 210 is surrounded by an inductive RF antenna 230 through which an alternating current is driven at a specified RF frequency in the high frequency (HF) to very high frequency (VHF) bands (from 3 to 30 MHz and 30 to 300 MHz, respectively). As discussed for the GIT design illustrated in FIG. 1, the alternating current may be supplied from solar panels, DC batteries, or any other suitable power source and may include, as necessary, an AC inverter/converter, power amplifier, and passive or active electrical elements such as an RF matching network. FIG. 2 illustrates antenna 230 as a coiled antenna for simplicity and to illustrate the principles of this invention. The coiled antenna is not limiting on the types of antennas that may be used in the various aspects of the invention.

[0075] The plasma liner 210 and antenna 230 are positioned inside a generated magnetic field (not shown). The magnetic fields have a specified strength as a function of position within the plasma liner 210. The magnetic fields rapidly expand radially in the reference frame of an accelerated plasma particle traveling out of the plasma liner 210 thereby forming a“magnetic nozzle”. The magnetic field strength inside plasma liner 210 is such that the ions that are generated within the plasma liner 210 are“weakly magnetized,” which implies that ions under a specific temperature perpendicular to the magnetic field will not have orbits that intersect the inner wall of plasma liner 210. When neutral propellant gas is injected into plasma liner 210, the induced oscillating magnetic fields generated by the currents in the antenna 230 both ionize the propellant gas 220, and then heat the subsequent plasma. Neither multiple RF stages, nor extra electron-generating mechanisms are used for RFT ignition or plasma heating. The heating directly impacts the electrons. Electrons are accelerated to very high energies (>50 eV) through inductive and stochastic interactions with the near RF fields 231 from the antenna 230. The electrons, undergoing significant elastic collisions inside plasma liner 210, expand rapidly along the magnetic field lines that run substantially parallel with the longitudinal walls of liner 210.

[0076] As described in more detail herein, the magnetic field geometry within liner 210 ensures that electrons maintain enough time in regions of high neutral (i.e., non-ionized propellant) density to produce significant ionization of the propellant gas via electron collisions with the neutral particles, and that electrons that are lost are largely lost via expansion in the magnetic nozzle, rather than upstream towards the closed end 211 of liner 210. The rapid flux of electrons into the plume of the thruster creates a momentary charge imbalance in the thruster.

The slower positively-charged propellent (e.g., xenon) ions are then pushed out of the plasma liner 210 via the charge imbalance at a rate sufficient to satisfy overall ambipolar fluxes of particles out of the system. The ion acceleration generated therein is the primary source of thrust when plasma liner 210 and its associated components are integrated into a thruster.

[0077] Inductive Heating Effects on Plasma Liner Geometry

[0078] The RF fields 231 generated by the antenna 230 that heat the plasma particles are directly induced by electrical currents in the antenna 230. Unlike wave-heated plasma discharges, the plasma in this production/thruster design is not heated by propagating (non- evanescent) waves launched in the plasma, such as in helicon discharges.¹ Unlike in“electron cyclotron resonance” sources, the RF signals need not be“resonant” with the particle motions in the plasma. The heating mechanism in this design is similar to heating mechanisms described by Kinder and Kushner² in simulations where their system was at low magnetic fields. In such systems, the fields induced by the antenna 230 are partially shielded/attenuated by the motions of charged particles in the plasma. This is represented in FIG. 2 by the curved wave lines 231 emanating from antenna 230 with decreasing thickness as the lines penetrate the plasma. The scale length over which this decay occurs is determined by the plasma“skin depth,”³

where p_s is the skin depth, c is the speed of light in vacuum, and co_pe is the electron plasma frequency in radians per second. The electron plasma frequency is given by: = 5.64

where n_e is the plasma electron density in particles per cubic cm (cm^-3).⁴ From Equations 1 and 2, it can be seen that the skin depth is inversely proportional to the square root of the electron density. Therefore, with increasing plasma density, the antenna-induced wave field amplitudes decay more rapidly versus radial position in the plasma.

[0079] The skin depth effect was simulated using a Computer Simulation Technologies (CST) simulation and the graphical results are shown in FIG. 3. The simulation used a coil antenna 230 wrapped around a plasma 223 with n_e = 10¹³ cm^-3, and a magnetic field of 600 Gauss uniform along the z axis. FIG. 3 shows a cut through the center of the antenna 230 and the plasma 223 in the y - z plane. In the simulation, an RF signal was applied through antenna 230 and the resulting electromagnetic fields were calculated everywhere within the domain. The induced magnetic fields are represented by local vector arrows. The size and shade of the arrows represent the local strength of the fields with lighter/larger arrows being stronger and

smaller/darker arrows being weaker. The fields near the antenna are strong, and the field strength decays the farther into the plasma the fields penetrate. It is well known that the induced axial magnetic field is largely uniform throughout the internal volume for multi-turn solenoid coils or antennas (such as the antenna 230 in FIG. 3) with a vacuum at the solenoid core.

Therefore, the observed decay of the induced fields in the plasma indicates that the CST simulation is accurately exhibiting the known plasma skin depth effect.

[0080] As described above, these induced magnetic fields in the plasma heat the constituent particles. The oscillating magnetic fields from the antenna induce time-varying electric fields in the plasma, described by Faraday’s Law, which subsequently drive currents and electron motions in the plasma. Some of the fast electrons ionize the neutral propellant background particles via electron impact, and other fast electrons escape the plasma liner, electrically pulling the slower positively charged ions out of the thruster, generating thrust or otherwise allowing the ions to escape the production chamber (i.e., in non-thrust-generating applications).

[0081] This method of energy transfer from the electrical antenna signal to the plasma is known as“inductive coupling,” and has been well documented and studied in the plasma processing community.⁷ Therefore, the magnitude of the induced electric fields that accelerate fast electrons are directly proportional to the amplitudes of the local oscillating magnetic fields driven by the antenna. This“inductive” heating effect is most pronounced at the edges of the plasma near the antenna and weaken near the center of the plasma-antenna system. In existing RF plasma systems, the physical extent of plasma is significantly greater than 5-1 Ops. In those systems, the inductive heating effect occurs only in a small volume of plasma relatively close to the plasma liner wall, but not in the interior bulk of the plasma. These larger systems rely on more complicated coupling of induced fields to propagating waves in the plasma to deposit energy in the larger interior plasma volume (as in, for examples, reference 1, 2, and 5).

