Patent Publication Number: US-2023136486-A1

Title: Two-stage low-power and high-thrust to power electric propulsion system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of priority of U.S. Application Ser. No. 62/981,828, filed on Feb. 26, 2020 and entitled Two-Stage Pulsed Magneto Plasma-Dynamic Accelerator, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to two-stage propulsion systems that may be used for maneuvering satellite devices, such as CubeSats, nano satellites, and microsatellites (e.g., less than 100 kg class satellites), or larger satellites. More specifically, the present invention relates to the onset of the magnetized arc and its positive effect on the momentum of a low-power two-stage pulsed magneto dynamic propulsion system. 
     BACKGROUND 
     Two-stage propulsion systems provide efficient maneuvering of satellites. This is particularly true when performing more than one specific application, such as orbit raising maneuvers where high thrust is required, and a specific thruster will be needed, and station-keeping, where one would prefer a thruster with high specific impulse (I isp ). Therefore, two separate single-stage thrusters are needed if both maneuvers are to be performed efficiently. 
     Some examples of two-stage propulsion systems are the P5-2 (5 kW) thruster which was designed and tested at the University of Michigan, the Helicon Hall Effect Thruster (600 W-1200 W), the Linear Gridless Ion Thruster (2 kW), the VASIMR engine (200 kW), the D-80 Thruster with Anode Layer (TAL, 3 kW), and the Very High Specific Impulse Thruster with Anode Layer (VHITAL, 25-36 kW), amongst many others. As an example, the VHITAL thruster yields a TPR of 26 mN/kW and an I sp  of 6000 s in single-stage mode, whereas in the two-stage mode, the TPR drops to 19.7 mN/kW but the I sp  increases to 8000 s. Single-stage operation in Hall-effect thrusters (HET) and TAL systems is limited to voltages of around 1 kV and after this point, they experience a significant drop in efficiency due to severe anode heating. This can be overcome by separating the ionization and the acceleration regions, i.e. with a two-stage system. These systems, however, have their drawbacks. 
     A two-stage propulsion system has two modes of operation versus a single stage system. In a two-stage mode, the ionization stage is separate from the acceleration stage. In a single stage operation, the thruster provides a high thrust-to-power ratio (TPR) and is ideal for orbital change maneuvers, whereas the two-stage operation provides a higher specific impulse and is ideal for station-keeping and interplanetary missions, where efficient use of the propellant is more important than thrust. The use of two-stage thrusters benefits a broad number of missions, such as all-electric satellites for geostationary applications (high-thrust LEO (Low Earth Orbit) to GEO (Geostationary Orbit) transfer, high I sp  station-keeping and drift corrections once in orbit. Interplanetary probes and sample return missions to asteroids also benefit from this development. 
     Magneto Plasma Dynamical (MPD) thrusters are powerful (with average power within the range of kW— hundreds of kW), high-thrust propulsion engines with electromagnetic Lorentz force J×B that accelerates and expels plasma and creates the thrust. MPD thrusters have the high thrust density and do not require ion-absorbing grid system, dangerous high voltages and lifetime-limited cathode neutralizers. In applied-field MPD thrusters that use an external coil to create a magnetic field, the Lorentz force is generated mainly as a result of vector product of a large current flowing in azimuthal direction in plasma and radial component of magnetic field of the coil. However, known MPD thrusters can achieve high efficiency (around 70%) only at very high power levels (˜20 kW). 
     The fast-growing popularity of small satellites for LEO and even interplanetary space missions means there is a need for new types of efficient, light-weight, reliable and low-power propulsion systems. 
     SUMMARY 
     The present invention provides a satellite propulsion system that comprises a first ionization stage the comprises a plasma source configured to produce an arc discharge and emit a preliminary plasma, the plasma source including an external magnetic field configured to magnetize the arc discharge. A second acceleration stage of the system comprises an accelerator positioned in series with the plasma source, the accelerator being configured to accelerate the preliminary plasma out through the accelerator, thereby creating an accelerated plasma flow. The application of an activation threshold voltage to the accelerator results in a surge in system performance parameters. 
     In certain embodiments, the system performance parameters include one or more of thrust, thrust-to-power ratio, and system efficiency; the plasma source has an output for emitting the preliminary plasma; and the accelerator is positioned near the output to receive the preliminary plasma emitted from the plasma source; the accelerator is an electrode; and/or the electrode is a metal cone that has an inlet opening and an outlet opening, the inlet opening is configured to receive the preliminary plasma and the metal cone is configured to accelerate the plasma flow through the outlet opening. 
