AIAA-87 -1407
Electron-Cyclotron-Resonance (ECR) Plasma Acceleration
J. C. Sercel Jet Propulsion Laboratory California Institute of Technology Pasadena, California
AIAA 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference June 8-10, 1987/Honolulu, Hawaii
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ELECTRON-CYCLOTRON-RESONANCE (ECR) PLASMA ACCELERATION
Joel C. Sercel* Jet Propulsion Laboratory California Institute of Technology Pasadena, California
Abstract P power per unit volume, W/m3 R position vector, m A research effort directed at analytically v velocity, mls and experimentally investigating Electron U energy, J or eV Cyclotron-Resonance (ECR) plasma acceleration V electrostatic potential, volts is outlined. Relevant past research is reviewed. T temperature, Kelvin or eV The prospects for application of ECR plasma acceleration to spacecraft propulsion are described. It is shown that previously unexplained losses in converting microwave magnetic dipole moment power to directed kinetic power via ECR plasma reaction cross section, m2 acceleration can be understood in terms of diffusion of energized plasma to the physical time constant, s walls of the accelerator. It is argued that line radiation losses from electron-ion and electron SubscriPts atom inelastic collisions should be less than estimated in past research. Based on this new A acceleration understanding, the expectation now exists that B Bohm efficient ECR plasma accelerators can be e electron designed for application to high specific impulse ex excitation spacecraft propulsion. ionization summation variable refers to lowest energy level Acronyms and Abbreviations p perpendicular r relative D-He3 Deuterium Helium-Three sp space charge induced ECR Electron-Cyclotron-Resonance to t total GE General Electric JPL Jet Propulsion Laboratory LeRC Lewis Research Center I. Introduction NASA National Aeronautics and Space Administration ECR plasma acceleration is an TE Transverse-Electric electrodeless process which promises to efficiently use microwave frequency Nomenclature electromagnetic radiation to accelerate a tenuous plasma to velocities of use for high B magnetic induction vector, T specific impulse spacecraft propulsion. The E energy, J or eV advantages of high specific impulse propulsion e electron charge (1.602 x 10-19 coul) are well known in the aerospace community. If F force, N high specific impulse propulsion technology can K Boltzmann's constant be implemented, propellant mass savings and L length of accelerator, m associated cost savings can be obtained for m mass of electron (9.1 x 10-31 kg) many current missions, and a wide variety of M mass of ion, kg desirable new missions can be enabled. Electric n number density, m- 3 propulsion represents the most likely near-term possibility for achieving high specific impulse propulsion. More advanced systems such as * Member Jet Propulsion Laboratory Technical beamed energy propulsion or fusion propulsion Staff, California Instititute of Technology still remain futuristic concepts. This paper re Graduate Research Assistant, Member AIAA. examines ECR plasma acceleration for application to electric propulsion, beamed This p.... r is doc'.," • work of Ihe U.S. Govemmenl .nd is nol subJocI 10 coPyrilhl prolocUon in Ihe United Slllts. energy propulsion, or fusion propulsion. Figure 1 shows a conceptual schematic of These free electrons move in Larmor an EGR plasma accelerator. Transverse-Electric orbits producing a field of magnetic dipoles (T E) mode microwave radiation is introduced with axes aligned opposite to the axis of the through a dielectric window into a neutral gas solenoid magnetic field. The opposition between region via a waveguide. The neutral gas region the electron-Larmor-orbit dipole field and the can be in an extension of the waveguide, in a applied diverging solenoid field results in a net resonant cavity, or in a flared portion of the force on the electrons. As this force waveguide that has a different internal radius accelerates the electrons, a space-charge than the power transmission waveguide. A potential is induced which accelerates the ions solenoid coil co-axial with the waveguide, but with the electrons down-stream toward a larger in radius, surrounds the neutral gas vacuum region. The quasi-neutral plasma then region. This coil is designed to produce a separates from the magnetic field with minimal magnetic field which decreases in intensity loss and moves away from the device into the away from the dielectric window in the vacuum region. direction the microwave radiation propagates. Overall conversion of microwave power to jet power involves several possible loss mechanisms including: (1) reflection of the Propellant applied microwave power, (2) exhaust plume Injection Neutral Gas divergence, (3) nonuniformities in the exhaust Region velocity profile, (4) propellant ionization energy costs, (5) ion-electron recombinations, (6) -----...... =-~~~.... ---..- B Lines incomplete propellant ionization, (7) plasma Microwave .•.• --- __ ~ interactions with the walls of the accelerator, Waveguide ...- and (8) radiation from the plasma. .... ___ Plasma •.•• Trajectory ~,::-" '": .. " History and Related Research ~ ECR plasma acceleration was first Dielectric Energizing investigated both experimentally and Zone analytically for application to electric Window ~ propulsion in the 1960s. Three groups of vacuum. researchers were involved in this early work: (1) Solenoid a group at General Electric Corporation 1 funded by Lewis Research Center (LeRC), (2) a NASA group at LeRC,2 and (3) a group at the University Fig. 1 Schematic of ECR Plasma Accelerator. of Tokyo.3 Although the early research was conducted with somewhat primitive apparatus A propellant, such as argon, is introduced and theoretical models (by today's standards), into the neutral gas region via peripherally enough research was done to verify the basic located injection ports. The intensity of the concept of the process. At the time of the solenoid magnetic field in the energizing zone is investigation, however, microwave sources were adjusted so that the electron-cyclotron quite massive and inefficient. Meanwhile, frequency is equal to the