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Multiple Equilibria of the Barotropic Vorticity Equation on a Sphere

Multiple states of the barotropic vorticity equation in which the balance is between the first and third terms on the r.h.s. of (1) are given. Solutions of this type were also considered by Charney and Devore (1979) in their discussion of thermally, rather than topographically, forced waves. Whereas in the case of topographic forcing the multiplicity arises from what they called form-drag instability in the wave-zonal flow interaction, in the thermal forcing case the associated instability appears to be the Rossby-wave instability discussed by Lorenz (1972), and the multiple states of the highly truncated model proved to be unstable when more degrees of freedom were added. The multiple statistically steady solutions described are thus novel in that they do not involve form-drag instability, they have stable statistics in calculations with a large number of degrees of freedoms, and they occur on the sphere, with no artificial confinement in a resonant cavity. Furthermore, the solutions are obtained with no external forcing of the zonal flow. The full non-linear equations for two-dimensional non-divergent motion between smooth, rigid boundaries on a sphere were used.

Suarez, M. J.↗

"Electrostructural Phase Changes" In Charged Particulate Clouds: Planetary and Astrophysical Implications

There is empirical evidence that freely-suspended triboelectrostatically charged particulate clouds of dielectric materials undergo rapid conversion from (nominally) monodispersed "aerosols" to a system of well-defined grain aggregates after grain motion or fluid turbulence ceases within the cloud. In United States Microgravity Laboratory Space Shuttle experiments USML-1 and USML-2, it was found that ballistically-energized grain dispersions would rapidly convert into populations of filamentary aggregates after natural fluid (air) damping of grain motion. Unless continuously disrupted mechanically, it was impossible to maintain a non-aggregated state for the grain clouds of sand-size materials. Similarly, ground- based experiments with very fine dust-size material produced the same results: rapid, impulsive "collapse" of the dispersed grains into well-defined filamentary structures. In both ground-based and microgravity experiments, the chains or filaments were created by long-range dipole electrostatic forces and dipole-induced dielectric interactions, not by monopole interactions. Maintenance of the structures was assisted by short-range static boundary adhesion forces and van der Waals interactions. When the aggregate containers in the USML experiments were disturbed after aggregate formation, the quiescently disposed filaments would rearrange themselves into fractal bundles and tighter clusters as a result of enforced encounters with one another. The long-range dipole interactions that bring the grains together into aggregates are a product of randomly-distributed monopole charges on the grain surfaces. In computer simulations, it has been shown that when the force vectors of all the random charges (of both sign) on a grain are resolved mathematically by assuming Coulombic interaction between them, the net result is a dipole moment on individual grains, even though the grains are electrically neutral insofar as there is no predominance, on their surface, of one charge sign over another. The random charges of both sign derive from natural grain-to-grain interactions that produce triboelectrification via charge exchange every time grain surfaces make contact with one another. The conversion from a random distribution of grains (upon which there are randomly distributed charges) into an organization of electrostatically-ordered aggregates, can be regarded (within the framework of granular-material science) as an "electrical or Coulombic phase change" of the particulate cloud. It is not totally dissimilar from the more normal phase-change concept in which, for example, a gas with long free-path-molecules suddenly becomes a solid as a result of structural ordering of the molecules (notably, also the result of electronic forces, albeit at a different scale). In both the gas-to-solid case, and the aerosol-to-aggregate case, the same materials and charges are present before and after the phase change, but their arrangement now has a higher degree of order and a lower-energy configuration. An input of energy into the system is required to reverse the situation. The aggregates in the USML experiments were observed to undergo at least two phase changes as noted above. The point about phase changes, and by implication, the "electrostructural" reorganizations in particulate clouds, is the following: (a) they can occur very rapidly, almost spontaneously, above a critical cloud density, (b) in going from a higher energy state to a lower energy state, they convert to a denser system, (c) energy must be required to reverse the situation, implying that energy is released during the high-to-low energy phase change. In applying this information to natural particulate clouds, some inferences can be made (it is stressed that reference is still to dielectric materials attracted by dipole forces). There are several natural settings to which the USML observations apply, and to which the phase-change implications likewise apply. Dense clouds of triboelectrically-charged, kinetically-energized grains are to be found in volcanic eruptions (particularly on earth), aeolian dust storms (particularly on Mars), meteorite impact ejecta curtains (on all planets), in "immature" debris rings around planets (e.g., that from which our own Moon may have condensed), and in gravitationally collapsing protoplanetary dust/planetesimal debris disks where dielectric granules are being increasingly brought into collisional relationships with one another (increasing both charge exchange and physical proximity). It is noted that in many of these cases, the degree of electrical charging on the grains is likely to be much higher than that in the USML experiments where charging was not enhanced above the "normal", naturally encountered level for the particular materials (quartz, glass, and various silicate minerals). Application of the phase-change concept suggests that volcanic, aeolian, and impact debris clouds may, under certain circumstances, undergo rapid, impulsive, or even catastrophic collapse into a denser state that will lead to rapid precipitation or fall-out of suspended particulates. Although this idea has been suggested previously by the author , the phase change concept possibly permits some new insights into cloud-system behavior. For example, in a protoplanetary debris disk, the work of gravity may suddenly be enhanced by electrostatically driven collapse of the system when materials reach a critical intergranular spacing or grain number density. This might reduce the rate of planet formation by orders of magnitude (considering the ratio of g-forces to electrostatic ones for very small grains in close proximity), and indeed, it might drive the collapse into a system configuration that would perhaps not be created by gravity alone. Additional information is contained in the original.