     In other embodiments, the magnetic field is created by a magnet positioned at an interface of the plasma source and the accelerator; the magnet is a magnetic ring; the activation threshold voltage is about 30 Volts; acceleration of the preliminary plasma by the accelerator occurs due to an electromagnetic Lorentz force; the plasma source comprising a cathode surrounded by an anode with an insulator therebetween; the preliminary plasma is almost fully ionized; and/or the system is configured for low-power consumption. 
     The present invention may also provide a low-power plasma thruster that comprises a plasma source that has an outlet for emitting plasma; an accelerator electrode that is positioned in series with the plasma source, and the accelerator electrode has an inlet positioned near the outlet of the plasma source for receiving the plasma; and means for increasing performance parameters of the thruster via application of a threshold voltage to the thruster. 
     In an embodiment, the threshold voltage is about 30 Volts. In another embodiment, the accelerator electrode is a metal cone. 
     The present invention may further provide a method of operating a propulsion system, that comprises the steps of energizing the propulsion system to produce a preliminary plasma using low power; applying a magnetic field to an arc discharge of the preliminary plasma; accelerating the preliminary plasma to create an accelerated plasma flow; and applying a threshold voltage to create a surge in performance parameters. 
     In certain embodiments, the step of accelerating the preliminary plasma includes use of an accelerator electrode that receives the preliminary plasma; the threshold voltage is applied to the accelerator electrode; the threshold voltage is about 30 Volts; and/or the performance parameters of the system include one or more of thrust, thrust-to-power ratio, and system efficiency. 
     This summary is not intended to identify essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter. It is to be understood that both the foregoing general description and the following detailed description are exemplary and are intended to provide an overview or framework to understand the nature and character of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying drawings are incorporated in and constitute a part of this specification. It is to be understood that the drawings illustrate only some examples of the disclosure and other examples or combinations of various examples that are not specifically illustrated in the figures may still fall within the scope of this disclosure. Examples will now be described with additional detail through the use of the drawings, in which: 
         FIGS.  1   a  and  1   b    are schematics of a two-stage MPD propulsion system and its processing circuitry of according to examples of the present invention; 
         FIGS.  2   a - 2   f    show the results demonstrating the onset of the arc in the second stage of the system, for the thruster with or without magnetic field system configurations; 
         FIG.  3   a    is a graph that shows the onset behavior of a vacuum arc in an MPD thruster: average power dissipated in MPD stage jumps after certain threshold of U MPD  voltage of ˜10 V (“No magnet”) and ˜30 V (“With magnet”) in accordance with an example of the propulsion system; 
         FIG.  3   b    is a graph showing the pulse-averaged  U arc    vs. U MPD  for the With magnet and No magnet system configurations; 
         FIG.  4   a    is a graph showing the pulse-averaged plasma potential with respect to a grounded cathode, versus U MPD , for With magnet and No magnet system configurations; 
         FIG.  4   b    is a graph showing the pulse-averaged I MPD /I arc  ratio vs. U MPD   U arc   , for With magnet and No magnet system configurations; 
         FIG.  5   a    is a graph showing the pulse-averaged ion density vs. axial coordinate, at U MPD =63 V, for With magnet and No magnet system configurations; 
         FIG.  5   b    is a graph showing the normalized (to their maxima at z=4 mm) curves of pulse-averaged ion density vs. z, for With-magnet and No magnet configurations, and simulation. 
         FIGS.  6   a  and  6   b    illustrate particle-in-cell (PIC) simulations of the physics of the thrust gain and the threshold behavior of a μCAT-MPD thruster of an exemplary embodiment of the present invention; 
         FIGS.  7   a  and  7   b    are graphs showing the thrust, estimated from the electrical measurements of the thruster in With-magnet and No-magnet system configurations; and 
         FIG.  8    is a graph showing Ion velocities with respect to Accelerating Voltage applied to each ring, respectively, of the propulsion system according to an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     In describing the illustrative, non-limiting preferred embodiments of the invention illustrated in the drawings, specific terminology will be resorted to for the sake of clarity. However, the invention is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes all technical equivalents that operate in similar manner to accomplish a similar purpose. Several preferred embodiments of the invention are described for illustrative purposes, it being understood that the invention may be embodied in other forms not specifically shown in the drawings. 