frequency of the significant progress was being made on dc applied microwave radiation. This frequency electric propulsion devices which showed matching provides a resonance between the promise of acceptable performance using the microwave field and- the electron-cyclotron technology and analysis tools of the 1960s. By motion that enhances microwave-to-plasma the middle of that decade, these advances had coupling. Some ionization occurs in the neutral presaged the temporary end of research into the gas region, but coupling there is limited because physics of ECR plasma acceleration. the electron-cyclotron motion is not at resonance with the microwave radiation. The A review of the early research gas enters the energizing zone via free publications and communication with the molecular diffusion. In the energizing zone the investigators suggests that state-of-the-art gas atoms are ionized by the microwave microwave technology and plasma diagnostiC radiation through electron-atom collisions in a tools can be used to make ECR plasma cascading process. The microwave energy is acceleration an important part of modern coupled to the electron-cyclotron motion in the spacecraft propulsion technology. energizing zone, which results in electron energies of 200 to 1000 eV.
2 The majority of the early experimental of this analysis was that the plasma trajectory work on this type of plasma accelerator was does cross the magnetic field lines, even conducted at the Space Sciences Laboratory of without particle collisions, and that the plasma the General Electric Company (GE) and funded by can emerge as a well-defined beam. the Lewis Research Center (LeRC).1,4 In this experimental effort, several different ECR This conclusion was in contrast to the plasma thrusters were tested. Various earlier theoretical analysis of Kilpatrick.S arrangements of gas injection schemes, Kilpatrick's work indicated that a plasma beam waveguide designs, and window materials were ejected from a diverging magnetic field will evaluated. Thrust was measured for a variety of closely follow field lines; unless the plasma is configurations at power levels of up to a few initially well-collimated with high initial kilowatts using several propellants. Over 95 directed kinetic energy.S The critical difference percent of the incident microwave power was between Kilpatrick's analysis and that of observed to be deposited in the plasma stream.4 Kosmahl was that Kosmahl studied a non A maximum efficiency for conversion of equilibrium plasma in which most of the thermal microwave power to jet power of 0.4 was energy was stored in electron motion. reported at specific impulses of a few thousand Kilpatrick studied a plasma in which collisions seconds.1 However, the validity of many of the resulted in near thermal equilibrium of all early thrust measurements was questioned. It charged species. Furthermore, Kilpatrick's was suggested that entrainment of gas from the analysis did not fully account for the magnetic vacuum chamber into the energizing zone was dipole-moment force that is responsible for ECR increasing the effective mass flow rate and plasma acceleration. producing erroneously high thrust measurements.4 In measurements not subject to Kosmahl defined a propulsive efficiency to concern about gas entrainment, thrust efficiency account for momentum losses resulting from was only about 10 percent, and specific impulse radial acceleration of the plasma during was measured to be less than 2000 seconds. separation from the magnetic field. This Electron energy measurements in the plasma propulsive efficiency depends primarily on the energizing zone suggested that electron thermal. solenoid geometry and the position at which motion was effectively converted to jet power.4 plasma of a given radial extension is introduced An unknown mechanism was robbing the to the field. Kosmahl showed that propulsive electrons of their thermal energy prior to the efficiencies between 0.90 and 0.97 could be plasma acceleration, thereby preventing optimal expected for a variety of th ruster accelerator performance. configurations. Kosmahl's dipole moment calculation is discused later in this paper in It was suggested at the time that this loss Section IV. mechanism was line radiation caused by electron-atom inelastic collisions. 4 A review of the experimental work Synchrotron and Bremsstrulung radiation losses published by Nagatomo at the University of are several orders smaller than line radiation Tokyo on ECR plasma acceleration indicates that losses. However, recent analysis suggests that the work performed by the Japanese on this line radiation also could not have been device was directed at experimentally obtaining responsible for the magnitude of the observed a fundamental understanding of the nature of the 3 energy loss. It now appears that plasma was acceleration mechanism. Nagatomo developed diffusing to the walls of the accelerator across several useful measuring techniques which gave magnetic field lines. This diffusion was accurate information on the basic physics of probably responsible - for the measured low this process. Specifically, Nagatomo used: (1) thrust efficiencies and can be limited through unusually small and sensitive electromagnetic informed accelerator design. probes to measure microwave field strength within the accelerator without disturbing the The first publication of a theoretical plasma, (2) hot Langmuir probes to measure the analysis of ECR plasma acceleration occurred electrostatic potential of the accelerating several years after the initiation of plasma, and (3) an innovative, simple thrust experimental work at General Electric balance to provide a direct measurement of the Corporation (GE). In this theoretical treatment, propulsive force between the plasma and the which was accomplished by Kosmahl at Lewis solenoid coil. The thrust measuring device Research Center (LeRC), conservation of the developed at the University of Tokyo is electron-cy'clotron dipole moment, zer.o especially interesting, because it obviates collisions, and axisymmetrical steady-state having to place both the thrust balance and fields were assumed.2 A significant conclusion waveguide structure in a vacuum chamber.