Marshall, J. R.↗

Uncertainty in Aerosol–Cloud Radiative Forcing Is Driven By Clean Conditions

Atmospheric aerosols and their impact on cloud properties remain the largest uncertainty in the human forcing of the climate system. By increasing the concentration of cloud droplets (Nd), aerosols reduce droplet size and increase the reflectivity of clouds (a negative radiative forcing). Central to this climate impact is the susceptibility of cloud droplet number to aerosol (β), the diversity of which explains much of the variation in the radiative forcing from aerosol–cloud interactions (RFaci) in global climate models. This has made measuring β a key target for developing observational constraints of the aerosol forcing.

Edward Gryspeerdt↗

The Effects of an Absorbing Smoke Layer on MODIS Marine Boundary Layer Cloud Optical Property Retrievals and Radiative Forcing

Clouds, aerosols, and their interactions are widely considered to be key uncertainty components in our current understanding of the Earth's atmosphere and radiation budget. The work presented here is focused on the quasi-permanent marine boundary layer . (MBL) clouds off the southern Atlantic coast of Africa and the effects on MODIS cloud optical property retrievals (MOD06) of an overlying absorbing smoke layer. During much of August and September, a persistent smoke layer resides over this region, produced from extensive biomass burning throughout the southern African savanna. The resulting absorption, which increases with decreasing wavelength, potentially introduces biases into the MODIS cloud optical property retrievals of the underlying MBL clouds. This effect is more pronounced in the cloud optical thickness retrievals, which over ocean are derived from the wavelength channel centered near 0.86 micron (effective particle size retrievals are derived from the longer-wavelength near-IR channels at 1.6, 2.1, and 3.7 microns). Here, the spatial distributions of the scalar statistics of both the cloud and aerosol layers are first determined from the CALIOP 5 km layer products. Next, the MOD06 look-up tables (LUTs) are adjusted by inserting an absorbing smoke layer of varying optical thickness over the cloud. Retrievals are subsequently performed for a subset of MODIS pixels collocated with the CALIOP ground track, using smoke optical thickness from the CALIOP 5km aerosol layer product to select the appropriate LUT. The resulting differences in cloud optical property retrievals due to the inclusion of the smoke layer in the LUTs will be examined. In addition, the direct radiative forcing of this smoke layer will be investigated from the perspective of the cloud optical property retrieval differences.

