Copyright 2011 Ilia Slobodov

Transcription

1 Copyright 2011 Ilia Slobodov

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3 Performance Characterization of the High Power Helicon Plasma Thruster with Varying Magnetic Nozzle Configurations Ilia Slobodov A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics University of Washington 2011 Program Authorized to Offer Degree: Aeronautics & Astronautics

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5 University of Washington Graduate School This is to certify that I have examined this copy of a master s thesis by Ilia Slobodov and I have found it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Committee Members: Robert Winglee Thomas Jarboe Date:

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7 In presenting this thesis in partial fulfillment of the requirements for a master s degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this thesis is allowable only for scholarly purposes, consistent with fair use as prescribed in the U.S. Copyright Law. Any other reproduction for any purposes or by any means shall not be allowed without my written permission. Signature Date

8 University of Washington Abstract Performance Characterization of the High Power Helicon Plasma Thruster with Varying Magnetic Nozzle Configurations Ilia Slobodov Chair of the Supervisory Committee: Professor Robert Winglee Earth and Space Sciences The High Power Helicon (HPH) experiment allows for the study of helicon physics in a unique parameter regime, operating at a lower frequency, higher power, and lower background pressure than most other helicon sources. Extensive prior work has been done on the HPH system [1], and it has potential in applications as diverse as a space thruster, a high purity plasma source for fusion experiments, and a system for orbital debris mitigation. Boosting the performance of the HPH system, in terms of the density, velocity, and overall flux of the ions downstream of the helicon source, is of key interest for many of these applications. Magnetic nozzles have been shown to improve the collimation of the plasma beam produced by HPH and produce greater ion velocities downstream. In the present work, several different magnetic nozzle configurations were studied and the performance between them was compared. This comparison was done primarily in terms of retarded field energy analyzer (RFEA) data, which characterizes the ion velocity distribution function (IVDF) of the plasma beam. Flux conserving magnetic nozzle configurations were found to provide optimal performance. Additionally, direct thrust measurements were perfomed for one of the configurations, and the thrust was compared to that predicted by the RFEA measurements. Other techniques to try to boost the performance of the HPH system were also investigated, including moving the antenna relative to the base magnetic field coils and installing a new radial gas feed system.

9 Table of Contents List of Figures... 2 List of Tables Introduction Comparison of HPH to Other Helicon Experiments Magnetic Nozzles Summary of Research Undertaken in this Thesis Theory Experiment Description Vacuum Chamber and Pumping Helicon Antenna Base Magnets Magnetic Nozzles Power Supply Gas Feed Diagnostics RFEAs Langmuir Probes Thrust Stand Magnetic nozzle configurations and results First Nozzle Configuration Flux Conserving Configuration Flux Conserving Configuration with Nozzles Close to Source Direct Comparisons of the Two Flux Conserving Configurations Thrust Data Radial Gas Feed Conclusions Recommended Further Work References VITA

10 LIST OF FIGURES Figure 1: Dispersion Diagram for Parallel Electromagnetic Waves... 9 Figure 2: m = +1 and -1 Helicon Wave Modes Figure 3: Inside of Vacuum Chamber Figure 4: Vacuum System Schematic from Labview Figure 5: Helicon Antenna Figure 6: Helicon Antenna Configurations - (a) N antenna (b) LH antenna (c) RH antenna. 16 Figure 7: Helicon Source Inside Magnets Figure 8: Base Magnetic Field Coils Figure 9: Old IGBT Power Supply Figure 10: Antenna Current Trace Figure 11: Gas Feed Schematic Figure 12: RFEA 3D View Figure 13: Photo of RFEA Figure 14: Electrical Schematic of RFEA Figure 15: Typical RFEA Current Trace Figure 16: Typical plot of Number of Ions vs Voltage Figure 17: Typical IVDF Figure 18: Langmuir Probes Figure 19: Langmuir Schematic Figure 20: Thrust Stand Figure 21: Magnetic Damping System Figure 22: Chamber Schematic Figure 23: Screenshot of Magnetic Field Calculator Figure 24: Magnetic Field Lines - Mirror Configuration: (top) 294 A (middle) 147 A (bottom) 74 A Figure 25: Density, mirror Figure 26: Velocity, mirror Figure 27: Flux, mirror Figure 28: Energy density, mirror Figure 29: Density Comparison, Mirror

11 Figure 30: Velocity Comparison, Mirror Figure 31: Flux Comparison, Mirror Figure 32: Energy Density Comparison, Mirror Figure 33: Magnetic Field Configurations - Flux Conserving Configuration Figure 34: Density, Near RFEA Figure 35: Velocity, Near RFEA Figure 36: Flux, Near RFEA Figure 37: Energy Density, Near RFEA Figure 38: Density, Far RFEA Figure 39: Velocity, Far RFEA Figure 40: Flux, Far RFEA Figure 41: Energy Density, Far RFEA Figure 42: Magnetic Field Lines for Close Nozzle Positions Figure 43: Antenna Current vs Time - (blue): Old Configuration, (red): New Configuration 51 Figure 44: Density, close nozzle positions Figure 45: Velocity, close nozzle positions Figure 46: flux, close nozzle positions Figure 47: energy density, close nozzle positions Figure 48: Energy Density Comparison of Flux Conserving Configurations Figure 49: Thrust vs Magnetic Field Strength Figure 50: Thrust vs Antenna Charge Voltage Figure 51: Thrust vs Shot Length Figure 52: Thrust Density with Argon Gas Figure 53: Thrust with Different Gases Figure 54: Radial Density Profile Figure 55: Radial Gas Feed Figure 56: No Radial Puff vs 4.5ms Radial Puff Figure 57: Ions Expelled vs Radial Gas Puff Duration Figure 58: 2000 us shot, radial puff vs no radial puff