     Referring to  FIGS.  1   a   - 8 , the present invention relates to a plasma thruster and propulsion system  10 , such as for small satellite propulsion. The plasma thruster and propulsion system  10  may be a low-power (less than about 30 W), two-stage pulsed magneto plasma dynamical (MPD) thruster  10 , based on magnetized vacuum arc metallic plasma, and suitable for orbit raising and interplanetary missions of satellites. “Dynamical” means that the accelerating object is quasi-neutral plasma itself (not only ions), and acceleration occurs due to electromagnetic Lorentz force. Therefore, the MPD thruster has an advantage over a gridded thruster, for example, because the MPD thruster expels the neutral plasma, such that it does not require to host on the satellite any negative particles emitter (charge neutralizer). As such, the MPD thruster is more energy-effective. 
     The principle of the MPD stage operation is as follows. Plasma ions and electrons are expelled from a cathodic spot on the surface of the cathode  20  towards the entrance of the accelerator cone  14 . The cone  14  serves as an electrode to control current distribution. The cone  14  attracts a large number of electrons, which flow toward the cone  14  and produce a large current. Plasma electrons rotate around and drift along magnetic field lines toward the surface of the cone  14 . Interaction between electron current density and the magnetic field lines leads to Lorentz force directed toward the exhaust of the thruster  10 . This Lorentz force accelerates both ions and electrons, fast electrons in turn accelerate ions due to electrostatic coupling, thereby increasing the total thrust of the system. An advantage of the MPD stage operation is that it is grid less, so the thrust will not decrease because of the absorption of the plasma particles by grid cells. 
     The propulsion system  10  of the present invention is configured to boost and improve the thrust-to-power ratio (TPR) by controlling the current in the second MPD stage; to control the transition from a single to two-stage regime by changing the voltage in the second stage of the system; and to increase thrust of the system by voltage in the second stage and by optimizing the magnetic field. 
     The thruster  10  of the present invention can be magnetized by an axially-symmetric dc magnetic field of ˜200 mT with both axial and radial components, such that the pulsed vacuum arc discharge in the MPD thruster  10  demonstrate a threshold behavior: such parameters as thrust, thrust-to-power ratio, the power dissipating by the MPD stage, total charge of ions expelling within the single pulse, and ion-to-arc charge ratio rapidly jump or surge after a certain threshold dc voltage (e.g. about ˜30 V) applied between the cathode and the accelerating (MPD) electrode. This effect can be used to controllably and drastically improve in several tens of times the thrust (from ˜2 μN to ˜210 μN), efficiency (from ˜1% to 50%) and thrust-to-power ratio (from ˜0.5 μN/W to ˜18 μN/W). 
     The plasma thruster  10  of the present invention can be scaled down in power and size so that the applied-field MPD thruster fits inside a small satellite. And even with such reduction scaling, the thruster  10  is configured for relatively high thrust (up to mN), high efficiency, high thrust-to-power ratio (˜tens of μN/W) simultaneously with the small mass, dimensions and low power consumption. The two-stage pulsed (up to ms pulse length) cm-sized low-power (0.1 W-30 W) MPD thruster  10 , can have the PPU  15  for the low-power (˜ several W) first-stage based on micro-cathode arc thrusters (μCATs), thereby creating almost fully-ionized preliminary plasma as a result of a trigger-less vacuum arc between two solid-state (metallic) electrodes. Preliminary plasma or plasma source  12  initiates in the first stage, and then the more powerful (˜several tens of W) arc discharges in an external magnetic field in the second stage, which creates the main accelerated plasma flow of the system  10 . And this plasma flow can be throttled by the varying the voltage on accelerating electrode, such as an accelerator cone  14 . 
     The plasma accelerator system  10  of the present invention presents the physical phenomena that occurs in the thruster (e.g. a two-stage μCAT-MPD thruster)—a surge in performance parameters, such as thrust, thrust-to-power ratio and efficiency, after a certain threshold voltage applied on the accelerating electrode  14 , thereby allowing a drastic increase in the above mentioned parameters. 
     In an example, the cone  14  is provided near the distal end  16  of the plasma source  12 . The cone  14  can be a thin metal wall having a hollow center forming a discharge chamber  24 . A positive signal is applied to the cone  14 , which accelerates the plasma by the Lorentz force. 