Meyer, Kerry↗

Unsteady Flowfield in a High-Pressure Turbine Modeled by TURBO

Forced response, or resonant vibrations, in turbomachinery components can cause blades to crack or fail because of the large vibratory blade stresses and subsequent high-cycle fatigue. Forced-response vibrations occur when turbomachinery blades are subjected to periodic excitation at a frequency close to their natural frequency. Rotor blades in a turbine are constantly subjected to periodic excitations when they pass through the spatially nonuniform flowfield created by upstream vanes. Accurate numerical prediction of the unsteady aerodynamics phenomena that cause forced-response vibrations can lead to an improved understanding of the problem and offer potential approaches to reduce or eliminate specific forced-response problems. The objective of the current work was to validate an unsteady aerodynamics code (named TURBO) for the modeling of the unsteady blade row interactions that can cause forced response vibrations. The three-dimensional, unsteady, multi-blade-row, Reynolds-averaged Navier-Stokes turbomachinery code named TURBO was used to model a high-pressure turbine stage for which benchmark data were recently acquired under a NASA contract by researchers at the Ohio State University. The test article was an initial design for a high-pressure turbine stage that experienced forced-response vibrations which were eliminated by increasing the axial gap. The data, acquired in a short duration or shock tunnel test facility, included unsteady blade surface pressures and vibratory strains.

Bakhle, Milind A.↗

Investigation of Longitudinal Aero-Propulsive Interactions of a Small Quadrotor Unmanned Aircraft System

Aerodynamic propulsive and airframe interactions significantly influence the forces and moments of multirotor vehicles. This paper presents recent results studying the influence of these effects on a small quadrotor vehicle in hover and forward flight. Aerodynamic interaction model development was explored utilizing system identification tools and incorporated into a previously developed NASA quadrotor flight dynamic simulation. The aerodynamic interaction model improved accuracy of the simulation in comparison to free-flight and static wind tunnel results. Comparisons between models of different fidelity were completed to demonstrate the effects of aerodynamic interaction on model accuracy and provide recommendations for modelling requirements.

George Altamirano↗

Subsonic aerodynamic characteristics of interacting lifting surfaces with separated flow around sharp edges predicted by a vortex-lattice method

Because the potential flow suction along the leading and side edges of a planform can be used to determine both leading- and side-edge vortex lift, the present investigation was undertaken to apply the vortex-lattice method to computing side-edge suction force for isolated or interacting planforms. Although there is a small effect of bound vortex sweep on the computation of the side-edge suction force, the results obtained for a number of different isolated planforms produced acceptable agreement with results obtained from a method employing continuous induced-velocity distributions. By using the method outlined, better agreement between theory and experiment was noted for a wing in the presence of a canard than was previously obtained.

Lamar, J. E.↗

Simulation System for Training in Laparoscopic Surgery

A computer-based simulation system creates a visual and haptic virtual environment for training a medical practitioner in laparoscopic surgery. Heretofore, it has been common practice to perform training in partial laparoscopic surgical procedures by use of a laparoscopic training box that encloses a pair of laparoscopic tools, objects to be manipulated by the tools, and an endoscopic video camera. However, the surgical procedures simulated by use of a training box are usually poor imitations of the actual ones. The present computer-based system improves training by presenting a more realistic simulated environment to the trainee. The system includes a computer monitor that displays a real-time image of the affected interior region of the patient, showing laparoscopic instruments interacting with organs and tissues, as would be viewed by use of an endoscopic video camera and displayed to a surgeon during a laparoscopic operation. The system also includes laparoscopic tools that the trainee manipulates while observing the image on the computer monitor (see figure). The instrumentation on the tools consists of (1) position and orientation sensors that provide input data for the simulation and (2) actuators that provide force feedback to simulate the contact forces between the tools and tissues. The simulation software includes components that model the geometries of surgical tools, components that model the geometries and physical behaviors of soft tissues, and components that detect collisions between them. Using the measured positions and orientations of the tools, the software detects whether they are in contact with tissues. In the event of contact, the deformations of the tissues and contact forces are computed by use of the geometric and physical models. The image on the computer screen shows tissues deformed accordingly, while the actuators apply the corresponding forces to the distal ends of the tools. For the purpose of demonstration, the system has been set up to simulate the insertion of a flexible catheter in a bile duct. [As thus configured, the system can also be used to simulate other endoscopic procedures (e.g., bronchoscopy and colonoscopy) that include the insertion of flexible tubes into flexible ducts.] A hybrid approach has been followed in developing the software for real-time simulation of the visual and haptic interactions (1) between forceps and the catheter, (2) between the forceps and the duct, and (3) between the catheter and the duct. The deformations of the duct are simulated by finite-element and modalanalysis procedures, using only the most significant vibration modes of the duct for computing deformations and interaction forces. The catheter is modeled as a set of virtual particles uniformly distributed along the center line of the catheter and connected to each other via linear and torsional springs and damping elements. The interactions between the forceps and the duct as well as the catheter are simulated by use of a ray-based haptic-interaction- simulating technique in which the forceps are modeled as connected line segments.