12 LIST OF TABLES Table 1: Magnetic Nozzle Attributes

13 ACKNOWLEDGEMENTS I would sincerely like to thank the following people, whose support made this work possible: Professor Robert Winglee, who provided me with this amazing opportunity to conduct research on a very interesting subject and offered great guidance, encouragement, and enthusiasm throughout these past two years. Dr. James Prager and Dr. Timothy Ziemba, who both provided vast amounts of technical knowledge and input, without which I would have been lost many times in carrying out this work. Thank you also to Race Roberson, who was always there in the laboratory to provide help and insight whenever I needed it. The experiment could not operate without the help of the many graduate and undergraduate students who have worked in the laboratory. Thank you to Ian Johnson, Reece Beigh, and Kyle McEleney. Thank you to Professor Thomas Jarboe for serving on my reading committee. I would also like to thank all my professors who helped me to understand plasma physics, space applications, and the mathematics that stands behind it all: Uri Shumlak, Robert Holzworth, Mehran Mesbahi, Arthur Mattick, Carl Knowlen, Nathan Kutz, Eric Shea-Brown, and Ka-Kit Tung. My family, who have been so loving and supportive all throughout my life and have always encouraged me to pursue my dreams. Thanks Mom, Dad, Aly! Lastly, I d like to thank my friends and hiking partners: Matt Drooyan, Lauren Linnell, Allison Caldwell, Laszlo Techy, and many others! Our mountain adventures over the weekends have helped me keep my sanity. 5

14 1. INTRODUCTION The High Power Helicon (HPH) experiment at the Advanced Propulsion Laboratory (APL) at the University of Washington (UW) uses a helicon plasma source to produce a dense plasma which is then accelerated downstream. It has been investigated for use for various applications including space thrusters, orbital debris mitigation, and plasma injection into fusion devices. Helicon plasma sources can efficiently produce high density plasmas [1]. Helicon waves are a type of Whistler wave that is radially confined by the geometry of the system in which it propagates. Whistler waves were first observed in nature during the First World War [2] and first observed in the laboratory in 1960 at the Zero Energy Toroidal Assembly [3]. Interest in helicon waves grew and experiments were designed specifically to study them in the laboratory [4]. Understanding of the physics of helicon waves has continued to grow since then [2], and along with this, a range of applications have been developed. Commercial applications include plasma etching [2][5], where helicons are ideal due to their ability to operate at low pressures, low magnetic field strengths, and with a variety of different gases. The main application of the HPH that has been explored at APL is its use as a space thruster. Like other electric thrusters, it has significant advantages over chemical rockets, including exhaust velocities of 30 km/s or more that are an order of magnitude faster than chemical rockets [6]. Higher exhaust velocities lead to much higher fuel efficiency on missions that have high delta-v requirements, leading to lower propellant masses and thus saving on launch costs. A variety of electric propulsion systems are already in use, such as electrostatic ion thrusters and hall thrusters. When compared with these devices, a helicon thruster has the advantage of not having charged grids or anode/cathode systems, thus eliminating degradation and lifetime issues [1]. Helicons have been researched for use both as a stand-alone thruster system such as the HPH or as plasma sources for other mechanisms that accelerate the plasma, such as the Variable Specific Impulse Magnetoplasma Rocket (VASIMR ). Using an ion cyclotron resonance heating (ICRH) system, VASIMR can achieve exhaust velocities of up to 150 km/s [7]. Helicons with annular geometry have also been considered as ion sources for more conventional hall thrusters [8][9]. 6

15 1.1 Comparison of HPH to Other Helicon Experiments Most other helicon experiments operate at a relatively low power, high frequency, and high background pressure. For example, Lehane and Thonemann conducted experiments with a 3 kw 15 MHz discharge in a chamber back filled with xenon to mtorr [4]. Boswell conducted experiments with a G field in a small chamber filled with argon to a pressure of 38 mtorr [2]. Other experiments also operate at these high pressures [12][13][14][15]. At the high pressures found in these experiments, the effects of the neutrals play a strong role in the physics. Additionally, plasma shots happen over time scales of milliseconds to seconds, which means plasma comes into equilibrium with the walls, further complicating the physics of the discharge. In contrast, the HPH experiment operates at pressures of Torr with shot lengths of only a few hundred microseconds and puts in tens of kilowatts of power into the plasma. It operates at a lower frequency of khz, which allows the use of lightweight and low cost solid state switching power supplies which have been developed for the HPH system. Rather than using a chamber back filled with the gas to be ionized, HPH uses a gas injection system that provides gas to the source region just before the helicon discharge, allowing the background pressure to be low. The HPH antenna produces high density plasma (up to m -3 in the source region) and expels it at velocities of tens of kilometers per second, depending on the gas that is used. The larger chamber size and low background pressure allows the physics of the helicon wave to be studied under spacelike conditions and with minimal wall interactions. 1.2 Magnetic Nozzles Magnetic nozzles serve much the same purpose as regular material nozzles, which is to convert the random thermal energy of a plume of exhaust into directed kinetic energy. Magnetic nozzles create a diverging magnetic field, and charged particles that travel down this field are accelerated by the decreasing magnetic pressure gradient. 1.3 Summary of Research Undertaken in this Thesis Prior research has been conducted on the use of the HPH experiment with magnetic nozzles positioned downstream of the helicon source. As has been mentioned, use of the nozzles enhanced the performance of the system by accelerating the ions to a higher velocity and improving the collimation of the beam. However, it was suspected that, due to the field strengths, 7