[0082] In one aspect, the invention includes a plasma production system 200 (e.g., for use in a GIT) in which all or substantially all of the propellant is ionized and/or the plasma 223 contained within the plasma production chamber (e.g., the plasma liner 210) is produced or heated by inductive heating induced by oscillating magnetic fields produced by the antenna 230. In particular, the dimension of the plasma production chamber (e.g., the plasma liner) as having a radius (RL; radius of plasma liner) that is less than about 7 p_s, 6.5 p_s, 6 p_s, 5.5 p_s, 5 p_s, 4.5 p_s, 4 p_s, 3.5 p_s, 3 p_s, 2.5 p_s, or 2 p_s, or, RL is about 1-6 p_s, 2-6 p_s, 3-6 p_s, 4-6 p_s, 5-6 p_s, 1-5 p_s, 2-5 p_s, 3-5 ps, 4-5 p_s, 1-4 p_s, 2-4 p_s, 3-4 p_s, 1-3 p_s, 2-3 p_s, or 1-2 p_s„ or RL is about 1 p_s, 2 p_s, 3 p_s, 4 p_s, 5 p_s, 6 p_s, or 7 p_s. This relationship may be expressed mathematically as:

RL < 1-7 p_s (3)

[0083] When the propellant is xenon, the system is optimized when RL = 3-6 p_s including, for example, when RL = 4-6 p_s, RL = 5-6 p_s, RL = 3-5 p_s, RL = 3-4 p_s, or RL ~ 3 p_s, RL ~ 4 p_s, RL ~ 5 p_s, or RL ~ 6 p_s. It is understood that the cofactor in Equation (3) describing the relationship between RL and p_s was determined in a simulation using a xenon propellant (FIG. 3). The cofactor describing this relationship may vary based on the propellant gas species, operational power and configuration of the antenna, and the magnetic field strength within the plasma liner.

[0084] Maintaining an appropriately small plasma liner radius realizes several advantages in all plasma production and propulsion RF systems including:

(i) allowing for substantially simpler RF plasma systems that do not rely on complicated RF wave coupling;

(ii) maintaining a primarily single and dominant heating mechanism throughout the majority (substantially all) of the plasma volume, ensuring more simple optimization; and (iii) allowing for high RF-plasma volumetric power density which ensures high power deposition into the plasma with low electrical power input into the antenna.

[0085] With the foregoing understanding of the relationship between the skin depth (p_s) and RL, several design principles are established. Making the plasma liner radius too small results in too little plasma being heated, and too much plasma being lost to wall interactions, both of which greatly reduce thrust performance and/or total plasma output. Furthermore, the plasma liner must be large enough to allow for complete charged particle orbits to exist, i.e., that the ion and electron orbital motion around the magnetic fields in the liner must not intersect the liner walls. The ions, being generally significantly more massive than the electrons, have significantly larger magnetic“Larmor” orbits than the electrons, and thus become the bounding orbit on the minimum radius of the plasma liner. The average orbit of an ion, in a distribution of ions with temperature Ti, is given by:

where [ , is the average ion Larmor orbit radius, Mi is the ion mass, ku is Boltzmann’s constant, e is the fundamental charge, and B is the background DC magnetic field strength.

[0086] Typical ion temperatures in such systems range from 0.02 eV to 10 eV, where 1 eV corresponds to 11,600 K. As an example, a typical situation for an RFT-2 discharge is a xenon plasma, with 0.1 eV ions, and 500 G background magnetic field, yielding pt = 7.4 mm.

[0087] Combining the previous two conditions, wherein RL < 5 p_s yields the geometrical bounds for the optimal size of the plasma liner to be:

or, in a more simplified form: p < RL < (5 C/C0pe) (5b) or p < RL < 5 ps (5c)

[0088] In some embodiments, RL is greater than 1.1 pi, 1.5 pi, 2.0 pi, 2.5 pi, 3.0 pi, 3.5 pi, 4.0 pi, or 4.5 pi, but less than 5.0 pi. In other embodiments, RL is greater than 1.1 pi, 1.5 pi, 2.0 pi, 2.5 pi, 3.0 pi, 3.5 pi, or 4.0 pi, but less than 4.5 pi. In other embodiments, RL is greater than 1.1 pi, 1.5 pi, 2.0 pi, 2.5 pi, 3.0 pi, or 3.5 pi, but less than 4.0 pi. In other embodiments, RL is greater than 1.1 pi, 1.5 pi, 2.0 pi, 2.5 pi, or 3.0 pi, but less than 3.5 pi. In other embodiments, RL is at 1.1 pi, 1.5 pi,

2.0 pi, 2.5 pi, 3.0 pi, 3.5 pi, 4.0 pi, or 4.5 pi, but less than 3.0 pi. In other embodiments, RL is at 1.1 pi, 1.5 pi, or 2.0 pi, but less than 2.5 pi.

[0089] Example 1: Yield Calculation And Testing

[0090] This foregoing geometrical scaling theory yields a performance prediction as follows. The energy density (e) in the plasma plume generated by the plasma production apparatus approximately scales as the product of the electron temperature ( T_e ), and the electron density e ~ n_eT_{e .} This product should be directly proportional to the amount of plasma heated by the induced fields from the antenna, and the amplitude of these fields. Mathematically this is given as: e ~ n_eT_e ~ p_sn_eB₀ (6) where Bo is the peak amplitude of the fluctuating induced magnetic field in the plasma, generated by the antenna. Bo is directly proportional to the square root of the RF power into the antenna Prf). Using Eqns. 1, 2, and 6 therefore yields:

P_rf ~ n_e ³T (7)

[0091] Thus, to validate that the operational mechanism of the plasma production system relies on near field inductive plasma heating, the measured input power can be compared to the measured plasma electron density and temperature at a fixed location in the plasma plume. [0092] A plasma production system was constructed in accordance with the geometrical principles described above. Other details regarding the structure and operational parameters of this test system are found in the other working examples described herein.