     The plasma source  12  in the first stage of the system  10  may comprise a cathode  20  that is surrounded by an anode  30 , with an insulator  40  therebetween, such as described in commonly owned U.S. Published Application No. 2020/0361636, the subject matter of which is herein incorporated by reference. The cathode  20 , insulator  40 , and anode  30  are concentrically and sequentially arranged with one another with the cathode  20  being innermost, as seen in  FIG.  1     a.    
     The anode  30  can be a tube that forms an outer ring or layer of the plasma source  12  and has a central bore. The insulator  40  can be a tube that has a central bore and a diameter that is smaller than the diameter of the anode  30 . The cathode  20  can be a rod. The cathode  20  can be received in the bore of the insulator  40 , and the insulator  40  is received within the bore of the anode  30 . The cathode  20  can slide forward and rearward in the insulator to remain flush with the anode  30  as the anode is consumed. 
     In one example, the accelerator cone  14  can have multiple rings, such as ring one  18   a , ring two  18   b , ring three  18   c , and ring four  18   d , as seen in  FIG.  1 B . Selective voltage can be applied to the rings  18   a - 18   d  to achieve the improved performance of the propulsion system  10 . 
     The plasma is ignited as a result of surface flashover of the anode-cathode gap, and then is expelled from the cathodic spot toward the opening of the accelerating electrode  14 . The cone  14  has an inlet opening and an outlet opening, with the outlet opening being larger than the inlet opening. This electrode had a frustum cone shape, with the smaller opening close to the end  16  of the plasma source  12 . Plasma is expelled from the large outlet opening of the cone as exhaust. The cone  14  can be located in the central plane of a magnetic pulsing solenoid, fed by a pulsing power unit (PPU)  15  and producing a magnetic field with variable value of 0-120 mT. The voltage U a  between grounded cathode and accelerated electrode (cone) can be set by a dc power supply (up to 63 V). The magnetic field is concentrated and the magnetic lines bent to enlarge the radial part of magnetic field in the thruster face-cone entrance interface  22 . 
     The system  10  of the present invention can be an electric propulsion system that is based on the well-researched ablative vacuum arc or ‘cathodic arc’ process. There is a physical phenomenon known to erode the negative electrode (cathode) with every discharge. In this case, this is desirable as the cathode  20  is the thruster&#39;s propellant. During each discharge, a small amount of metallic propellant is eroded, ionized, and expelled by a large temperature and pressure gradient from inside the cathodic spot. The efficiency is enhanced by a magnetic field caused by the arc current as it travels through a magnetic coil that is connected in series with the thruster prior to arcing between the electrodes. 
     The first stage of the system  10  produces the preliminary plasma that will ultimately be accelerated using an electric field in the second stage. In an example of the present invention, a single coaxial μCAT, with the central copper cathode  20 , and an outer annular copper anode  30  was used as the first-stage (preliminary source of plasma  12 ). This plasma was expelled toward the opening of the accelerating MPD electrode or cone  14  with a positive dc bias U MPD  of up to 63 V. The thruster&#39;s first-stage face and the opening of the accelerating electrode  14 , that is the thruster face-cone entrance interface  22 , were placed in the field of an axially-magnetized permanent magnet or magnetic ring  50  with induction of ˜ 0.2 T on its axis ( FIG.  1   a   ). Large electron current J toward the positively-biased accelerating MPD electrode  14 , as a result of interaction between the radial component of magnetic field B r , resulted in a Lorentz force J×B r  which in turn led to the acceleration of the plasma toward the opening of the accelerating electrode  14 . Because U MPD  can be easily varied, the thrust gain is also controllable. 
     In the first stage or ionization stage of the propulsion system  10 , a voltage is provided to energize the system. The booster circuits convert the energy, thereby producing an instantaneous peak arc discharge. This instantaneous current ablates a small fraction of the anode  30  and ionizes it, producing a quasi-neutral plasma that does not require a neutralizer. The plasma plume is almost fully ionized hence eliminating potential self-contamination due to the charge exchange process in the case of a weakly ionized plasma. 
     In an example, the system  10  includes the first-stage pulsing power unit (PPU)  15 , which can be an inductively storage pulsing circuit which stores energy in a ferrite-core inductor of 550 μH and releases it with a powerful IGBT gated by a rectangular-pulse signal generator with firing pulse repetition rate f=10 Hz. The average thrust was experimentally measured in the two ways: 
     (1) indirectly, by fixing the thruster on a thrust stand base, placing the thruster exhaust in front of the light-weight plate mounted on a movable arm of a micro-newton-level torsional thrust stand; and 
     (2) by calculating using experimental data according to the formula 
     