16 the previous research may actually have been creating a magnetic mirror configuration, preventing a substantial fraction of the ion beam from traveling downstream and being detected. Using magnetic field models, new positions and currents were determined for the nozzles to try to maximize their effect in accelerating and collimating the beam without pinching the magnetic field lines. The new magnetic field configurations were flux conserving, that is, the number of field lines passing through the source region is equal to the number of field lines passing through the first nozzle and then the second nozzle. Additionally, the magnetic field lines never converge towards each other if they are followed downstream from the source, avoiding any mirror effects. Experiments with the flux conserving magnetic configurations found higher plasma beam velocities, leading to a higher flux of ions as well as more thrust. Additionally, the effects of moving the antenna forward relative to the base magnetic field were observed. Lastly, a new radial gas feed system was installed inside the helicon source region to try to replenish neutral argon gas as it was ionized, allowing longer operation of the helicon shots. 8

17 2. THEORY The helicon wave is an electromagnetic wave that propagates along the magnetic field direction in a magnetized plasma and is confined to a radial geometry. Specifically, it is a whistler wave, which is one of several types of electromagnetic waves that travel parallel to the magnetic field in a magnetized plasma. These waves are shown on the dispersion diagram [10]: Figure 1: Dispersion Diagram for Parallel Electromagnetic Waves As can be seen in the diagram, the whistler portion of the R-wave occurs at low frequencies, where ω << Ω e, the electron cyclotron frequency. However, these waves are still high frequency compared to the ion cyclotron frequency, Ω i. Due to operating in this frequency regime, where the wave frequency is not matched with either the ion or electron cyclotron frequencies, it can be assumed that the ions are too slow to respond to the wave oscillations while the electrons gyrate so quickly that they can be neglected. The electron movement is then restricted to the guiding center motion and the plasma current is carried by the E B drift [1]. Let us begin by deriving the dispersion relation of the helicon wave [1][11]. We begin with Maxwell s equations, not including Gauss s Law since we assume quasineutrality: 9

18 (2.1) (2.2) (2.3) We linearize the equations with the assumption that quantities consist of an equilibrium component (denoted by a 0 subscript) and an oscillating perturbation: ( ) ( ) (2.4) Additionally, we assume that the applied magnetic field B 0 points purely along the z direction. Substituting our expressions for the perturbations into Maxwell s equations, we obtain: (2.5) (2.6) (2.7) where we have ignored the displacement current. In addition to Maxwell s equations, we need the electron fluid equation of motion. Linearizing immediately: ( ) (2.8) The last term on the right represents all the collisional processes. It should be noted that the magnetic viscosity and pressure terms have been neglected. As mentioned above, helicon waves propagate at high enough frequencies for us to be able to ignore the ion motion. Thus, the current in the plasma is given by: (2.9) Solving for E 1 gives: ( ) (2.10) where ω c is the electron cyclotron frequency. Since the helicon wave frequency is much lower than the electron cyclotron frequency, the second term in equation 2.10 can be neglected. Taking the curl of equation 2.10, we obtain: ( ) (2.11) We then apply equation 2.7: ( ) (2.12) 10

19 Here, k z is the z component of the wavenumber k. Due to the radial boundary conditions, the wave number can only take on discrete values. It can be expressed in terms of the electron plasma frequency and electron cyclotron frequency as: (2.13) Applying Ampere s Law, we can see that the current and the perturbation to the magnetic field are parallel: (2.14) Furthermore, the curl of equation 2.12 gives: (2.15) In cylindrical coordinates, we can decompose the vector B 1 into its three scalar components: B r, B θ, and B z. Considering the z component, we have: ( ) (2.16) This is the Bessel equation and has Bessel function solutions. Since we are solving it on the inside of a helicon tube (a cylinder) with real values at the center (r=0), the coefficients for the Bessel functions of the second kind will be zero. So, the resulting solutions are of the form: ( ) (2.17) This relates to the other two components of the perturbed magnetic field as follows: (2.18) We can substitute in the solutiuon for B z given in 2.17 to get: (2.19) ( ( ) ( )) (2.20) ( ( ) ( )) (2.21) We can get rid of the derivatives using the recursion relations for Bessel functions to obtain: 11

20 [( ) ( ) ( ) ( )] (2.22) [( ) ( ) ( ) ( )] (2.23) Since this is being derived for an antenna wrapped inside a quartz tube, we imply an insulating boundary condition, that is, j r = 0 at r = a. This gives: ( ) ( ) (2.24) Focusing on the m = +1 mode which the HPH antenna is designed to excite and approximating the solution for thin long tubes where k k and kza << 1, we get: ( ) [ ( ) ( )] (2.25) Expanding using Taylor series and inserting into equation 2.13, we obtain the dispersion relation for the m = ±1 mode of the helicon wave [1]: (2.26) So, we have derived the dispersion relation. We can see that the velocity of the beam along the axial direction, ω/k z, is proportional to B 0 /n 0. The helicon waves look as follows [1]: Figure 2: m = +1 and -1 Helicon Wave Modes These modes rotate in time while maintain their shape. The electrons undergo many gyrations around the field as it rotates, while the ions are too slow to respond. This creates an azimuthal electron current in the plasma, which interacts with the radial component of the guiding magnetic field to produce a jxb force downstream, accelerating the plasma. 12