Basdogan, Cagatay↗

Fifth Annual Workshop on Space Operations Applications and Research (SOAR 1991), volume 2

This document contains papers presented at the Space Operation, Application and Research Symposium, hosted by NASA Johnson Space Center (JSC) and held at JSC in Houston, Texas, on July 9-11, 1991. More than 110 papers were presented at this Symposium, sponsored by the U.S. Air Force Phillips Laboratory, the University of Houston-Clear Lake, and NASA JSC. The technical areas covered were Intelligent Systems, Automation and Robotics, Human Factors, and Life Sciences, and Environmental Interactions. The U.S. Air Force and NASA programmatic overviews and panel discussions were also held in each technical area. These proceedings, along with the comments and suggestions made by the panelists and keynote speakers, will be used in assessing the progress made in joint USSAF/NASA projects and activities. Furthermore, future collaborative/joint programs will also be identified. The SOAR '91 Symposium is the responsibility of the Space Operations Technology Subcommittee (SOTS) of the USAF/NASA Space Technology Interdependency Group (STIG). The Symposium proceedings includes papers covering various disciplinees presented by experts from NASA, the Air Force, universities, and industry.

Kumar Krishen↗

Fifth Annual Workshop on Space Operations Applications and Research (SOAR 1991), volume 1

More than 110 papers were presented at this Symposium, sponsored by the U.S. Air Force Phillips Laboratory, the University of Houston-Clear Lake, and NASA JSC. The technical areas covered were Intelligent Systems, Automation and Robotics, Human Factors and Life Sciences, and Environmental Interactions. The U.S. Air Force and NASA programmatic overviews and panel discussions were also held in each technical area. These proceedings, along with the comments and suggestions made by the panelists and keynote speakers, will be used in assessing the progress made in joint USAF/NASA projects and activities. Furthermore, future collaborative/joint programs will also be identified. The symposium proceedings includes papers covering various disciplines presented by experts from NASA, the Air Force, universities, and industry.

Krishen, Kumar↗

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Hall, P.↗

Near-planar TS waves and longitudinal vortices in channel flow - Nonlinear interaction and focussing

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an O(1) relative amount. All the types of nonlinear interaction, however, can result in the formation of focused responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Hall, Philip↗

Thrust Stand Measurements of the Microwave Assisted Discharge Inductive Plasma Accelerator