[0093] Figure 4 shows measurements of the product of ³ and T_e ² in the plume of the test system as a function of input power for three different xenon mass flow rates. One (1)“standard cubic centimeter per minute,” or“seem” corresponds closely to 0.1 mg/s of xenon. The density and temperature were measured in the plume using a Langmuir probe. As shown in FIG. 3, for each of the mass flow rates investigated thus far, the power law product scales approximately linearly with the input power, as predicted by the model of near field inductive heating described above. Thus, inductive heating is the dominant, if not sole, physical mechanism responsible for xenon ionization and plasma heating in the test system. Other modes of RF energy transfer do not appear to be present to any significant extent.

[0094] Due to the relationships described herein between the liner radius, the skin depth and the ion Larmor radius, the plasma generation in the liner is optimized for ionization rate.

Therefore, implementation of such a plasma source to applications such as a Gridded Ion Thruster will improve those systems’ overall efficiency by drawing less spacecraft power to ionize the propellant, while still maintaining the same level of thrust output as traditional designs.

[0095] Antenna Geometry and Skin Depth

[0096] The specific geometry of the antenna has a strong effect on the heating efficacy in the plasma. The goal of the antenna design is to maximize“plasma loading.” Plasma loading refers to the amount of propellant/plasma ionization and plasma heating, generated by the antenna, per unit (Watt) of input power. In near field inductive discharges, plasma loading is determined by the volume of the plasma exposed to the near fields from the antenna, which is determined by the surface area of the liner adjacent to the antenna and the skin depth of the RF fields in the plasma. As discussed above, the heating rate in the plasma is proportional to the skin depth and the amplitude of the RF signal. The skin depth also is partially determined by the antenna geometry. Another aim of the invention is to design antenna geometries that result in constructive interference with the induced magnetic and electric fields in the plasma, thereby increasing their local amplitudes and maximizing the plasma loading. [0097] Figures 5A-5B, 6A-6B, and 7A-7D illustrate the effect of antenna geometry. FIGS. 5A-B show the results of a CST simulation of the coaxial induced magnetic field for a defined RF current driven through an antenna, defined internally as‘ A6.’ Antenna A6 was a“half helical” antenna, as shown in FIG. 9 of Chen, 2015, ⁵ with an inner diameter and length of 17 mm each. The“half helix” geometry consists of two coaxial circular loops of conducting material with the same inner diameter, separated axially by a distance greater than their diameters and less than the length of the plasma liner they are wrapped around. The loops are electrically connected by at least two straps that travel in a helical fashion from the back loop to the front loop. If the straps rotate in a clockwise fashion from one loop to the next, the antenna is“right handed.” Conversely if the straps travel in a counter clockwise fashion, the antenna is“left handed.” The A6 antenna is right handed. Two“legs” are attached, one to either loop on the helix, which are designed to interface in an AC electrical circuit. The AC electrical current is applied to these legs to run currents through the geometry of the antenna, inducing

electromagnetic fields in the antenna core, such that when a plasma is generated underneath the antenna it is heated by these fields.

[0098] For the simulation, a 2.5 A, 10 MHz sinusoidal current was driven through the antenna, approximately corresponding to a power of 100 W into the antenna. The plasma density modeled at the core of the antenna has a density of 10¹³ particles per cubic cm, which were exposed to a DC magnetic field of 500 Gauss oriented along the axis of the antenna uniformly. FIG. 5A shows a cut plane through the antenna and its central axis (Z). The straps of the antenna are represented by the approximately rectangular shapes at 7= ±10 mm. The darkness of the local gray scale shows the magnitude of the induced magnetic field inside the plasma. The simulation was run with a plasma of fixed density at the core of the antenna and with a DC background magnetic field. The defined plasma density and magnetic field strength are representative of xenon plasma generated by the plasma production device/thruster described herein. FIG. 5B shows the magnitude of the induced coaxial magnetic field through the midpoint of the antenna (Z = 7 mm). The greater the area under the curve, the more effective the antenna is at heating the plasma.

[0099] FIGS. 6A-B show the results of a CST simulation using a different antenna geometry, designated antenna A2. Everything else about the simulation was the same as with the A6 antenna. The A2 antenna is a coiled antenna constructed from a flattened rectangular wire in which three turns are wound around the plasma liner from back to front circulating in a clockwise fashion. The A2 antenna is considered a“coil” as it consists of a single strap that wraps around the plasma liner in a circular, helical fashion. In a right-handed configuration, the antenna strap rotates in a clockwise fashion from the closed end of the liner to the open end. Likewise, in a left-handed configuration, the antenna strap rotates in a counter clockwise fashion from the closed end of the liner to the open end. At the beginning and end of the coil, two legs are attached that interface with the driving electrical circuit. The coil design does not consist of loops that are individually connected with straps, like the half helix. Instead, the entire antenna consists of a single connected spiraling strap that constitutes the main helical portion of the antenna. Thus, the current in the entire antenna at every point is traveling in such a fashion that the induced magnetic fields per Ampere’s law in the center of the antenna always constructively interfere. In contrast, half helix designs, consisting of connected loops that circle the liner that are individually connected by straps, require the currents in the antenna to split into two halves as they circulate across the hoop. This configuration therefore causes the induced magnetic fields under the antenna to destructively interfere with each other, causing a reduction in the inductive heating efficacy and sub-optimal performance in miniature inductive RF thruster designs.

[00100] As with A6, the inner diameter of the antenna and the length were both 17 mm. The properties of the simulation are identical to that described in connection with antenna A6, except for the specific antenna geometry. FIG. 6A shows a cut plane through the antenna and its central axis (z). The straps of the antenna are represented by the approximately rectangular shapes at Y = ±10 mm. FIG. 6B shows the magnitude of the induced coaxial magnetic field through the midpoint of the antenna (Z = 7 mm).