21 3. EXPERIMENT DESCRIPTION This section will describe the setup of the HPH experiment, including the vacuum chamber, the helicon antenna, the base magnetic field magnetsthe magnetic nozzles, the power supply, and the gas injection system. The diagnostics that are used on the system will be discussed in Chapter 4. Visible in the figure below are the helicon source and base magnetic field coils, the first and second magnetic nozzles, and several diagnostics inserted from the right side the chamber. 3.1 Vacuum Chamber and Pumping Figure 3: Inside of Vacuum Chamber The HPH experiment sits inside a cylindrical stainless steel vacuum chamber 2.8 m in length and 0.8 m in radius. The chamber has a number of ports and windows for various sizes, allowing for pumping, insertion of probes and electrical connections, as well as viewing and photography. The base pressure of the chamber with the experimental equipment inside is usually in the range 13

22 of Torr. This pressure is lower than many other helicon experiments in the literature and provides a more space-like environment for testing the HPH as a thruster. This pressure is achieved using a Varian Turbo-V 551 Navigator turbomolecular pump backed by a Varian DS- 602 rotary vain roughing pump. Pressure is monitored by a Bayard-Alpert style ionization gauge in the low pressure regime and by Pirani gauges during the pumpdown process. A schematic of the vacuum system and its control interface from Labview is shown below: Figure 4: Vacuum System Schematic from Labview When the chamber is at atmospheric pressure and must be pumped down, the first step is to turn on the roughing pump and open the roughing ISO valve. Then, the manual valve on the roughing pump is slowly opened, taking care not to put excessive load on the roughing pump or the filter on its high pressure exhaust side. Generally, this means monitoring the dial on the roughing pump and ensuring it does not exceed 6 psig. The roughing pump on its own can only bring the chamber down to about 100 mtorr, lower pressures can only be achieved using the 14

23 turbomolecular pump (turbo pump). The turbomolecular pump cannot be activated at atmospheric pressure; it is only designed to operate at lower pressures. Thus, the usual procedure is to wait until pressure is in the mtorr range using the roughing pump, and then to turn on the turbo pump. To do this, the valves must first be aligned for operation of the turbo pump using the Labview VI. This opens the tubo ISO valve and the large gate valve on the chamber. Afterwards, the Turbo Pump On button must be pressed. The turbo pump takes several minutes to accelerate to full speed (42,000 rpm). During this acceleration phase, the turbo pump operates at a relatively high power (several hundred watts) and its temperature increases by several degrees. This part of the pumpdown process should be carefully monitored, since if there are any leaks on the chamber that cause the pressure not to drop as expected, the turbo pump could overheat or be otherwise damaged. If the pressure pumps down as expected, the turbo pump will quickly reduce its power draw to just W and its temperature will remain approximately the ambient temperature. If the chamber is under vacuum and must be brought up to air, the first step is to close the manual valve on the roughing pump. Next, the turbo pump must be turned off and the valves must be aligned for up to air in the Labview VI. An up to air valve on the chamber can then be opened slightly to begin letting air into the chamber. However, care must be taken not to let in too much pressure too quickly, as the turbopump must be allowed to spin down to a stop before the chamber pressure gets too high (in the several Torr range). Once turned off, the turbopump controller does not display the speed of the turbopump, so the only way to determine if it is still spinning is by listening to the audible sound of the turbopump. After it has come to a stop, the up to air valve can be opened all the way, allowing the chamber to come up to atmospheric pressure. 3.2 Helicon Antenna In the HPH experiment, the helicon antenna is made of braided copper wire 5.2 mm wide wrapped around a quartz glass tube, 3.5cm in radius and 15 cm long. It is affixed to the tube using Kapton tape, as shown in the figure below. The back of the tube is closed with a quartz plate which prevents neutrals or plasma from flowing out the back of the antenna, while the front of the tube is open, allowing material to travel downstream. 15

24 Figure 5: Helicon Antenna The HPH experiment uses a singly wrapped half-wave helical antenna, the same one that has been in use in the experiment for some time [17]. It is a Nagoya Type III antenna of the same style that has been widely used by experimentalists in the field [2]. Based on studies [18] of the effects of handedness of the antenna with respect to the base magnetic field, a left-handed (LH) antenna geometry was chosen. This antenna was seen to excite the m = +1 mode most efficiently, compared to the untwisted (N) antenna or the right-handed (RH) antenna, which are shown in the figure below. In the figure, the base magnetic field would be pointing to the right. Figure 6: Helicon Antenna Configurations - (a) N antenna (b) LH antenna (c) RH antenna 16

25 Figure 7: Helicon Source Inside Magnets The quartz tube on which the helicon antenna is wound is held inside the coils that generate the base magnetic field with nylon screws, visible in the above figure. The base magnetic field coils are described in section 3.3. The gas feed that injects gas into the HPH is visible in the center, and is described in section 3.6. The plasma density inside the source region is measured by the internal Langmuir probe, the two prongs of which are shown coming in vertically through the top of the quartz tube. 3.3 Base Magnets The base magnetic field needed to guide the helicon wave propagation is provided by a set of coils, shown below. There are a total of six coils, each consisting of 43 turns of copper wire. Generally, they are all connected in series, although the system also allows for flexibility where each coil is independently powered, making it possible to shape the magnetic field in the source region. 17