       
         
           
             
               T 
               = 
               
                 0.63 
                 
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             , 
           
         
       
     
     where m i , v i  are single ion mass and their average velocity, I i (t) is total ion current waveform with duration τ i , Z=2 is ion mean charge stage. Thrust-to-power ratio TPR was measured by dividing the average thrust T over the total power P tot  which is the sum of average powers dissipated in the first-stage P orc , in the second (MPD) stage P MPD , and in the PPU (P PPU ): 
     
       
         
           
             
               
                 
                   
                     TPR 
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     where τ arc , T MPD  and τ PPU  are current pulses durations in the first stage, MPD stage and in PPU, respectively. Efficiency η was estimated by dividing the average power of thruster exhaust over P tot : η=100%×(T·v i /P tot ). 
     The physical nature of the arc discharge allows any conductive (solid) material, e.g. copper, to be used as a propellant. The eroded material is, to a large degree, fully ionized. Additionally, it is common that the particles are multiply ionized. The arc discharge can ablate any conductive material, which allows the propulsion system or thruster  10  to operate with different metals, each with different physical properties, giving the mission designer flexibility when it comes to the mission&#39;s design. Only an electrical connection is required to operate the thruster, since the propellant and all necessary components are integrated within the thruster&#39;s structure. This provides the ability and flexibility of attaching the thruster  10  to deployable booms to increase the torque for RCS maneuvers. 
     The system  10  is configured to improve and optimize thrust and thrust-to-power ratio via the Magneto Plasma Dynamical (MPD) approach in the second stage of the system  10 . Referring to  FIGS.  2   a - 2   e   , the results demonstrating the onset of the arc in the second stage of the system  10 , for the thruster with or without the magnetic field, are shown. The absence of the magnetic field results in long powerful pulses in the first stage, and the discharge arc tends to switch to dc mode ( FIG.  2   a   ). Once the magnetic field is added, the first stage produces plasma in very short and low-power pulses ( FIG.  2   b   ). This shows there is a threshold for “activation” of the second stage—after ˜10 V without or no magnet ( FIG.  2   c   ), and ˜30 V with magnet ( FIG.  2   d   ). Without the magnetic field, the exhausting total ion current is weakly dependent on MPD stage (U MPD ) voltage and more or less constant in time ( FIG.  2   e   ). However, with the magnetic field (With magnet), the current drastically jumps after a certain threshold of voltage, e.g. ˜30 V ( FIG.  2   f   ). 
       FIG.  3   a    is a graph that shows the onset behavior of the vacuum arc in the MPD thruster: average power dissipated in MPD stage jumps after certain threshold of U MPD , voltage of ˜10 V (No magnet) and ˜30 V (With magnet).  FIG.  3   b    is a similar graph showing the pulse-averaged  U arc    vs. U MPD  for the With magnet and No magnet cases. The dashed lines in the  FIG.  3   b    graph represent the average value of  U arc   . 
     Without the magnet, the average power, dissipating in the first stage of the system  10 , does not depend on MPD stage voltage and remains comparable with the power in the second stage. However, with magnet, the first-stage power abruptly drops to just several watts, and after certain U MPD  voltage (˜30 V), the highest power now is dissipating in the MPD stage, but this power with magnet is much less than without magnet, as shown in  FIG.  3   a   . These demonstrate that the magnetic field positively effects the thruster&#39;s performance by decreasing the power losses in the first stage, preventing switching into dc arc, and enhancing the plasma generation and its acceleration in the second stage. 
     Such threshold-like behavior is observed not only in “with magnet” case, but also in the “no magnet”, as seen in  FIG.  3   a   . This suggests that this happens due to electric field-related effect, and the magnetic field enhances that effect. One factor responsible for the threshold voltage value, is related to the first-stage pulse-averaged arc burning voltage: 
     
       
         
           
             
               
                 
                   
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     The dependences of  U arc    on U MPD  for the “with magnet” and “no magnet” cases are given in  FIG.  3   b   . One can see that pulse-averaged  U arc    weakly depends on U MPD  voltage, but strongly depends on the presence of magnetic field. Also we may see that the average values of  U arc   (27.6 V and 16.6 V) are very close to the respective threshold voltage values for the “with magnet” and “without magnet” cases (˜30 V and ˜10 V, respectively). 
     At the initial moment of the arc ignition (when there is no plasma), the anode-cathode voltage formed by the first-stage of the system  10  has a form of a quite high (with the amplitude of up to several hundreds of volts) but very short peak. Once plasma is ignited, this voltage drops down to the arc burning voltage defined by the cathode material and which can be estimated according to equation (2) above. First-stage plasma acquires potential close to the potential of the anode  30  (i.e. arc burning voltage), therefore, any voltage on MPD stage below this plasma potential (i.e. below the pulse-averaged arc burning voltage) will repel electrons from the MPD electrode  14  and therefore electron current I MPD  toward MPD electrode will be close to zero. After increase of U MPD  to the values higher than  U arc   , plasma electrons feel the accelerating field from the cathode  20  toward the MPD electrode  14 , and their current I MPD  toward MPD electrode grows with the U MPD  voltage. 
       FIG.  4   a    is a graph showing the pulse-averaged plasma potential with respect to grounded cathode, versus U MPD , for “with magnet” and “no magnet” cases. The dashed lines in  FIG.  4   a    correspond to the pulse-averaged arc burning voltages.  FIG.  4   b    is a graph showing the pulse-averaged I MPD /I arc  ratio vs. U MPD   U arc   , for “with magnet” and “no magnet” cases. 
     In the case with the presence of the magnetic field, the first-stage plasma electrons are magnetized, and therefore pulse-averaged arc burning voltage becomes much higher. Therefore, in order to attract electrons toward MPD electrode  14 , higher U MPD  voltages are required. This leads to the higher threshold values. This assumption is supported by the measurements of a pulse-averaged plasma potential versus U MPD  in the “with magnet” and “no magnet” cases. Experimental setup for this measurement included a ceramic tube with mounted Langmuir probe tip (e.g. a ring with diameter 2 mm and the length 1 mm). The ring was mounted on the end of the ceramic tube, placed at and aligned with the axis of the thruster, with the ring directed toward the cathode. The Langmuir probe was movable along the axis with 0.5 mm step. During the experiment, the position of the probe tip was fixed at around 0.5 mm from the anode. Floating potential was measured by a voltage sensor, connected to the probe tip via a BNC cable. Floating potential was measured in the two modes: with and without the magnet, versus U MPD  voltage (0-63 V), for the same other experimental parameters kept unchanged. The floating potential waveform data was used to directly calculate pulse-averaged plasma potential  φ p    according to the formula: 
         ϕ p   = ϕ fl   +1 n ( m   i /2π m   e ) kT   e /2 e   (3)
 