3 Current work on the absorption of evaluated to first approximation. Finally, it has microwave radiation into a plasma by ECR is the been shown that cross-field diffusion can result subject of intensive investigation by groups in significant wall losses if not correctly studying magnetic confinement fusion. 6 A few accounted for in accelerator design. key differences exist, however, between the fusion application of ECR absorption of The next activity planned in this program microwave radiation and the propulsion is to gain a more complete understanding of EGR application of this mechanism. First, the fusion plasma acceleration based on a unified analysis community is interested in the higher of the phenomena that act in concert to produce temperatures appropriate to nuclear fusion ECR plasma acceleration. To accomplish this research. Second, in the fusion application it is end, a numerical model of ECR acceleration is desirable to transfer the electron thermal being developed. It is expected that this energy to the ions. In the propulsion application numerical model will further illuminate the it is desirable to transfer the electron kinetic physics of EGR plasma acceleration, and will energy only to the directed kinetic energy of the provide valuable information to be used in the flowing plasma. Finally, the high magnetic detailed design of an experimental program. fields associated with magnetic confinement fusion research mandate radiation frequencies In the experimental program, a research one to two orders-of-magnitude higher than device will be constructed and tested. those required for the propulsion application. In Performance of this device will then be summary, it is much more difficult to apply ECR compared to the predictions of the numerical heating to fusion research than to plasma model to point out deficiencies of understanding. acceleration for spacecraft propulsion. It is Interferometric measurements of the Doppler worth noting that the interest in high-power, shift of optical emission from the exhaust high-frequency microwave sources for fusion plume will be used to determine the exhaust research has been an important factor in the velocity profile. Langmuir probes will be used recent development of high-power microwave to measure the temperature and density of sources. electrons in the plasma. Electromagnetic probes will be used to measure the local intenSity of At least two research efforts in the microwave field in the energizing zone to microwave thermal propulsion are characterize the coupling of microwave power complementary with the present research on EGR to the plasma. plasma acceleration. Asmussen7 ,8 and Micci9 ,10 have both been studying thermal propulsion Table 1 presents estimated design applications of microwave technology. The characteristics and operating parameters of the microwave apparatus developed by these planned EGR research device. The values given researchers is similar to that which will be are approximate and are presented only to used in the experimental portion of the research communicate the nature of the experimental discussed here. program and the physical regime in which the device will operate. III Present Research Program Although the focus of the current program The goal of the recently initiated present is on the physics of EGR plasma acceleration, research program is to develop a unified this program is also expected to identify understanding of EGR plasma acceleration. To practical constraints associated with the accomplish this goal a combined analytical and eventual feasibility of applying this process to experimental program is being conducted. spacecraft propulsion. Among the practical constraints of interest are the limits to the As part of the analytical part of this useful range of exhaust velocity and power level program a literature survey was completed, the that can be met by EGR propulsion. This results of which are described in Section \I of research will also provide valuable information this paper. This literature survey provided for use in selecting of the best propellant fluid background for the preliminary scoping from the wide range of fluids which now appear calculations presented in Section IV of this to be applicable. paper. To summarize, the collisionless dipole moment calculation of Kosmahl has been IV. Preliminary Theory of ECR Plasma verified through numerical solution of the Acceleration equations of motion for electrons and ions in EGR plasma acceleration. Also, the effects of Fundamental to EGR plasma acceleration is elastic and inelastic collisions have been the conversion of electron Larmor motion into