26 3.4 Magnetic Nozzles Figure 8: Base Magnetic Field Coils The HPH system makes use of two magnetic nozzles which are positioned downstream of the helicon source. The attributes of the two nozzles are summarized in the table below: Table 1: Magnetic Nozzle Attributes First Nozzle Second Nozzle Radius 13cm 23cm Width 13cm 15cm Number of Turns of Wire Current Variable, depending on nozzle configuration Variable, depending on nozzle configuration Power Supply High Voltage Xantrex Power Supply High Current IGBT Pulse Power Supply 18

27 3.5 Power Supply The HPH experiment relies heavily on Insulated Gate Bipolar Transistor (IGBT) switching pulse power supplies. These are used to drive the helicon antenna as well as the second magnetic nozzle, which are both fired for short pulses. The base magnetic field and the first magnetic nozzle, in contrast, are powered by standard laboratory DC power supplies. This section will describe the IGBT power supplies used with the HPH experiment. The HPH system uses power supplies developed in house at the APL. These consist of a row of IGBTs connected in parallel, controlled by a single IGBT driver. The power supply board waits for a fiberoptic signal, and when it detects one, it shuts all the IGBTs, dumping the energy from the capacitors into the system. In the case of the second magnetic nozzle, the current would flow in one continuous pulse through the nozzle wiring. In the case of the helicon antenna, the IGBTs were made to open and shut at a specific frequency (588 khz), in tune with the natural frequency of the helicon antenna, leads, and tuning capacitor ring, which act as an LRC circuit. A photo of the IGBT power supply for the helicon antenna is presented: Figure 9: Old IGBT Power Supply The row of IGBTs is clearly visible on the board in the bottom left of the picture, the blue energy storage capacitors are in the top left, and the tuning capacitor ring is in the top right. The 19

28 tuning capacitors are used to match the natural frequency of the LRC circuit to the desired operation frequency of the HPH system. The power supply system is housed inside a metal box to reduce the effects of electrical noise. The power supply that was used for the majority of the experimental work had 12 IGBTs rated to 205 A of pulse current and 1200 V. To operate at a resonant frequency of 588 khz, the power supply uses approximately 50 nf of tuning capacitors. Since the supply is operating at a resonant frequency, the magnitude of the current that flows through the system rings up over time, allowing it to eventually reach a current of about 1500 A. The following figure presents a typical trace of the current as a function of time during a shot of the HPH experiment: Antenna Current (A) Time ( s) Figure 10: Antenna Current Trace As can be seen in the graph, when the antenna is first turned on, it begins to ramp up as the current resonates through the circuit. The ramp up slows down as the current exceeds about 1000 A and would asymptote to a steady value of just over 1500 A if the antenna is allowed to run by itself. In this case, however, gas is injected into the system using the gas feed (to be discussed in the next section) and the igniter triggers ionization of the gas. As the energy of the helicon antenna is dumped into the plasma, the current on the antenna quickly diminishes, down to a minimum of about 500 A. As the plasma is expelled out of the source region, the current slowly 20

29 ramps back up. This current profile in the antenna is characteristic of all successful shots of the HPH experiment. 3.6 Gas Feed The gas feed injects gas into the helicon source region. A schematic of the gas feed is presented below: Figure 11: Gas Feed Schematic Gas, typically argon, enters from a tank of pressurized gas via a regulator which allows a specific pressure to be used. Prior work has generally been conducted using 20 psig gas [1] and this work continues using this gas pressure. Besides argon, experiments have also conducted with hydrogen, helium, helium/nitrogen mixture, and krypton. The gas feed, and, indeed, the entire system has the advantage of being flexible and capable of using a wide variety of gases. The amount of gas that enters the system is controlled using a gas puff valve, shown in the figure above. This puff valve can be opened for time periods of as short as approximately 1 ms when switched using a high voltage (200 V) spike. It can be operated for time periods of many tens of milliseconds in this fast switching regime. Opening the puff valve for longer periods than about ms using the high voltage spike can cause damage to the puff valve. After passing through the valve, the gas flows a steel tube which is inserted through a feedthrough on a Quick Flange into the vacuum chamber. Inside the vacuum chamber, the tube narrows to a lower diameter, causing the gas to flow more quickly. This has been shown to improve plasma performance in prior work. After flowing downstream to the end of the gas feed, the gas passes through igniter grids, which create an electrical arc to produce a seed plasma. The end of the gas feed, where the igniter grids are located, is typically positioned near the center of the helicon antenna. When the helicon is active, the oscillating magnetic field of the antenna quickly ionizes the majority of the neutral gas into plasma starting with the seed plasma provided by the igniters. 21