[00101] As observed in the comparison of FIGS. 5A-B and 6A-B, antenna A2 is predicted to be significantly more effective than antenna A6 at inducing magnetic fields in the plasma, increasing the heating rate. The increased effectiveness results from the windings in A2 which are designed so that the induced magnetic fields from each strap interfere with each other constructively inside the plasma, locally increasing the magnitude of the induced fields in the plasma, increasing the penetration of the heating fields into the plasma liner. Conversely, the more traditional A6 design (e.g., see, reference 5; Chen et al.) induces fields in the plasma that destructively interfere with each other. As such, the A6 antenna style is severely sub-optimized for the skin depth heating mechanism described herein

[00102] Example 2: Antenna Design Testing

[00103] The two antenna designs (A2 and A6) were tested in identical plasma production devices by measuring the properties of the exhaust plume using a Langmuir probe, as described above. FIGS. 7A-7D provide experimental evidence to confirm the CST simulation prediction of improved heating performance by antenna A2 relative to antenna A6. All operational and physical parameters were held constant for this comparison, except for the antenna geometry and the applied power sweep. The comparison was performed over a variety of powers to

demonstrate the universality of this improvement.

[00104] Specifically, FIGS. 7A-7D the measured effective electron temperature ( T_e ), plume density, relative change in plume current density, and relative change in plume current density per Watt of input power, respectively, for the plasma production devices using antennas A2 (squares) and A6 (circles). In thruster applications, plume current is proportional to the thrust out of the system. FIGS. 7A and 7B demonstrate that, while antenna A2 approximately ionizes the same fraction of the plasma (FIG. 7B), the plasma is significantly hotter using antenna A2 versus antenna A6 (FIG. 7A). Furthermore, FIGS. 7C and 7D demonstrate that, for a given Watt of input power into the antenna, the antenna A2 generates a significantly stronger plume current than antenna A6. Therefore, antenna A2 has significantly better plasma loading than antenna A6.

[00105] In order to further improve operational parameters, including plasma loading, a novel “flat spiral coil hybrid” antenna (“FSCH antenna”) was designed. The FSCH antenna has a flat spiral portion and a coil portion in direct communication, contact, and connection. The“flat spiral” portion has a spiral configuration that expands in a radial direction from a central point but with no change/extension of the coils in a longitudinal direction. In other words, a“flat” spiral is planar. The coil portion may be a standard coil which refers to the shape formed when a coil travels in a helical pattern around a fixed axis in a longitudinal (axial) direction but does not increase in radial size. Thus, the FSCH antenna does not undergo a gradual transition in radius and axial position from the flat spiral portion to the coil portion. Instead, the FSCH has a definite transition point and connection between the flat spiral and coil portions. Generally, the common axis of the FSCH antenna is the central axis of the spiral portion and the longitudinal axis of the coil portion. In other words, the plane of the spiral portion is perpendicular to the longitudinal axis of the coil portion. In contrast FSCH antenna shape, the shape of another spiral (e.g., a three-dimensional spiral) changes simultaneously in radius and length as it wraps around a common axis, thereby creating a“beehive” shape.

[00106] The flat spiral portion is disposed against the closed end of the cylindrical plasma production chamber and the coil portion is wound around the cylindrical body of the chamber. Thus, the plane of the flat spiral is substantially perpendicular to the longitudinal axis of the plasma production chamber and the coil portion.

[00107] The flat spiral portion of the FSCH antenna is centered on the center point of the circular closed end of cylindrical plasma production chamber and spirally-extends towards the peripheral edge. The spiral portion may cover about 25%, 50%, 75%, or substantially 100% of the diameter (d) of the closed end.

[00108] The coil portion may begin anywhere along the length of the plasma production chamber but preferably begins as close to the closed end as practical. The coil portion extends towards the open end for any length or dimension. In some embodiments, the coil portion covers at least 25%, 50%, 75%, 80%, 85%, 90%, 95%, 99%, or substantially 100% of the length of the cylindrical plasma production chamber.

[00109] The spiral portion and the coil portion, independently, may be right-handed or left- handed. It is preferred that the spiral portion and the coil portion have the same direction (i.e., both are either right-handed or left-handed), although opposite directionality may be used.

[00110] RF Frequency Effects on Performance

[00111] When an electron is generated during a plasma-forming ionization event, the electron is exposed to the electric fields in the plasma (E o) that are induced by the driven magnetic fields (Bo) from the antenna as described by Faraday’s Law. The subsequent motion of these electrons before they make further collisions is given from Newton’s equations as:

where v_e is the electron velocity, v° is the initial electron velocity, m_e is the electron mass, E o is the amplitude of the fluctuating induced electric fields in the plasma, and /is the RF driving frequency. Equation 8 shows that the electron velocity in the plasma, exposed to the induced electric fields, is a strong function of its initial velocity, the driving frequency, and the amplitude of the fluctuating electric fields. Electrons in the plasma that are accelerated to sufficiently high speeds before they collide with a neutral propellant atom, will ionize the propellant upon this impact. The probability of this ionization event is a strong function of the speed of the electron relative to the neutral atom, and generally exhibits a peak. For example, xenon gas is most effectively ionized by electrons with kinetic energies ranging between 40 and 60 eV.⁶ Thus, for a given value of v°, E₀ and / an electron in the plasma liner (plasma production chamber) can become“trapped” in an energy range that is optimal for ionization of the background gas.

[00112] Figure 8 describes this“phase space trapping” effect. In both panels, the x-axes show a time sequence in y.v, and the y-axes show units of electron energy in eV. The dark horizontal lines demarcate a region of energy (40-60 eV) where the neutral xenon gas is most efficiently ionized by electrons with those of kinetic energies. The black curved lines in FIG. 8 A represent the changes in electron energy over time due to the presence of the oscillating induced electric field, E o, for four different starting electron velocities,/·, which correspond to electron starting kinetic energies described by e₀ = O.Sm_ev§ ² (9)

Likewise, in FIG. 8B the black tracks represent changes in electron kinetic energy over time due to the oscillating fields, with different field oscillation frequencies,/ The more time a given electron spends in the band of likely ionization (40-60 eV), the more frequently ionization events occur until the plasma in the plasma liner is fully ionized. Therefore, the total integrated time an electron spends between the 40 and 60 eV lines in Fig. 8 is proportional to the rate of ionization within the plasma liner. This relationship demonstrates that the frequency and power of the RF waves launched by the antenna thereby have a direct impact on the plume density and performance in thruster applications.