4 Table 1. Estimated Design Characteristics and Operating Parameters of Planned ECR Research Device.
Catagory Parameter Value
Device R-F Power Level 1 kW Characteristics Microwave Frequency 2.45 GHz Accelerator Area 0.05 m2 Peak Magnetic Field On Axis 0.1 Tesla Solenoid Diameter 0.3 m R-F to Jet Efficiency .. 0.5 Vacuum Required 10-5 torr
Propulsion Working Fluid Argon Parameters Exhaust Velocity 30,000 mls Thrust 10-2 N Mass Flow Rate 10-6 kgls Atom Flow Rate 1019 s- 1
Plasma Electron Temperature 102 eV Parameters Ion Temperature 10-1 eV Electron Larmor Radius 10-4 m Ion Larmor Radius 10-3 m Peak Atom Density 1018 m-3 Peak Electron or Ion Density 1017 m-3 Debye Length 10-4 m
directed kinetic energy of flowing plasma via which ion stream-wise motion is tied to expansion through a diverging magnetic field. electron stream-wise motion via induced space However, to appreciate the limitations of ECR charge fields. Initially, the plasma enthalpy in plasma accelerat"lon, several additional this model ·IS stored as magnetic dipole energy phenomena must be understood as they relate to associated with electron Larmor motion this process. These phenomena include: (1) [~B=(1/2)mv~]. Following the method established electron-electron elastic scattering, (2) by Alfven, the complete motion of the electrons coupling of microwave power to plasma at was described as the superposition of the electron-cyclotron-resonance, (3) line radiation Larmor motion about B-lines, and the and inelastic collisions, and (4) diffusion of translational motion of the electron guiding plasma across magnetic field lines. These centers. processes are briefly discussed below. The governing equations used in Kosmahl's A unified theory of ECR plasma analysiS are presented next. The force on a acceleration is not yet complete, so the following discussion presents only preliminary dipole in a diverging magnetic field is given by: findings. The calculations shown are based on many simplifying assumptions which are being ( 1 ) removed in current work. The purpose of this discussion is to communicate an understanding In a plasma such as applicable in this of the operation of this device and to suggest an process, the mean dipole vector of gyrating achievable performance level. electrons is anti-parallel to the local B-field. Eq. (1) reduces to: Plasma Acceleration Mechanism (2) As mentioned earlier in this paper, a collision less model of ECR plasma acceleration The total force on a gyrating electron is: was developed by Kosmahl.2 In Kosmahl's model, a tenuous, collisionless plasma was assumed in the solution of a three-dimensional equation in Ftot = F~ - e( Rex B + VVsp) = mRi (3)
5 and the total force on an ion in this model is: of both electrons and ions will be on the order of 10 4 m/s. From conservation of mass in steady state operation, this implies that the ion density must fall to approximately 10 16 m· 3 at where Vsp is the space-charge-induced this halfway pOint. The mean time between potential, R is the position vector of the guiding electron-ion elastic scattering collisions at center trajectories, and m and M are the this point is of order 10- 4 s. From this electron and ion mass, respectively. Kosmahl information, the mean stream-wise distance solved these equations numerically together between electron elastic scattering collisions with the continuity equations. The most in the energizing zone, and at a point halfway important results of his computation can be through the acceleration process, is 10-3 m and summarized in a few sentences. In the absence 1 m, respectively. of collisions, the plasma trajectory does not depend on the ion mass or the magnitude of the Because electrons in the energizing zone dipole moment, but is strongly affected by the move an average of only 10- 3 m before geometry of the magnetic field. Both \lV and sp undergoing scattering collisions, their kinetic V sp are approximately proportional to the energy is distributed between the three product ).lB, which goes to zero as the plasma translational degrees of freedom. Therefore, moves away from the accelerator. The final although the scattering frequency is much lower azimuthal energy of the plasma particles was than the electron-cyclotron frequency, only two found to be negligibly small compared to the thirds of the electron's kinetic energy translational energy associated with their guiding center trajectories. contribute to the electron magnetic dipole moment, and only about two thirds of the electron motion is initially available to supply Elastic Scattering of Electrons dipole moment effects for plasma acceleration. As the plasma begins to accelerate and the Elastic scattering of electrons has two kinetic energy associated with the electron important effects on the process of ECR plasma transverse motion is converted to directed acceleration. The first of these effects is motion of the plasma, some of the energy in dynamical friction on the electron motion. This longitudinal electron motion is returned to tends to thermalize the electrons and somewhat transverse motion through further elastic reduce the total energy available for plasma scattering. This continues until the plasma acceleration. Second, the scattering of becomes essentially collisionless, electrons upstream from the energizing zone approximately halfway through the acceleration into the neutral gas region results in- the process. production of ions in that region. This upstream flow of plasma could also lead to wall losses or sputtering from the dielectric window if not At the point where collisions become properly accounted for in accelerator design. negligible, any electron kinetic energy remaining in longitudinal modes of motion is essentially For the plasma conditions of Table 1, the frozen out of the flow and does not contribute to characteristic time for electron-atom elastic further dipole moment plasma acceleration. scattering collisions is estimated to be of order Some of the electron energy remaining in longitudinal modes of motion may contribute to 10-6 s in the energizing zone of an ECR plasma propulsive thrust and enhance efficiency by accelerator. This estimate is based on an producing ambipolar diffusion in the direction of assumed elastic scattering cross section of· 5 x the plasma flow; but such a process has not yet 10-20 m2 . The characteristic time for electron been carefully studied. electron scattering collisions is two orders larger than for electron-atom scattering. The mean electron velocity in the stream-wise This approximate analysis suggests that direction in the energizing zone is the same as elastic scattering of electrons may reduce the the mean ion stream-wise velocity there and is effective efficiency of the acceleration process expected to be of order 103 mls (based on from the collisionless value of over 90 percent numerical solution of Kosmahl's dipole-moment to as low as, perhaps, 60 percent. It is likely problem). that ambipolar diffusion and the return of electron kinetic energy to transverse motion At the down stream point where the through scattering could raise this value to as electron thermal energy is reduced to half of its high as 85 percent, but further analysis will be original value, the mean stream-wise velocity required to verify this assertion.