Pulsed inductive plasma thrusters [1-3] are spacecraft propulsion devices in which electrical energy is capacitively stored and then discharged through an inductive coil. This type of pulsed thruster is electrodeless, with a time-varying current in the coil interacting with a plasma covering the face of the coil to induce a plasma current. Propellant is accelerated and expelled at a high exhaust velocity (O(10-100 km/s)) by the Lorentz body force arising from the interaction of the magnetic field and the induced plasma current. While this class of thruster mitigates the life-limiting issues associated with electrode erosion, pulsed inductive plasma thrusters require high pulse energies to inductively ionize propellant. The Microwave Assisted Dis- charge Inductive Plasma Accelerator (MAD-IPA), shown in Fig. 1, is a pulsed inductive plasma thruster that addressees this issue by partially ionizing propellant inside a conical inductive coil before the main current pulse via an electron cyclotron resonance (ECR) discharge. The ECR plasma is produced using microwaves and a static magnetic field from a set of permanent magnets arranged to create a thin resonance region along the inner surface of the coil, restricting plasma formation, and in turn current sheet formation, to a region where the magnetic coupling between the plasma and the theta-pinch coil is high. The use of a conical theta-pinch coil also serves to provide neutral propellant containment and plasma plume focusing that is improved relative to the more common planar geometry of the Pulsed Inductive Thruster (PIT) [1, 2]. In this paper, we describe thrust stand measurements performed to characterize the performance (specific impulse, thrust efficiency) of the MAD-IPA thruster. Impulse data are obtained at various pulse energies, mass flow rates and inductive coil geometries. Dependencies on these experimental parameters are discussed in the context of the current sheet formation and electromagnetic plasma acceleration processes.

Hallock, Ashley K.↗

Thrust Stand Measurements Using Alternative Propellants in the Microwave Assisted Discharge Inductive Plasma Accelerator

Storable propellants (for example water, ammonia, and hydrazine) are attractive for deep space propulsion due to their naturally high density at ambient interplanetary conditions, which obviates the need for a cryogenic/venting system. Water in particular is attractive due to its ease of handling and availability both terrestrially and extra-terrestrially. While many storable propellants are reactive and corrosive, a propulsion scheme where the propellant is insulated from vulnerable (e.g. metallic) sections of the assembly would be well-suited to process these otherwise incompatible propellants. Pulsed inductive plasma thrusters meet this criterion because they can be operated without direct propellant-electrode interaction. During operation of these devices, electrical energy is capacitively stored and then discharged through an inductive coil creating a time-varying current in the coil that interacts with a plasma covering the face of the coil to induce a plasma current. Propellant is accelerated and expelled at a high exhaust velocity (O(10-100 km/s)) by the Lorentz body force arising from the interaction of the magnetic field and the induced plasma current. While this class of thruster mitigates the life-limiting issues associated with electrode erosion, many pulsed inductive plasma thrusters require high pulse energies to inductively ionize propellant. The Microwave Assisted Discharge Inductive Plasma Accelerator (MAD-IPA) is a pulsed inductive plasma thruster that addressees this issue by partially ionizing propellant inside a conical inductive coil before the main current pulse via an electron cyclotron resonance (ECR) discharge. The ECR plasma is produced using microwaves and a static magnetic field from a set of permanent magnets arranged to create a thin resonance region along the inner surface of the coil, restricting plasma formation, and in turn current sheet formation, to a region where the magnetic coupling between the plasma and the theta-pinch coil is high. The use of a conical theta-pinch coil also serves to provide neutral propellant containment and plasma plume focusing that is improved relative to the more common planar geometry of the Pulsed Inductive Thruster (PIT). In this paper, we describe thrust stand measurements performed to evaluate the specific impulse and thrust efficiency of the MAD-IPA for a variety of propellants. Propellants tested include both widely-used, non-reactive noble gases like argon, and rarely-used propellants such as water, hydrazine and ammonia. Dependencies of impulse data on propellant species are discussed in the context of the current sheet formation and electromagnetic plasma acceleration processes.