     where (φ fl ) is the pulse-averaged probe floating potential. Here, the electron temperature T e  was assumed to be independent from the presence of the magnetic field and was taken to be equal to 3.5 eV for copper vacuum arc plasma. One can see from  FIG.  4   a    that the plasma potential significantly changes with U MPD , while  U arc   , as follows from  FIG.  3   b   , changes slightly. This is understood because for the fixed electron temperature, plasma potential will be strongly dependent on electron loss rate determined by the potential on the neighboring electrodes (mainly, on MPD electrode). However, one can see that plasma potential is connected with the arc burning voltage, because this potential starts growing after U MPD  exceeds  U arc    for corresponding “with magnet” or “no magnet” cases. 
     Another reason for the an abrupt increase in thruster performance is due to a drastic growth in current to the second MPD stage of the system  10  happening when U MPD  exceeds the plasma potential, are the ratios of pulse-averaged  I MPD   / I arc    versus U MPD / U arc    given in  FIG.  4   b   . It is seen that for the both cases, there is no  I MPD    current at U MPD  less than  U arc    (i.e. for U MPD / U arc    less than 1), and there is a significant increase of  I UPD   / I arc    after this value. 
     To find out the region of ions acceleration inside the volume of the cone  14  we assume that the total flow of ions entering the narrow part of the cone  14  will be the same at the exhaust of the cone  14  (since MPD electrode is positive and ions will be reflected from its walls). Therefore, the expression for the ion flow valid for any cross-section of the cone and even further: 
         j   io   S   0   =j   z   S   z   (4)
 
     where j i0  is the ion current density at the plane of the cone narrow opening having cross-sectional area S 0 , j z  and S z  are the corresponding values at any axial coordinate z. Assuming that v i (0)=v i (z), the final expression for the normalized ion density function vs. axial coordinate: 
         n   i ( z )/ n   i (0)= r   0   2   /r   0   +z·tg α) 2    (5)
 
     One can expect that if the ions are accelerating with z coordinate (v i (0)≠v i (z)), the experimentally-measured n i (z)/n i (0) will go steeper than the calculated according to equation (5) above, and this could help to find the region of ions acceleration. Such experiment was conducted using the axially-movable Langmuir probe described above. The initial axial coordinate (z=0) was adjusted to the cathode surface, then the probe tip coordinate was varied in step of 2 mm, from 1 mm up to 22 mm with respect to the cathode surface. The probe tip was biased with a battery set to −53 V with respect to ground. Ion current waveform was measured as a voltage across a 100 Ohm resistor. Since the probe surface was directed perpendicular to the supersonic plasma flow, a Bohm formula was used to calculate a pulse-averaged ion density  n i    from the probe current: 
           n   i   =(√{square root over ( m   i )}/ A   p   ·Z·e ·√{square root over (2 kT   e )})   I   i     (6)
 
     where A p  is the probe surface area, 
     
       
         
           
             
               〈 
               
                 I 
                 i 
               
               〉 
             
             = 
             
               
                 1 
                 
                   τ 
                   i 
                 
               
               ⁢ 
               
                 
                   
                     ∫ 
                     0 
                   
                   
                     τ 
                     i 
                   
                 
                 
                   
                     
                       I 
                       i 
                     
                     ( 
                     t 
                     ) 
                   
                   ⁢ 
                   dt 
                 
               
             
           
         