6 As mentioned above, elastic scattering of propagation occurs in what is commonly electrons has the additional effect of directing referred to as the whistler mode, with some some electrons upstream from the energizing attenuation of the microwave power resulting zone into the neutral gas region. These from electron collisions within the plasma. At electrons will not travel upstream at their resonance, ideal theory suggests that no thermal diffusion velocity, but will move by propagation will occur; all the electromagnetic ambipolar diffusion. In other words, a local radiation is either absorbed or reflected by the electric field is established with a polarity that plasma. retards the upstream migration of electrons while, at the same time, it accelerates the In ECR plasma acceleration, damping due to migration of ions. The mean migration velocity Doppler broadening associated with electron of the two charged species can be simply shown motion (an effect quite similar to the to be equal to the ion acoustic velocity. Based phenomenon of Landau damping) has a favorable on the plasma parameters of Table 1, the ion impact on the reflection and attenuation acoustic velocity is estimated to be of order 104 characteristics of the plasma. 11 Specifically, m/s. the resonance effect actually occurs over a frequency band with a width corresponding to an Moving at the ion acoustic velocity with a appreciable fraction of the field frequency. characteristic time for elastic scattering of Furthermore, because the plasma in ECR 10-6 s, the scattered electrons· travel a mean acceleration is flowing, the effects of particles distance of 10- 2 m before undergoing further being carried downstream from their point of scattering collisions with atoms in the neutral origin must be considered. The longitudinal gas region. Approximately the same mean acceleration of charged species, as they are distance is required before these electrons created, results in a gradual plasma boundary undergo inelastic collisions with the atoms in which reduces reflection of the microwave the neutral gas region, because the total radiation. electron-atom inelastic scattering cross section is similar to the elastic cross section. These effects have been experimentally The primary effect of these inelastic collisions observed to reduce reflection to negligible is damping of the motion of the electrons via levels (resulting in over 95 percent of the ionization and excitation of the neutral gas applied microwave power being absorbed into atoms. Recombination reactions are much less the plasma) at electron densities appropriate to likely. This mechanism can ionize atoms as far ECR acceleration.4 The thickness of the as several centimeters upstream of the energizing zone was observed in past research energizing zone. Also, if the neutral gas region to be fixed at a few centimeters as determined is too narrow, plasma can impact the dielectric by electron damping effects. 1 ,3,4 This window, resulting in sputtering and energy loss. observation has important implications for the design of useful ECR devices. Specifically. it Microwave-to-Plasma Coupling allows the ion production rate in an ECR accelerator to be controlled simply by For the acceleration mechanism described regulating the conditions in the neutral gas above to be of use, not only must the atoms be region. This is true because the rate at which ionized, but the electrons must be energized. atoms diffuse out of the neutral gas region into This is accomplished by coupling microwave the energizing zone is a function of the radiation to electron motion within the conditions in the neutral gas region. energizing zone. I!"J this application, the microwave radiation propagates in a direction For a specified mass flow rate. the mean parallel to the magnetic field lines. density of gas atoms entering the energizing zone varies inversely with the mean thermal This coupling problem is classically diffusion velocity _ Because the mean thermal addressed by treating the plasma as a continuum diffusion velocity is proportional to the square medium with an index of refraction having both root of the gas temperature. controlling gas real and imaginary parts. The results of this temperature effectively controls gas density. classical treatment of the propagation problem Increasing gas density increases the rate of are well known and is outlined in a few production of ions in the energizing zone sentences: The propagating radiation displays because it increases the electron-atom collision one cutoff and one resonance, with the frequency_ resonance occuring at the lower of the two frequencies and being equal to the electron To see how the ionization rate can be cyclotron orbital frequency. Below resonance, controlled. consider that if the atom
7 temperature in the neutral gas region is 600 where Ui is the ionization energy, (j i is the Kelvin, the mean thermal diffusion velocity is ionization cross section, Vr is the electron about 180 m/s. To meet the mass flow rate and speed relative to atoms, and the summation over other conditions of Table 1, the resulting gas j refers to the jth excitation reaction resulting density is approximately 10 18 m- 3 , and the from electron-atom collisions in which Uj required thickness of the energizing region is refers to energy level and OJ refers to the 10-2 m, as observed. If the atom temperature collision cross section to produce that excited were increased to 1500 Kelvin, the mean state. The notation:<(jvr> represents the product thermal diffusion velocity would increase to of a reaction cross section and the electron approximately 550 m/s. If this mass flow rate velocity averaged over the electron velocity were maintained, the resulting atom density distribution. Assuming no recombination or wall would be approximately one third its prior value. losses, Eq. (5) can be normalized to produce an The required thickness of the energizing zone, expression for the energy expended in producing therefore, would triple. If the required each ion: thickness of the energizing zone became too large to be maintained by electron damping effects, atoms would pass through the Ei = Ui + ~«ojVr>Uj}/