30 4. DIAGNOSTICS The HPH system uses several different types of diagnostics to obtain information on the plasma. These include Langmuir probes to measure the density, retarding field energy analyzers (RFEAs) to measure the ion velocity distribution function, B-dot probes to measure the transient magnetic fields. Additionally, a high speed camera is used to capture images of the HPH in operation, allowing visualization of the regions of collisionality in the beam. The chamber is also equipped with an SRS RGA 100 residual gas analyzer to measure the partial pressures of the gases that are present (up to an atomic mass of 100). Data is also recorded on the voltage and current in the helicon antenna during the experiment operation. Lastly, a thrust stand was used to measure the thrust delivered by the plasma beam. In the present research, we focus on the results obtained from RFEAs and Langmuir probes as well as the thrust stand, and so the principles behind these will be discussed here. 4.1 RFEAs RFEAs are used to characterize a plasma by measuring its ion velocity distribution function (IVDF). A three dimensional schematic of the RFEA used at the HPH experiment is shown below: Figure 12: RFEA 3D View 22

31 It is housed in a rectangular steel case with a circular orifice on one side, through which ions can enter. The steel case is mounted on a tube which can be inserted into the vacuum chamber through one of the feedthroughs available. Wiring that connects the RFEA to the electronics which sits outside the vacuum chamber is passed through this tube. A photo of one of the RFEAs at APL is presented, with the orifice, case, and steel tube visible: Figure 13: Photo of RFEA The RFEA consists of 55% transparent nickel grids which serve as the repellor, discriminator, and suppressor. At the back of the RFEA, a nickel plate is used as the collector. Plasma enters the RFEA through the orifice on the front. All of the grids are separated by 0.4 mm, except that the distance between the repellor and discriminator is 0.9 mm. The repellor grid screens out the electrons in the plasma so that they do not enter the RFEA. The discriminator, which can be varied in voltage, only lets those ions which have energies exceeding the set voltage pass through it. The suppressor screens out any secondary electrons that may be emitted due to interactions of the ion beam with the other grids [16]. The electrical schematic of the RFEA, below, shows the grids: 23

32 Figure 14: Electrical Schematic of RFEA The remaining ions hit the collector plate and generate a current proportional to the number of ions hitting the plate. A typical oscilloscope trace of the current as a function of time looks as follows. Typical characteristics include an initial peak followed by a dip and then a flatter section RFEA Current (ma) Time ( s) Figure 15: Typical RFEA Current Trace 24

33 The RFEA allows the number of ions at or above a set energy to be measured. By sweeping this cutoff energy in small increments across a range, we can obtain the ion velocity distribution function (IVDF). The current, I, caused by the ions hitting the RFEA s collector plate is given as: (4.1) where A is the collecting area of the probe, e is the ion charge (assumed to be equal to the electron charge since the plasma is mostly singly ionized), n is the ion density at the collector, and v is the ion velocity. The <nv> term represents the ion flux, which is also given by the second moment of the velocity space distribution function, f(v). This directly relates the current measured by the RFEA probe to the IVDF as follows: ( ) (4.2) where v i, the ion velocity, is simply obtained from its kinetic energy: (4.3) where V D is the voltage on the discriminator grid. A typical plot of the collector current as a function of the discriminator voltage at a fixed point in time throughout the shot is shown below: 3.5 x Figure 16: Typical plot of Number of Ions vs Voltage 25

34 IVDF: We can take the derivative of the collector current with respect to the voltage to obtain the ( ) ( ) (4.4) The IVDF for the above current-voltage curve is shown in the figure below. Since each shot of the HPH experiment is only a few hundred microseconds in length and the RFEA discriminator voltage cannot be swept during this time period, the IVDF is instead measured by taking multiple repeated shots and varying the discriminator voltage for each shot. This technique relies on the repeatability of the HPH experiment, which has been demonstrated in prior work [1]. Typical RFEA sweeps involve going from 0 to 80 V in 2 V increments. The voltage resolution is limited since, in the current state of the experiment, taking large numbers of shots is a relatively time consuming manual procedure. 16 x Figure 17: Typical IVDF The current on the collector plate is measured by passing it through a 1 V per 1 A Stangenes either 10 or 100 times (depending on the magnitude of the original signal). The voltage output 26

35 from the Stangenes is captured by an oscilliscope and logged by a Labview program, which also applies a low pass filter to the data. Additionally, the program applies a mathematical correction to compensate for the fact that it takes time for the magnetic field to permeate into the iron core of the Stangenes. The resulting data is then exported to MATLAB and a median filter is applied to each data point so as to smooth it out. The above plots of the current vs voltage and the IVDF are the final outputs of this filtering process. The magnitude of the RFEA data can be interpreted by taking into account the transparency of the grids, making assumptions about the formation of plasma sheath regions inside the probe, and trying to approximate the effective collecting area. However, it is usually more accurate to take a density measurement using a Langmuir probe at the same location and then scale the RFEA data to give an identical value of density at that location, which then also sets the magnitude of all the other moments of the IVDF that can be obtained from the RFEA. Langmuir probes are discussed in the following section. 4.2 Langmuir Probes A Langmuir probe is a type of diagnostic that is used to determine the density and temperature of the plasma. It can also be used to measure the electron plasma potential. Langmuir probes used throughout the course of this work have two tungsten probe tips with a constant voltage difference between them, provided by a battery and capacitor. The tungsten probe tips are held fixed with epoxy to ceramic tubes, which connect to a steel tube running through a quick disconnected to electronics outside of the vacuum chamber. Langmuir probes with three different sizes of probe tips were used, with the smaller probe used in the source region where the density is high and the bigger probes being used farther downstream where the density is low. These three styles of Langmuir probe are shown in the figure below. The collecting areas of the three probes, respectively, are: 2.7 mm 2, 16.5 mm 2, and 38.8 mm 2, with tip separation distances of 2.6 mm, 3.0 mm, and 2.2 mm. 27