[00113] FIG. 9 describes this frequency effect. The x-axis and y-axis show the initial electron energy and RF frequency, respectively. The z-axis illustrates the relative likelihood of the electron ionizing the neutral xenon gas. The specific shape of this probability curve is a function of the antenna geometry. FIG. 9 shows that for a fixed antenna geometry, the probability of ionization strongly depends upon the RF frequency and the initial electron kinetic energy. Thus, the RF frequency can be optimized and fixed combination of (i) a specific antenna geometry, (ii) input power, and (iii) propellant flow rate to optimize the ionization efficiency of the neutral propellant gas without significantly altering other system variables which may be limited or preset for other design considerations and aspects.

[00114] From this, it can be seen that the frequency of the applied RF (f) is bounded for optimum propellant ionization. Specifically,/ must be high enough to maximize propellant ionization but must be less than about 25% (e.g., less than about 20%, 15%, 10%, or 5%) of the electron cyclotron frequency (fe ), in radians per second, as described by: eB o

fee = (10) m_e wherein B₀ is the axial magnetic DC field strength in the plasma liner (plasma production chamber) and m_e is the mass of an electron. For example, for an axial magnetic field strength of 500 Gauss (0.05 Tesla), 25% of fee is 350 MHz. Thus, the RF frequency (f) should be kept to less than 350 MHz in this example. At these upper bounds, the dominant energy transfer mechanism between the antenna and the plasma becomes the“electron cyclotron resonance,” which has been extensively documented in plasma physics literature. The miniaturized inductive plasma source described herein is not designed around this optimization, keeping the cyclotron resonance as the upper bound for this source’s operational frequency. As discussed elsewhere, the RF frequency is preferably maintained above 3 MHz (e.g., in the HF or VHF range).

[00115] Plasma Production Device Design

[00116] Based on the foregoing simulations and experimental results, an integrated plasma production apparatus 201, 202 design was developed and illustrated in FIGS. 10A-10B. The apparatus 201, 202 has a cylindrical plasma liner 210 having a closed end 211 and an open end 212. In some embodiments, plasma liner 210 has a diameter of about 1-5 cm. In some embodiments, plasma liner 210 has a length, from closed end 211 to open end 212, of about 5-10 cm. [00117] A propellant delivery system 229 is located external to plasma liner 210 and has at least a propellant tank 225 configured to deliver a flow of gaseous propellant 220 to the interior of plasma liner 120. Propellant tank 225 serves as a reservoir for pressurized propellant 220. Optionally, propellant delivery system 229 also comprises flow regulator 227 as part of a propellant injector 226 configured to meter the flow of propellant 220 into plasma liner 210. In some embodiments, propellant 220 is delivered to the interior of plasma liner 210 at a rate of about 0.01 - 5.0 mg/s.

[00118] Antenna 230 is configured to deliver an RF field 231 to the interior of plasma liner 210. As shown in FIG. 10A, antenna 230 may be a coiled antenna (e.g., A2), a half-helix (e.g., A6), helical, or in any other suitable configuration sufficient to cause ionization of propellant 220 into plasma 223 when propellant 220 is exposed to RF field 231 under appropriate power conditions as described herein. Antenna 230 may be fashioned from silver or related alloys, gold or related alloys, aluminum, stainless steel, steel, copper, bronze, graphite, tungsten, or possibly any rigid and electrically conducting material, or any other suitable material for this purpose. In some embodiments, antenna 230 is fashioned from a flattened rectangular or square wire, a transmission line, a vapor-deposited material on an insulating substrate, or any other rigid and electrically conducting material processing technique. In some embodiments, antenna 230 comprises a coil, half-helix, or helical portion having 1-20 turns (e.g., 1-15, 1-11, 1-9, 1-7, 1-5, 1-3, 1-2, 2-15, 2-11, 2-9, 2-7, 2-5, 2-3, 3-15, 3-11, 3-9, 3-7, 3-5, 4-15, 4-11, 4-9, or 4-7 turns) in a clockwise or counter clockwise fashion, with electric and mechanical interfaces to feed the antenna with current and to mechanically mater the antenna to the thruster around the external surface of plasma liner 210. In some instances, the electric and mechanical interfaces may be the same feature. In some embodiments, antenna 230 is in direct contact with the external surface of plasma liner 210.

[00119] FIG. 10B illustrates an integrated thruster design having a flat spiral, flat spiral-coil hybrid (“FSCH”) antenna 230. In this case, the FSCH antenna 230 has a flat spiral portion 230a that is disposed against the exterior surface of the closed end 211, and coil portion 230b wrapped around the cylindrical body of plasma liner 210 in the direction of open end 212. The coil portion may have similar or the same characteristics as described above for antenna lacking the flat spiral portion. [00120] Antenna 230 is powered by power control system 260 which may comprise battery 261 and, optionally, inverter 262. In some embodiments, power control system 60 provides DC current which is converted to AC current by inverter 262 prior to delivery to antenna 230. In some embodiments, power control system 260 provides DC current which is converted to a small AC current by inverter 262 and is then amplified to a large AC current prior to delivery to the antenna 230 by a power amplifier. A frequency modulator or“clock” is used to define the frequency of oscillation of the AC current. In some embodiments, passive electrical circuitry (e.g., a matching network) may be placed between the driver circuit and the antenna.