8 applied to spacecraft propulsion is the power Combining terms, lost to the walls of the accelerator due to diffusion of charged, energized species across tA == L[(2M)/KTe]112 (12) magnetic field lines. To understand this loss mechanism, the characteristic time required for If L is assumed to be approximately twice the diffusion to the walls was compared to the time radius of the accelerator (an assumption which required for plasma acceleration through the is consistent with previous accelerator designs) accelerator due to the dipole moment body force. the characteristic time for diffusion can be The ratio of these two quantities was then used directly compared to the characteristic time for to characterize the relative significance of acceleratio n: cross-field diffusion in EGR plasma acceleration. ts ItA == 2.8eRB/(KMT e) 112 ( 13)
The time constant for diffusion across For effective operation of this device, it is magnetic field lines in a cylindrical geometry desirable to have ts ItA > 1. If this condition is such as the EGR plasma accelerator can be not met, a significant fraction of the plasma estimated by the Bohm time: energy could be lost to the accelerator wall via radial diffusion. (9) The EGR plasma accelerators which were where B is the magnetic field strength, R is the tested in the 1960s operated at ts/tA < 1. Hence, radius of the accelerator, and T e is the electron these devices could not have been expected to temperature. 14, 15 Eq. (9) can be derived using yield high efficiency. As the plasma was the empirical Bohm formula based on Fick's produced and the electrons energized, a diffusion law. significant fraction of the plasma diffused across field lines to make contact with the wall of the accelerator. Therefore, a significant The Bohm formula predicts diffusion rates fraction of the ionization and excitation energy several orders of magnitude higher than the required to produce the plasma was lost to the diffusion rate predicted by classical diffusion accelerator wall, along with any useful kinetic calculations. This may explain why the energy or electron thermal energy the plasma magnitude of the diffusion losses was not had acquired. This explains why most of the accurately determined in the 1960s work on EGR measured thrust efficiencies of the early plasma acceleration. The reason for the devices were in the range of 10 percent. departure from classical theory to Bohm diffusion is not well understood; but it has been An analysis has been completed which also suggested that the process is related to plasma accounts for the presence of a sheath in limiting instabilities or Ex B drifts. Because Bohm the diffusion losses in EGR plasma acceleration. diffusion has been found to give good results The details of this analysis will not be over a wide variety of plasma conditions, it is reproduced here. It was found that the assumed that it is sufficiently accurate to formation of a sheath has only a small effect in model the transport of plasma across the reducing wall losses because the electron magnetic field in EGR plasma acceleration. temperature and hence the ion acoustic velocity is high enough to allow the plasma to move freely across the sheath to the wall. The approximate time over which the plasma is accelerated down stream in ECR Discyssion of Preliminary Theory plasma acceleration can be estimated based on the average velocity of the plasma, v , and the av The scoping calculations presented above characteristic distance over which the plasma represent a preliminary theory of EGR plasma is accelerated, L: acceleration. The purpose has been to provide the ground work for the development of a more (10) rigorous, unified theory of this process. Based on these calculations, it is expected that the The average plasma velocity is related to planned research device will produce thrust the electron energy and the atomic mass of the efficiencies of approximately 50 percent. ions according to the approximate expression: Elastic scattering of electrons in the acceleration process is expected to account for vav == [KTe/(2M)]1/2 (11) the largest portion of energy losses in this
9 device. Other significant loss mechanisms are microwave power. Conceptual designs have been expected to include inelastic collision processes proposed for ECR devices operating at unit and cross-field diffusion. power levels as high as several gigawatts.16
An important component of an electric V. Applicatjon to Spacecraft Propulsion propulsion system based on ECR plasma acceleration is the required microwave source. Limitations on the efficiency and specific mass When ECR plasma acceleration is applied performance of magnetron or klystron to spacecraft propulsion, any suitable microwave supplies were viewed as a microwave source can be used as the power significant problem with ECR propulsion when it supply. This process has the potential to was first investigated in the 1960s. operate as part of an electric propulsion system, Technological advancements since the 1960s in beamed energy propulsion, or in fusion suggest that a microwave source for electric propulsion. These potential applications of ECR propulsion can be designed for electric to plasma acceleration are briefly described in the microwave power conversion efficiencies of 85 ensuing discussion. to 90 percent, an operational life time of several years, and a specific mass of about 0.5 Desirable attributes of an effective kg/kW.17,18 propulsion technology include: (1) high thrust efficiency, (2) flexibility to operate throughout Before ECR plasma acceleration can a specific impulse range appropriate to missions become practical for application to electric of interest, (3) unit power handling capability propulsion, an overall propulsion system deSign well matched to available power supplies, (4) must be produced. In such a design the Simplicity, (5) reliability, (6) long life, and (7) efficiency of both the microwave source and the flexibility to use propellant fluids which are thruster are two important parameters. Both