36 Figure 18: Langmuir Probes The circuit used for the Langmuir probes is shown in the following figure. A battery is used to set the voltage between the Langmuir probe tips, and a capacitor is put in series with the battery to hold the voltage constant during the shot, since the battery itself is unable to provide the necessary current while the Langmuir probe is exposed to plasma. The probe is not connected directly to an oscilloscope, but is isolated using a 1 V / 1 A Stangenes transformer. This safeguards the oscilloscope, and also allows the signal wire to be looped multiple times through the transformer, boosting the current measured by the oscilloscope. Generally, the Langmuir circuits have been used with 10 windings through each Stangenes transformer. The signal is also passed through an RC filter to reduce noise. 28

37 Figure 19: Langmuir Schematic The Langmuir probes are operated in the ion saturation regime where possible. In that case, the current I in the Langmuir probe is related to the electron density n e in the plasma as follows: (4.5) where A is the probe area, e is the electron charge, and c s is the ion sound speed, given by: (4.6) where T e and T i are the electron and ion temperatures, respectively, and m i is the ion mass. However, due to the nature of the flowing plasma, the probes often could not be operated in the ion saturation regime without arcing between the probe tips. As a result, they were often operated at lower voltages, for which the above relationship between current and electron density is not valid. Resultingly, Langmuir probe density measurements in this work are best regarded as order of magnitude estimates only. 4.3 Thrust Stand To measure the thrust produced by the plasma beam directly, a high resolution thrust stand was designed and built. A photo of this system inside the chamber is shown below: 29

38 Figure 20: Thrust Stand The thrust stand consists of a circular pendulum supported on a rigid structure. The displacement of the pendulum from its equilibrium position is measured to a very high precision using an optical measurement system, seen pointed at a small mirror on the back of the pendulum in the figure above. The pendulum target sits in the path of the beam, centered on the chamber axis. It is supported by two thin vertical ceramic tubes, which are mounted to a razor blade at the top. This razor blade sits on top of a pair of perpendicularly mounted razor blades with small grooves machined into them, allowing it to swing freely with very minimal mechanical friction. A set of permanent magnets generate eddy currents in an aluminum plate mounted at the top of the pendulum, above the razor blades, provide passive damping. This reduces noise in the system and allows the pendulum to return to rest in a reasonable amount of 30

39 time between successive shots of the experiment. The magnetic damping system is shown in the figure below: Figure 21: Magnetic Damping System The plasma shot occurs over very short timescales, only a few hundred microseconds, thus the pendulum essentially sees an instantaneous impulse which causes it to start oscillating. The amplitude of its oscillation can then be related to the force exerted on it by the plasma beam, allowing a determination of the thrust produced by the HPH system. The pendulum follows the equation of motion of a damped harmonic oscillator: ( ) (4.7) where I is the moment of inertia about the fulcrum (the edge of the razor blade), which was estimated (using SolidWorks) to have a value of kg m 2, γ is the damping coefficient, and ω 0 is the natural frequency of the pendulum which is given by: 31

40 (4.8) where y is the vertical distance from the fulcrum to the center of mass of the pendulum, estimated to be m. The solution to the damped harmonic oscillator in the under damped case (where γ 2 << ω 2 ) is given by: ( ) ( ) (4.9) where the actual frequency ω is determined by the natural frequency and the damping coefficient: (4.10) The impulsive force produced by the plasma beam at t = 0 imparts an initial nonzero velocity on the pendulum. Thus, the pendulum imparts an initial angular momentum, which is given by: (4.11) where R is the distance from the fulcrum to the mirror (where the distance is measured using the optical system), F is the magnitude of the force produced by the plasma beam, and Δt is the time over which it acts (assumed to be equal to the shot length). But, we also know that the angular momentum is related to the change in angular velocity: (4.12) Setting equations 4.9 and 4.10 equal to each other, we have: (4.13) Multiply through by R and change variables from θ to x to get: (4.14) Returning to the solution for the damped harmonic oscillator, equation 4.7, we can now find the value of the constant A: ( ) ( ) ( ) ( ) (4.15) We have the initial condition that v(0) = v 0, given by equation Thus: (4.16) So the full solution can be written as: 32

41 ( ) ( ) ( ) (4.17) To measure the impulse delivered by the plasma beam, the distance vs. time measurement x(t) from the thrust stand is simply fit to the above solution form. This gives the product F 0 Δt, which can be divided by the length of the shot to determine the thrust. The thrust can be normalized to a thrust per unit area by dividing by the area of the pendulum target (which is a circle 10 cm in diameter). 33

42 5. MAGNETIC NOZZLE CONFIGURATIONS AND RESULTS The experimental setup consists of the helicon source with its base magnetic field magnets and two magnetic nozzles downstream, as shown in the schematic diagram of the chamber below. Figure 22: Chamber Schematic The first nozzle has a radius of 13 cm, a width of 11 cm, and has 486 turns of wire. The second nozzle has a radius of 25 cm and a width of 13 cm, and has 60 turns of wire. The positions of the nozzles and diagnostics in the chamber are measured from the front edge of the quartz tube that the helicon antenna is wound around. Three nozzle configurations were compared throughout the course of this work. These configurations and the results for each case are discussed in the following sections of this chapter. The magnetic fields generated by the nozzles are computed using a LABVIEW program that was developed in house. It works by calculating the magnetic field generated by a current loop as a function of position, and sums this over all of the current loops which are inputted into the model. A screenshot of this program: 34