Hallock, Ashley K.↗

Effect of Inductive Coil Geometry on the Thrust Efficiency of a Microwave Assisted Discharge Inductive Plasma Accelerator

Pulsed inductive plasma thrusters [1-3] are spacecraft propulsion devices in which electrical energy is capacitively stored and then discharged through an inductive coil. The thruster is electrodeless, with a time-varying current in the coil interacting with a plasma covering the face of the coil to induce a plasma current. Propellant is accelerated and expelled at a high exhaust velocity (O(10-100 km/s)) by the Lorentz body force arising from the interaction of the magnetic field and the induced plasma current. While this class of thruster mitigates the life-limiting issues associated with electrode erosion, pulsed inductive plasma thrusters require high pulse energies to inductively ionize propellant. The Microwave Assisted Discharge Inductive Plasma Accelerator (MAD-IPA) [4, 5] is a pulsed inductive plasma thruster that addressees this issue by partially ionizing propellant inside a conical inductive coil via an electron cyclotron resonance (ECR) discharge. The ECR plasma is produced using microwaves and permanent magnets that are arranged to create a thin resonance region along the inner surface of the coil, restricting plasma formation, and in turn current sheet formation, to a region where the magnetic coupling between the plasma and the inductive coil is high. The use of a conical theta-pinch coil is under investigation. The conical geometry serves to provide neutral propellant containment and plasma plume focusing that is improved relative to the more common planar geometry of the Pulsed Inductive Thruster (PIT) [2, 3], however a conical coil imparts a direct radial acceleration of the current sheet that serves to rapidly decouple the propellant from the coil, limiting the direct axial electromagnetic acceleration in favor of an indirect acceleration mechanism that requires significant heating of the propellant within the volume bounded by the current sheet. In this paper, we describe thrust stand measurements performed to characterize the performance (specific impulse, thrust efficiency) of the MAD-IPA thruster. Impulse data are obtained at various pulse energies, mass flow rates and inductive coil. geometries. Dependencies on these experimental parameters are discussed in the context of the current sheet formation and electromagnetic plasma acceleration processes.

Hallock, Ashley↗

Thrust Stand Measurements of a Conical Pulsed Inductive Plasma Thruster

Pulsed inductive plasma thrusters [1-3] are spacecraft propulsion devices in which electrical energy is capacitively stored and then discharged through an inductive coil. The thruster is electrodeless, with a time-varying current in the coil interacting with a plasma covering the face of the coil to induce a plasma current. Propellant is accelerated and expelled at a high exhaust velocity (O(10-100 km/s)) by the Lorentz body force arising from the interaction of the magnetic field and the induced plasma current. While this class of thruster mitigates the life-limiting issues associated with electrode erosion, pulsed inductive plasma thrusters can su er from both high pulse energy requirements imposed by the voltage demands of inductive propellant ionization, and low propellant utilization efficiencies. The Microwave Assisted Discharge Inductive Plasma Accelerator (MAD-IPA)[4], shown in Fig. 1 is a pulsed inductive plasma thruster that is able to operate at lower pulse energies by partially ionizing propellant with an electron cyclotron resonance (ECR) discharge inside a conical inductive coil whose geometry serves to potentially increase propellant and plasma plume containment relative to at coil geometries. The ECR plasma is created with the use of permanent mag- nets arranged to produce a thin resonance region along the inner surface of the coil, restricting plasma formation and, in turn, current sheet formation to areas of high magnetic coupling to the driving coil.

Hallock, Ashley K.↗

Thrust Stand Measurements of a Conical Inductive Pulsed Plasma Thruster

Inductive Pulsed Plasma Thrusters (iPPT) are spacecraft propulsion devices in which electrical energy is capacitively stored and then discharged through an inductive coil. The thruster is electrodeless, with a time-varying current in the coil interacting with a plasma covering the face of the coil to induce a plasma current. Propellant is accelerated and expelled at a high exhaust velocity (O(10 .. 100 km/s)) by the Lorentz body force arising from the interaction of the magnetic field and the induced plasma current. While this class of thruster mitigates the life-limiting issues associated with electrode erosion, inductive pulsed plasma thrusters can suffer from both high pulse energy requirements imposed by the voltage demands of inductive propellant ionization, and low propellant utilization efficiencies. A conical coil geometry may o er higher propellant utilization efficiency over that of a at inductive coil, however an increase in propellant utilization may be met with a decrease in axial electromagnetic acceleration, and in turn, a decrease in the total axially-directed kinetic energy imparted to the propellant.

Hallock, Ashley K.↗