inexpensive, easily stored, readily available, and the total propulsion system mass and the power safe. All existing electric propulsion lost to the solenoid coils must be considered. technologies require compromises on these Such a system design has not yet been attributes. For example, electrostatic ion attempted, so information concerning possible thrusters promise long life and high efficiency, but are not well suited to operation at the system performance is limited. However, relatively low specific impulse appropriate to approximate calculations suggest that if the Earth-orbital missions. By contrast, recent breakthroughs in the area of electrothermal arcjets can operate effectively superconductor technology lead to appropriate at lower specific impulse and with less exotic high-field solenoids, which can operate at propellants, but suffer from relatively low temperatures at or above the boiling point of thrust efficiency and limited life. nitrogen, total system mass for electric ECR propulsion systems will be less than 1 kg/kW Electric Propulsion (excluding the primary electric power supply). This impressive specific-mass performance can An electric propulsion system based on be accomplished only at power levels of tens of ECR plasma acceleration could avoid some of the kilowatts or higher. performance compromises which limit existing electric propulsion technologies. When fully Beamed Energy Propulsion developed, this process can potentially be made to operate at thrust efficiencies comparable to Figure 2 shows a conceptual schematic of those of electrostatic ion thrusters throughout a how ECR plasma acceleration could be used in a range of specific impulse that encompasses the beamed energy propulsion system. In this traditional domains of both thermal and application, a remotely located transmitter electrostatic devices. The electrodeless nature would be used to launch a microwave beam of this process suggests that ECR thrusters may toward the spacecraft.16 On the spacecraft, a possess an inherently long life and be capable of parabolic antenna would serve to focus the processing a w'lde variety of propellant fluids. microwave power into the thruster. This Based on present understanding, power handling concept would free the spacecraft from the capability per unit is expected to be limited by requirement of carrying an expensive or massive cavity wall losses (which depend on the ratio of on-board power supply to operate at specific the surface area of the plasma to its volume) to impulses now achievable only by a few electric a minimum of approximately 100 watts. In propulsion devices. Because the collector would principle, maximum unit power handling have to be rather large to effectively capture a capability is limited only by available microwave beam transmitted over useful
10 distances, a premium would be placed on VI. Summary minimizing the mass density of the collector. One possible approach would be to use an ECR plasma acceleration is an inflated antenna to receive the incoming electrodeless process by which microwave microwave radiation as shown in Figure 2. power is converted to directed energy in a flowing plasma. This process can be used in a wide variety of spacecraft propulsion 6 applications. The first such application is likely to be in electric propulsion systems. More advanced applications may include beamed energy propulsion and fusion propulsion. The advantages of ECR plasma acceleration for future spacecraft propulsion stem from its potential for high specific impulse, high efficiency, long life, and the flexibility to use a wide variety of propellant fluids.
The dipole moment body force which acts 1 Payload 5 between an applied diverging magnetic field and 2 Truss Structure the electron motion in a plasma is an efficient 3 Rotary Joint mechanism for accelerating the plasma in ECR 4 Inflatable Antenna propulsion. Past researchers have shown that 5 ECR Plasma Thruster the electron-cyclotron-resonance effect can be 6 Propellant Tank used to effectively couple microwave power to 7 Waveguide an appropriate plasma. A small but non 8 Antenna Focal Point negligible power loss results from line radiation 9 Incoming Microwave Beam caused by electron-atom collisions. Losses due to double ion production or incomplete propellant ionization are expected to be Fig. 2 Concept of Beamed Energy Application important, but not dominant. Devices tested in of ECR Plasma Accelerator. the 1960s probably suffered from excessive cross-field diffusion losses which can be Fusion Propulsion limited in future accelerator designs.
An even more advanced spacecraft VII. Acknowledgements propulsion application of ECR plasma acceleration would be its use as a thruster in a The research reported in this paper was propulsion system using a magnetic confinement performed, in part, by the Jet Propulsion nuclear fusion reactor as its energy source. Laboratory, California Institute of Technology as Recently, Logan has proposed harnessing the part of its Innovative Space Technology Center, microwave synchrotron radiation that will be which is sponsored by the Strategic Defence produced by magnetic confinement fusion Initiative Organization/Innovative Science and re acto rs. 1 9 Analysis suggests that up to two Technology Office through agreement with the thirds of the fusion power output of a D-He3 National Aeronautics and Space Administration. reactor can be extracted in the form of The author acknowledges the contributions of microwave radiation .19 It is suggested that this his academic advisor, Prof. F. E. C. Culick, and Mr. microwave power can. be coupled out of the F. linoya of the California Institute of fusion reactor cavity via low-loss Technology. The author also acknowledges waveg u ides. 19 If such microwave power output discussion and critical review of this work by can be extracted from a fusion reactor, it can several engineers from the Propulsion Systems then be delivered directly to an ECR plasma Section at the Jet Propulsion Laboratory. accelerator to provide power for an extremely high performance spacecraft propulsion system.