[00121] Plasma production apparatus 201, 202 also has a magnet system 280 having radially- disposed magnets 281 about plasma liner 210 such that each magnet produces a magnetic field 285 of the same polarity (either positive or negative) within plasma liner 210. As shown in FIG. IOC, magnet system 280 may also have a planar magnet 282 in combination with radially- disposed magnet(s) 281. The arrows in magnets 281 and 282 indicate the direction of polarization. In some embodiments, the radially disposed magnets are held a fixed distance axially with the planar magnet. All magnets are coaxially aligned relative to the plasma liner axis. The radial magnet is held at an axial distance no greater than the length of twice the liner away from the planar magnet. The planar magnet ranges in diameter between 0.5 cm and 4 cm, and in thickness between 0.1 cm and 3 cm. In some embodiments the radial magnet or magnets are magnetically polarized in the radial direction (positive or negative). In some embodiments the radially disposed magnets are magnetically polarized in the positive or negative axial direction. In some embodiments the radially disposed magnet is polarized at an angle in between purely radial and purely axial. In some embodiments there are multiple radially disposed magnets, with varying magnetic polarization directions. The location and strength of the minimum axial magnetic field strength generated by this sequence of magnets on the axis of the plasma liner describes the position and size of the region of maximum ion Larmor orbit radii. At this location the plasma liner radius needs to be no larger than 5 Larmor orbit radii to maintain sufficiently high volumetric power density inside the plasma. This condition is always held in place by the upper bound on the plasma liner radius defined by the plasma skin depth, as defined in Equations 5a through 5c.

[00122] In some embodiments, magnet system 280 forms within plasma liner 210 a magnetic field 285 characterized as having a first throat section 286 towards the closed end 211 of plasma liner 210, a plasma containment region 287 approximately centrally-located within plasma liner 210, a second throat section 288 toward the open end 212 of plasma liner 210, and a diverging section 289 approximately at opening 213 of plasma liner 210 and extending away from opening 213. The first throat section 286 and second throat section 288 are characterized as having a relatively high magnetic field strength, and plasma containment section 287 and diverging section 289 are characterized as having a relatively low magnetic field strength. The magnetic field strength of first throat section 286 and second throat section 288 need not be the same and depend upon the strength and configuration of the local magnets. Diverging section 289 and opening 213 together form a nozzle.

[00123] In operation, neutral propellant 220 is delivered to the interior of plasma liner 210 where it is ionized by RF fields 231 generated by antenna 230. Neutral propellant 220 is ionized into electrons 222 and positively-charged propellant ions 221. Electrons 222 and ions 221 are further heated by RF fields 231. Magnetic field 285 generally serves to prevent plasma ions from impacting the interior surfaces of plasma liner 210. However, it is understood that ions of sufficiently high energy still may impact plasma liner 210, thereby reducing efficiency and eroding those interior surfaces. First throat section 286 has a relatively high magnetic field strength relative to plasma containment section 287 which serves both to protect closed end 211 and associated structures from plasma corrosion and to slow and reverse plasma ions (esp. electrons 222) back into the body of plasma containment section 287, thereby increasing the ionization efficiency. Likewise, second throat section 288 has a relatively high magnetic field strength relative to plasma containment section 287 which serves to regulate the outflow of plasma ions (electrons 222 and positive ions 221) from the plasma liner. Electrons that are repelled by second throat section 288 return to plasma containment section 287, thereby increasing ionization efficiency. The“electron rebound effect” caused by the throat sections 286, 288 serve to increase the apparent length of plasma liner 210 by increasing the electron residence time within the plasma liner 210 and concomitantly increasing the time for which that electron is available to participate in an ionization event. It is understood that improved ionization efficiency comes at the expense of thrust moment. The balance between ionization efficiency and thrust moment may be regulated by the magnetic field strength of second throat section 288. [00124] FIGS. 11 A-B are graphs showing the characteristic field strength (Bz) of magnetic field 285 as a function of the length (Z) of plasma liner 210 in two different configurations. FIG. 11 A illustrates a relatively high magnetic field strengths at first throat section 286 and second throat section 288. The high field strength at the first throat section 286 corresponds to the closed end of plasma liner 210 and serves to repel plasma ions from the closed end back into the body of the plasma liner 210, thereby reducing erosion of the closed end and reducing the loss of generated plasma. In some embodiments, the magnetic field strength at second throat section 288 is less than or is equal to the magnetic field strength at first throat section 286 but greater than the field strength in the plasma liner 210 body, indicated plasma containment section 287. Plasma generation efficiency is increased by increasing the relative difference in the magnetic field strength between plasma containment section 287 and second throat section 288. A larger “magnetic hill” between sections 287 and 288 serves to rebound more ions and electrons into plasma containment section 287, increasing the probability of neutral propellant ionization. FIG. 1 IB illustrates another magnetic field configuration in which the field strength at“throat” section 288 is equal to or less than the field strength in plasma containment section 287. In this embodiment, the magnetic field strength is solely diverging in the proximal (closed end) to distal (open end) direction. As illustrated in FIG. 1 IB, the magnetic field strength may not decrease linearly or otherwise proportionally over the liner length, although it may. For example, the magnetic field strength in section 288 may be the same as, or only slightly less than, the minimum field strength in section 287, and then decrease at a higher rate towards and beyond the open end. In these cases, the magnetic nozzle is described as monotonically decreasing, or solely diverging, in axial strength from the closed end of the plasma liner to the open end of the plasma liner.

[00125] Integrated Gridded Ion Thruster Design

[00126] The foregoing plasma production apparatus 200, 201, 202 (“PPA”) may be adapted for use in a GIT design. In particular, the GIT may incorporate 1, 2, 3, 4, 5, or more PPAs, depending upon the quantity of plasma (and thrust) desired from the integrated GIT. Although the following description may reference one particular plasma production apparatus

configuration, it is understood that any of the configurations described herein may be easily and independently substituted in the integrated GIT designs. Furthermore, the following descriptions of integrated GIT designs may omit certain features of the PPAs described above in order to promote simplicity and an understanding of the integrated design. The omission of any particular element is not necessarily an admission that the element is omitted from the integrated design.