       
     
     is a pulse-averaged ion current calculated from the ion current waveform measured by the probe tip. 
     The results of the experiments and simulation are given in  FIG.  5   a    and  FIG.  5   b   .  FIG.  5   a    is a graph showing the pulse-averaged ion density vs. axial coordinate, at U MPD =63 V, for “with magnet” and “no-magnet” configurations. Axial coordinates for the face of the thruster first stage, and cone boundaries are given by the green solid lines in  FIG.  5   a   .  FIG.  5   b    is a graph showing the normalized (to their maxima at z=4 mm) curves of pulse-averaged ion density vs. z, for “with magnet” and “no magnet” configurations, and simulation (blue line). 
     One can see that absolute values of ion density for “with magnet” configuration in times higher than for the “no magnet”. It is a rapid drop of ion density in the few millimeters from the cone opening for “with magnet” configuration, which can be probably due to the localization of ion accelerating region in this area (the region with the high density of magnetic field and with the highest current density flowing from the first stage towards the accelerating cone). However, for the “no magnet” configuration, there is no drop of ion density; instead of dropping, ion density slightly grows to some maximum at about z=4 mm, and then goes down ( FIG.  5   a   ). After a local maximal point at z=4 mm inside the cone, ion density curves decay for the both configurations ( FIG.  5   b   ). This decay is due to a free expansion of the plasma, and may happen at the constant velocity of ions in this region. 
     The physics of the thrust gain and the threshold behavior of the μCAT-MPD thruster system  10  is illustrated using particle-in-cell (PIC) simulations shown in  FIGS.  6   a  and  6   b   , showing the normalized axial component of the Lorentz force for U MPD =0 (a) and U MPD =63 V. The white lines in  FIGS.  6   a  and  6   b    depict the magnetic field and the purple lines denote the electric field. These simulations have been performed using the open-source, two-dimensional electrostatic particle-in-cell code Starfish. The computational domain consisted of a Cartesian mesh with varying resolution and linear splines denoting the thruster. The magnetic field was modeled in FEMM and subsequently imported into the simulation. Electrons and copper ions are introduced at random position within the “beam” by picking random positions within a cylindrical region extending from the cathode to the nozzle exit. Both ions and electrons were sampled from the Maxwellian distribution with T=5000 K and drift velocity v z =50 km/s. The fully kinetic electrostatic particle-in-cell (ES-PIC) method was then used to advance particle velocities and positions. The simulation was run for 5000 5×10 −12  s time steps which was a sufficient time to establish a steady state within the electron population. Particle velocities were interpolated to the grid to compute mesh-averaged macroscopic stream velocities. Subsequently, electron current density was computed from j e =−en e   , and the Lorentz force was computed by taking a cross-product with the magnetic field. The two simulations in  FIGS.  6   a  and  6   b    compare the impact of the accelerator electrode voltage on this component. With U MPD =0, no noticeable contribution to thrust from the Lorentz force is observed. However, with U MPD =63 V, there is a clear axial contribution. 
     From the simulation results given for U MPD =63 V ( FIG.  6   b   ), one can see that the region of the maximal values J×B force (at the distances between 1 and 3 mm from the cathode surface) agrees well with the experimentally-observed region of the acceleration of the ions ( FIG.  5   a   , With magnet case). This further proves that it is the J×B force that causes the increase in thrust. 
     The discovered onset of the magnetized vacuum arc in two-staged μCAT-MPD thruster system  10  allows drastically increasing its thrust, TPR and efficiency, as illustrated in  FIGS.  7   a  and  7   b   .  FIGS.  7   a  and  7   b    are graphs showing the thrust, estimated from the electrical measurements of the thruster in With magnet and No magnet configurations (a), and indirectly-measured thrust (b) using the thrust stand in configuration With magnet”. The first numbers in the brackets mean thrust-to-power ratio (in μN/W) and second ones with percent mean efficiency for the respective data points. 
     From the  FIGS.  7   a  and  7   b   , one can see that with the magnetic field, at low U MPD , voltages (0-30 V), the thrust and TPR values (2-10 μN and 0.5-2 μN/W) remain low and comparable with the respective parameters of single-stage μCATs achieved before without any acceleration stages. However, after U MPD , voltage increase from ˜30 V to its maximal value of 63 V, both thrust and TPR rapidly grow and reach 210 μN and 15 μN/W, respectively, together with the high efficiency of ˜50%. In the thruster without the magnet ( FIG.  7   a    “No magnet”), thrust, TPR, and efficiency grow insignificantly with U MPD . 