11 References
1. Miller, D. B., Bethke, G. W., and Crimi, G. F., 11. Ben Daniel, B. J, et al., "Electron "Final Report: Investigation of Plasma Conductivity at Cyclotron Resonance," Physics of Accelerator (Cyclotron Resonance Propulsion ~, Vol. No.6, p. 884, 1963. System)," prepared for NASA Lewis Research Center by General Electric Company, NASA CR- 12. Kieffer, L. J., and Dunn, G. H., "Electron 54746, Philadelphia, Pennsylvania, November 1, Impact Ionization Cross-Section Data for Atoms, 1965. Atomic Ions, and Diatomic Molecules: I. Experimental Data," Reviews of Modern Physics, 2. Kosmahl, H. G., "Three-Dimensional Plasma Vol. 38, No.1, January 1966. Acceleration Through Axisymetric Diverging Magnetic Fields Based on Dipole Moment 13. Dugan, J. V. and Sovie, R. J., "Volume Ion Approximation," NASA TN 0-3782, Lewis Production Costs in Tenuous Plasmas: A General Research Center, Cleveland, Ohio, January 1967. Atom Theory and Detailed Results for Helium, Argon, and Cesium," NASA TN 0-4150, Lewis 3. Nagatomo, M., "Plasma Acceleration by High Research Center, Clevland, Ohio, 1967. Frequency Electromagnetic Wave in Static Magnetic Field Gradient," from the Proceedings 14. Chen, F. F., Introduction to Plasma Physics of the Seventh International Symposium on and Controlled Fusion, Second Edition, p.191, Space Technology and Science, Tokyo, Japan, Plenum Press, New York, 1984. 1967. 15. Bohm, 0, "The Use of Probes for Plasma 4. Crimi, G. F., Eckert, A. C., Miller, D. B., Exploration in Strong MagnetiC Fields," ~ "Microwave Driven Magnetic Plasma Accelerator Characteristics of Electrical Discharges in Studies (Cyclops)," prepared for NASA Lewis Magnetic Fields, Eds. Guthrie, A. and Wakereling, Research Center by General Electric Company, R. K., p. 65, McGraw-Hili, New York, New York, NASA CR-72227, Philadelphia, Pennsylvania, 1949. March 24, 1967. 16. Minovitch, M. A., "Solar Powered, Self 5. Kilpatrick, W. D., "Propulsion Application of Refueling, Microwave Propelled Interorbital the Modified Penning Arc Plasma Ejector," AIAA Transportation System," Conference paper AIAA- Journal, Vo!. 1, No.4, pp. 806-813, April 1963. 83-1446, presented at the AIAA 18th Thermophysics Conference, June 1-3, Montreal, 6. Bornatici, M. et aI., "Electron-Cyc.lotron Canada, June,1983. Emission and Absorption in Fusion Plasmas", Nuclear Fusion Vol. 23, p. 1153 , 1983. 17. Brown, W.C., "The SPS Transmitter Designed Around the Magnetron Directional Amplifier," 7. Asmussen, J., Nakanishi, S. and Whitehair, paper C1 presented at the Conference on Solar S., "Demonstration of a New Electrothermal Power Satellites, State of the Art, June 5 and 6, Thruster Concept", Applied Physics Letters, Vol. Paris, France, June 1986. 44, No. 10, May 15, 1984. 18. Brown, W.C., "New Findings With Respect to 8. Dahimene, M., and Asmussen, J., "The the Interactive Behavior Between a Carburized Performance of a Microwave Ion Source Thoriated Tungsten Cathode and a Crossed Field Immersed in a Multicusp Static Magnetic Field," Device," Conference paper presented at the Tri Journal of vacuum Science Technology, Vol. 4, Service Cathode Workshop, Naval Research No.1, January/February 1986. Laboratory, Anacostia, Washington D.C., March 1984. 9. Micci, M. M., "Prospects for Microwave Heated Propulsion," Conference paper AIAA-84- 19. Logan, G. B., "D-3He Fusion Using Direct 1390, presented at the 20th Joint Propulsion Conversion of Microwave Synchrotron Radiation", Conference, AIAA/SAE/ASME, June 11-13, Invited paper presented at the American Cincinnati, Ohio, June 1984. Physical Society Division of Plasma Physics, Baltimore, Maryland. November 1986. 10. Knecht, J. P., and Micci, M. M., "Analysis of a Microwave-Heated Planer Propagating Hydrogen Plasma," AIAA preprint from the Pennsylvania State University, University Park, Pennsylvania, 1986.
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