43 Figure 23: Screenshot of Magnetic Field Calculator 5.1 First Nozzle Configuration First, the original nozzle configuration had the first nozzle at a distance of 25 cm downstream and the second nozzle at a distance of 72 cm downstream. The second nozzle was operated at the maximum voltage that could be supplied by its pulse power supply: 400V, which corresponds to a current of 294 A. The first nozzle operated at a current of 7 A. The shapes of the magnetic field lines were calculated for three cases: with the second nozzle on to the full 294 A, with the second nozzle set to half current (147 A), and with the second nozzle at one quarter of its full current (74 A). resulting graphs are presented in figure 24. As it turned out, this magnetic field configuration creates a magnetic mirror downstream of the helicon source, so it will periodically be referred to as the mirror configuration. 35

44 Figure 24: Magnetic Field Lines - Mirror Configuration: (top) 294 A (middle) 147 A (bottom) 74 A 36

45 In this magnetic field configuration, an RFEA sweep with data points at 2 V increments was taken. The helicon was fired with 200 μs shot lengths. The RFEA was located 67 cm downstream from the helicon source. As described in Chapter 4, the RFEA is used to obtain the IVDF as a function of time during the helicon shot. Given the IVDF, we can take its moments to obtain the density, velocity, flux, and energy density of the ion beam. These are presented in the following figures. 5 x Density (m -3 ) Figure 25: Density, mirror In figure 25, the density is scaled so as to match Langmuir probe data. We see that it peaks in the range of m -3. The peak of the density occurs about halfway through the shot, with a rapid falloff in density afterwards. The velocity in figure 26 shows an initial peak at 15 km/s and rapidly declines to just over 5 km/s. In figure 27, the density and velocity are multiplied to show the ion flux as a function of time. Here, we can see two distinct peaks, one at the start of the shot and another one later in time. Figure 28 shows the energy density, which is directly related to the thrust delivered by the plasma beam. Thrust measurements will be discussed in more detail in the following chapter Time ( s) 37

46 20 15 Velocity (km/s) Time ( s) Figure 26: Velocity, mirror 3 x Figure 27: Flux, mirror 38

47 4 x 1025 Energy Density (nv 2 ) [s -2 m -1 ] Time ( s) Figure 28: Energy density, mirror When it was first suspected that the magnetic field strength might be too high and create a magnetic mirror effect, the first change was to simply reduce the field on the second magnetic nozzle. It was cut to one half and one quarter, and this was compared with the full field case. The density, velocity, flux, and energy density plots for all of these cases are presented below. Since the RFEA measurements are taken on axis, the mirror effect does not actually reduce the number of ions, since magnetic mirrors only reflect ions with some component of perpendicular velocity (a pitch angle), which means they are not on the axis to begin with. In fact, a stronger magnetic field would collimate the beam more tightly, and we would expect an increase in density measured by the RFEA on axis. Indeed, this is what we see in figure 29; reducing the magnetic field reduced the measured density. 39

48 5 x Full Field Half Field Quarter Field Density (m -3 ) Time ( s) Figure 29: Density Comparison, Mirror Full Field Half Field Quarter Field Velocity (km/s) Time ( s) Figure 30: Velocity Comparison, Mirror 40

49 However, when we look at the velocity in figure 30, we can see that there is a slight increase in velocity when the magnetic field on the second nozzle is decreased. This is because the ions do not have to travel up a strengthening magnetic field, thus avoiding that energy loss. Nevertheless, it is a small effect, and as we can see in the plots of the field lines, there are still substantial regions where the magnetic field pinches down, even with the quarter field case. Figures 31 and 32 show the flux and energy density in this configuration, respectively. Since the velocity decrease and density increase as the field is increased act against each other, the results here are mixed. In figure 32, we can see that the initial peak of the energy density is lower when the field is at full strength, but later in time, the second peak of the energy density is higher than the half field or quarter field cases. Overall, the differences are minimal. Flux (nv) [m/s * n particles] 3 x Full Field Half Field Quarter Field Time ( s) Figure 31: Flux Comparison, Mirror 41

50 Energy Density (nv 2 ) [s -2 m -1 ] 4 x Full Field Half Field Quarter Field Figure 32: Energy Density Comparison, Mirror Based on these results, it was decided to develop a new flux conserving nozzle configuration, described in the next section, which avoids creating regions of converging magnetic field lines as the ions travel downstream Time ( s) 5.2 Flux Conserving Configuration The next step in the investigation was to completely change the magnetic nozzle configuration to a new, flux conserving one. The premise of the flux conserving configuration is that all of the magnetic field lines that emanate from the helicon source expand out slightly and just fit through the first nozzle and then expand out some more and just fit through the second nozzle, while moving into a region of weaker magnetic field, converting thermal energy to direct kinetic energy and keeping the beam collimated. The first magnetic field configuration had the first nozzle 15 cm downstream and the second nozzle 51 cm downstream. The currents were 4.7 A and 19 A, respectively, much less than the currents which were used in the prior nozzle configuration. The magnetic field lines for this configuration are as shown in figure

51 Figure 33: Magnetic Field Configurations - Flux Conserving Configuration 43