     Referring to  FIGS.  1 B and  8   , application of J×B via biasing segmented electrodes leads to significant increase in ion velocity. The four rings  18   a - 18   d  of cone  14  are acting as accelerating anodes. The voltage can be applied to each ring  18   a ,  18   b ,  18   c , and  18   d  individually. The voltage at each ring  18   a - 18   d  can be the same or different than the voltages received at the other rings  18   a - 18   d . For the rings one and three  18   a  and  18   c , initial velocities of ions range from 26 to 30 kmps. As shown in the example of  FIG.  1   a   , the rings can be a conductive material such as a metal strip, wire or conductor. The rings  18   a - 18   d  can extend circumferentially about the entire inner circumference of the cone  14  inside the discharge chamber  24 . For instance, the rings  18   a - 18   d  can be connected to the inner surface of the cone and project outward from the inner surface of the cone. Or the rings  18   a - 18   d  can be integrally with the cone  14  and recessed at the inner surface to be flush with the inner surface of the cone  14 . The cone is outwardly tapered with respect to the distal end  16  of the plasma source  12 ; accordingly, the rings  18   a - d  get incrementally larger the further from the plasma source  12 , with the closest ring (here, the first ring  18   a ) having the smallest diameter and the furthest ring (here, the fourth ring  18   d ) having the largest diameter. The rings  18   a - d  are spaced apart from one another at equal distances along the cone  14  with respect to the plasma source  12 , though the distances need not be equal. Each ring  18   a - 18   d  forms a complete circle and the rings are arranged substantially parallel to one another, though in one embodiment the rings  18   a - 18   d  need not be a complete circle but can instead partially extend about the inner surface of the cone  14 . 
     Upon increasing the voltage applied to rings  18   a  and  18   c , the ion velocities for ring three  18   c  reached a maximum 70 kmps, but the ion velocities for both the rings  18   a  and  18   c  fell down to the same initial ion velocities of 27 Kmps at 320V and reached the saturation point, i.e. ion velocity does not decrease with further increase of applied voltage. A similar situation is observed in case of ring four  18   d . Though the initial ion velocity is 44 kmps for ring  18   d  and reached a velocity of 73 kmps at 40V, the ring  18   d  nonetheless got saturated to 62 kmps at 200V. But in case of ring two  18   b , though the initial ion velocities for ring two  18   b  coincided with ring one  18   a  and ring three  18   c , the ion velocities of ring two  18   b  did not reach the saturation point, unlike the other rings. And among all the rings  18   a - 18   d , the maximum average velocity of 82 kmps is attained by ring two  18   b . From these results, considering the rings  18   a - 18   d  attribution towards ion velocities and based upon the power limitations, one can choose to selectively supply the power to the respective rings  18   a - 18   d  to acquire the desired results. Thrust and TPR growth at high U MPD  voltages does not demonstrate any trends to saturation at this level of U MPD  voltage. As such, there is potential of further increase at higher voltage. 
     A processing device (such as a computer, processor or controller) can be provided with the system  10  that controls one or more of the operations of the system, including but not limited to: (1) the arcing pulse repetition rate, (2) pulsing power unit charge voltage and, therefore, energy that will be released within one pulse, (3) current amplitudes in magnets or magnetic coils (for focusing, accelerating magnetic fields etc., (4) and voltage values on accelerating electrodes. By varying the mentioned parameters electrically, it is possible to achieve dynamic control of the system  10 . 
     Therefore, the system  10  of the present invention provides a way to improve thrust together with the thrust-to-power ratio and efficiency of low-power MPD thrusters—due to the onset of the magnetized arc after the certain threshold voltage is applied on the second activation stage. 
     It will be apparent to those skilled in the art having the benefit of the teachings presented in the foregoing descriptions and the associated drawings that modifications, combinations, sub-combinations, and variations can be made without departing from the spirit or scope of this disclosure. Likewise, the various examples described may be used individually or in combination with other examples. Those skilled in the art will appreciate various combinations of examples not specifically described or illustrated herein that are still within the scope of this disclosure. In this respect, it is to be understood that the disclosure is not limited to the specific examples set forth and the examples of the disclosure are intended to be illustrative, not limiting. 
     As used in this specification and the appended claims, the singular forms “a”, “an” and “the” include plural referents, unless the context clearly dictates otherwise. Similarly, the adjective “another,” when used to introduce an element, is intended to mean one or more elements. The terms “comprising,” “including,” “having” and similar terms are intended to be inclusive such that there may be additional elements other than the listed elements. 
     Additionally, where a method described above or a method claim below does not explicitly require an order to be followed by its steps or an order is otherwise not required based on the description or claim language, it is not intended that any particular order be inferred. Likewise, where a method claim below does not explicitly recite a step mentioned in the description above, it should not be assumed that the step is required by the claim. 
     It is noted that the description and claims may use geometric or relational terms, such as right, left, above, below, upper, lower, top, bottom, linear, arcuate, elongated, parallel, near, perpendicular, circle, ring, etc. These terms are not intended to limit the disclosure and, in general, are used for convenience to facilitate the description based on the examples shown in the figures. In addition, the geometric or relational terms may not be exact. For instance, walls may not be exactly perpendicular or parallel to one another because of, for example, roughness of surfaces, tolerances allowed in manufacturing, etc., but may still be considered to be perpendicular or parallel.