[00127] Single PPA Designs

[00128] FIG. 12A illustrates one integrated GIT design in which plasma liner 210 also functions as GIT discharge chamber 110. In some embodiments, plasma liner 210 is cylindrical and, in combination with the antenna 230 design and power, has a radius (RL) that is < 1-7 p_s, as described above. Given the limitations on RL, it is expected that a GIT built according to this design would produce a relatively small amount of thrust, making it applicable for high precision orbital maneuvers but alone would not be powerful enough for station keeping or orbital transfer.

[00129] FIG. 12B illustrates an alternative single PPA integrated GIT design in which the PPA 200 is positioned upstream of a relatively large diameter GIT discharge chamber 110.

Neutral propellant 225 is introduced through the closed end 222 of the PPA 200 and ionized to form plasma 223 (i.e., consisting of positive ions 221 and electrons 222). Plasma 223 is ejected from PPA 220 by magnetic fields 285 produced by magnet system 280, as described above. Positive ions 221 also may be pulled from PPA 220 by from electrostatic attraction from negative grid 140. GIT chamber 110 comprises magnets 180, as described above in the context of a standard GIT. Optionally, GIT discharge chamber 110 also comprises antenna 130 (not shown) adapted to ionize any propellant 220 that exits PPA 200. Negative grid 140, neutral grid 150, cathode 170, and the associated high voltage power source are constructed according to the existing principles of GIT design and as described above. Thus, this integrated GIT design produces plasma 223 from neutral propellant 225 in PPA 200. The propellant ions are accelerated to some degree as they exit PPA 200 and enter GIT discharge chamber 110 where they are further accelerated by charged grid system according to standard GIT principles.

[00130] Multiple PPA Designs

[00131] FIG. 13 illustrates a multiple PPA integrated GIT design. Specifically, the integrated thruster is illustrated as having two PPAs 200a and 200b which produce and delivery plasma to a single GIT discharge chamber 110. The features of the PPA systems and GIT 100 are described above. [00132] It is understood that the multiple PPA designs may comprise 2, 3, 4, 5, 6, or more individual PPA units 200 that produce and deliver plasma to a single GIT discharge chamber 110. The PPAs 200 may have identical configurations and specifications or different

configurations and specifications, depending upon the desired application. In some

embodiments, it may be beneficial to have one or more relatively small PPA units and one or more relatively large PPA units which may be fired independently. For example, the small PPA(s) may be fired when small but high precision maneuvers are desired and the large PPA unit(s) and/or all PPA units may be fired for larger thrust applications such as orbital transfer.

The multiple PPA designs provide the further advantage of redundancy in that thruster function is not completely reliant on any single plasma generation device.

[00133] The plurality of PPA units may be supplied from a common propellant delivery system 229 or each PPA may have a dedicated propellant delivery system 229, or a combination of both. In embodiments having a common propellant delivery system 229 supplying a plurality of PPAs, the propellant delivery system 229 may further comprise controllable valves to selectively deliver propellant to only a subset of PPAs or all PPA simultaneously. Optional one way flow and/or check valves may be included to prevent propellant loss caused by a failure in the propellant delivery system of one PPA. Likewise, the plurality of PPA units may be supplied from a common power control system 260 or multiple dedicated (or overlapping) power control systems 260.

[00134] It will be appreciated by persons having ordinary skill in the art that many variations, additions, modifications, and other applications may be made to what has been particularly shown and described herein by way of embodiments, without departing from the spirit or scope of the invention. Therefore, it is intended that scope of the invention, as defined by the claims below, includes all foreseeable variations, additions, modifications or applications.

REFERENCES

1) Scime et ah, J. Plasma Phys., 2015.

2) Kinder, et ah, J. Appl. Phys., 90(8), 2001.

3) Chen, F.F., Introduction to Plasma Physics and Controlled Fusion , Plenum Press, New York, NY, 1984.

4) Huba, J.D., NRL Plasma Formulary , Naval Research Laboratory, Washington DC, 2009. ) Chen, Plasma Sources Sci. Technol. , 24 : 014001, 2015.) Stephan, et al., J. Chem. Phys., 81(7), 1984.

) Hopwood , Plasma Sources Sci. Technol. 1 : 109-116, 1992.

Claims

What is claimed is:

1. A device comprising:

(a) an upstream plasma production apparatus comprising:

(i) a substantially cylindrical plasma production chamber having a cylinder body, a first closed end and a first open end;

(ii) a magnet system comprising one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber such that each magnet produces a magnetic field of the same polarity within the plasma production chamber;

(iii) a propellant tank and a flow regulator in communication with the plasma production chamber and configured to deliver a gaseous propellant into the plasma production chamber; and

(iv) a radio frequency (RF) antenna electrically coupled to an AC power source, and configured to deliver an RF energy to an interior region of the plasma production chamber; and

(b) a downstream gridded ion thruster comprising:

(i) a discharge chamber in communication with the first open end of the plasma production chamber, and a downstream second open end, wherein the second open end comprises a negatively-charge grid and a grounded grid downstream of the negatively-charge grid; and

(ii) a cathode.

2. The device of claim 1, wherein the plasma production apparatus is configured to ionize and heat substantially all of a plasma by inductive heating.

3. The device of claim 1 or 2, wherein the plasma production chamber radius (RL) is equal to 1-7 times the skin depth (p_s) of the RF energy.

4. The device of any one of claims 1-3, wherein the plasma production chamber radius (RL) is equal to 1.1 - 5.0 times the Larmor orbit radius (pi) of a plasma ion produced from the propellant.

5. The device of any one of claims 1-4, wherein the RF energy frequency is less than 25% of an electron cyclotron frequency (/ce).

6. The device of any one of claims 1-5, wherein the antenna comprises a coiled region.

7. The device of any one of claims 1-6, wherein the antenna comprises a flat spiral region external to the plasma production chamber and disposed on an external surface of the first closed end,

8. The device of claim 7, wherein the flat spiral region has 1-10 turns.

9. The device of claim 7 or 8, wherein the flat spiral region comprises a spiral region radius and the first closed end comprises a closed end radius, and wherein the spiral region radius is 10%-100% of the closed end radius.

10. The device of any one of claims 7-9, wherein the spiral region is configured to cause a constructive interference in magnetic fields produced within the plasma production chamber.

11. The device of any one of claims 7-10, wherein the antenna further comprises a coiled region disposed on the external surface of the cylinder body, wherein the coiled region is selected from the group consisting of a coil, a helix, and a half-helix.

12. The device of claim 11, wherein the coiled region and the spiral region are wound in the same direction.

13. The device of claim 12, wherein the coiled region and the spiral region are wound in a right-handed direction.

14. The device of any one of claims 1-13, wherein the magnet system produces an upstream first throat region and a downstream second throat region within the plasma production chamber, wherein the first throat region and the second throat region are separated by a plasma containment region having a lower magnetic field strength than either of the first throat region or the second throat region.

15. The device of any one of claims 1-14, wherein the magnet system further comprises at least one planar magnet disposed behind the first radially-disposed magnet, wherein the at least one planar magnet produces a magnetic field of the same polarity within the plasma production chamber as the one or more radially-disposed magnets, and wherein the magnetic field of the at least one planar magnet is substantially parallel to the longitudinal axis of the plasma production chamber.

16. The device of any one of claims 1-15, wherein the RF energy has a frequency of 3-300 MHz.

17. The device of any one of claims 1-16, wherein the AC power source has a power of 25-500 W.

18. A device comprising:

(a) a plurality of upstream plasma production apparatuses, wherein each plasma production apparatus comprises:

(ii) a magnet system comprising one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber such that each magnet produces a magnetic field of the same polarity within the plasma production chamber; and

(iii) a radio frequency (RF) antenna electrically coupled to an AC power source, and configured to deliver an RF energy to an interior region of the plasma production chamber;

(b) one or more propellant tanks configured to deliver a gaseous propellant into the plurality of plasma production apparatuses; and

(c) a downstream gridded ion thruster comprising:

(i) a single discharge chamber in communication with the first open end of each of the plasma production chambers, and a downstream second open end, wherein the second open end comprises a negatively-charge grid and a grounded grid downstream of the negatively-charge grid; and

(ii) a cathode.

19. The device of claim 18, wherein each of the plasma production apparatuses is configured to ionize and heat substantially all of a plasma by inductive heating.

20. The device of claim 18 or 19, wherein the plasma production chamber radius (RL) of each of the plasma production chambers is equal to 1-7 times the skin depth (p_s) of the RF energy.

21. The device of any one of claims 18-20, wherein the plasma product chamber radius (RL) each of the plasma production chambers is equal to 1.1 - 5.0 times the Larmor orbit radius (pi) of a plasma ion produced from the propellant.

22. The device of any one of claims 18-21, wherein the RF energy frequency is less than 25% of an electron cyclotron frequency (fe ).

23. The device of any one of claims 18-22, wherein at least one antenna comprises a coiled region.

24. The device of claim 23, wherein the at least one antenna comprises a flat spiral region external to the plasma production chamber and disposed on an external surface of the first closed end,

25. The device of claim 24, wherein the flat spiral region has 1-10 turns.

26. The device of claim 24 or 25, wherein the flat spiral region comprises a spiral region radius and the first closed end comprises a closed end radius, and wherein the spiral region radius is 10%-100% of the closed end radius.

27. The device of any one of claims 24-26 wherein the spiral region is configured to cause a constructive interference in magnetic fields produced within the plasma production chamber.

28. The device of any one of claims 24-27, wherein the antenna further comprises a coiled region disposed on the external surface of the cylinder body, wherein the coiled region is selected from the group consisting of a coil, a helix, and a half-helix.

29. The device of claim 28, wherein the coiled region and the spiral region are wound in the same direction.

30. The device of claim 29, wherein the coiled region and the spiral region are wound in a right-handed direction.

31. The device of any one of claims 18-30, wherein the magnet system in at least one plasma production apparatus produces an upstream first throat region and a downstream second throat region within the plasma production chamber, wherein the first throat region and the second throat region are separated by a plasma containment region having a lower magnetic field strength than either of the first throat region or the second throat region.

32. The device of any one of claims 18-31, wherein the magnet system in at least one plasma production apparatus further comprises at least one planar magnet disposed behind the first radially-disposed magnet, wherein the at least one planar magnet produces a magnetic field of the same polarity within the plasma production chamber as the one or more radially-disposed magnets, and wherein the magnetic field of the at least one planar magnet is substantially parallel to the longitudinal axis of the plasma production chamber.

33. The device of any one of claims 18-32, wherein the RF energy has a frequency of 3-300 MHz.

34. The device of any one of claims 18-33, wherein the AC power source has a power of 25-500 W.

35. A gridded ion thruster comprising:

(a) a substantially cylindrical plasma production chamber having a closed end and an open end;

(b) one or more radially-disposed magnets configured to establish a magnetic field within the plasma production chamber and oriented substantially parallel to a central longitudinal axis of the plasma production chamber such that each magnet produces a magnetic field of the same polarity within the plasma production chamber;

(c) a propellant tank and a flow regulator in communication with the plasma production chamber through the first end and configured to deliver a gaseous propellant along the central longitudinal axis of the plasma production chamber;

(d) a radio frequency (RF) antenna external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber; and

(e) an electrode comprising a negatively-charged grid and a neutral grid covering the open end, and a cathode;

36. A plasma production device comprising:

(a) a substantially cylindrical plasma production chamber having a first closed end and a second open end;

(c) a propellant tank and a flow regulator in communication with the plasma production chamber through the first end and configured to deliver a gaseous propellant along a central longitudinal axis of the plasma production chamber;

37. A plasma production device comprising:

wherein the plasma product chamber radius (RL) is equal to 1.1 - 5.0 times the Larmor orbit radius (pi) of a plasma ion.

38. A plasma production device comprising:

(d) a radio frequency (RF) antenna external to the plasma production chamber, electrically coupled to an AC power source, and configured to deliver an RF energy to an interior portion of the plasma production chamber; and (e) an electrode comprising a negatively-charged grid and a neutral grid covering the open end, and a cathode;

wherein the RF energy frequency is less than 25% of an electron cyclotron frequency

(fee)·