Justin M. Little

Thrust and efficiency model for electron-driven magnetic nozzles

A performance model is presented for magnetic nozzle plasmas driven by electron thermal expansion to investigate how the thrust coefficient and beam divergence efficiency scale with the incoming plasma flow and magnetic field geometry. Using a transformation from cylindrical to magnetic coordinates, an approximate analytical solution is derived to the axisymmetric two-fluid equations for a collisionless plasma flow along an applied magnetic field. This solution yields an expression for the half-width at half-maximum of the plasma density profile in the far-downstream region, from which simple scaling relations for the thrust coefficient and beam divergence efficiency are derived. It is found that the beam divergence efficiency is most sensitive to the density profile of the flow into the nozzle throat, with the highest efficiencies occurring for plasmas concentrated along the nozzle axis. Increasing the expansion ratio of the magnetic field leads to efficiency improvements that are more pronounced for incoming plasmas that are not concentrated along the axis. This implies that the additional magnet required to increase the expansion ratio may be worth the added complexity for plasma sources that exhibit poor confinement.

The Inuence of Induced Currents on Magnetic Nozzle Acceleration and Plasma Detachment

The inuence of induced currents on the acceleration and detachment of a uniformplasma expanding through a magnetic nozzle is investigated. A collisionless two-uid modelis used to solve for the ow of a cold-ion, hot-electron plasma through a diverging mag-netic eld. An iterative procedure is then employed to converge upon a magnetic eldsolution consistent with the plasma dynamics. The ratio of the kinetic energy density tothe magnetic eld energy density at the nozzle throat,

Plasma detachment and momentum transfer in magnetic nozzles

The nature of momentum transfer and the resulting thrust generation in magnetic nozzles is investigated. First, it is shown analytically using a Green’s function formulation that thrust transmission results from the interaction of the magnetic eld induced by the currents in the plasma with the current in the applied eld coil and is equal and opposite to the integral of the volumetric and surface Lorentz force densities due to the applied magnetic eld acting on the plasma. Second, using a two-uid plasma model, it shown that, contrary to previous belief [Ahedo and Merino, Phys. of Plas., 18(5) 2011], positive thrust production can occur for a detachment mechanism that induces paramagnetic plasma currents, as long as a criterion, which ensures the dominance of the force density due to the diamagnetic current at the plasma-vacuum boundary (which contributes to thrust) over that due to paramagnetic current, which results from the inertial detachment process (and which diminishes thrust), is satised. The model also shows that the thrust eciency suers with increasing magnetic eld divergence and plasma magnetization, which enhance the relative contribution of the paramagnetic current; and that inertial detachment occurs when a hybrid particle of mass mH = (meMi) 1=2 becomes demagnetized.

Critical Condition for Plasma Confinement in the Source of a Magnetic Nozzle Flow

The existence of a theoretically predicted critical magnetic field strength for efficient plasma confinement in helicon plasma thrusters is verified experimentally in the source of a magnetic nozzle (MN) flow. Control of the plasma confinement is crucial for enhancing the mass utilization efficiency of electric propulsion systems that employ MNs. Langmuir probe measurements of the density at the MN throat of a helicon plasma thruster as a function of the applied magnetic field strength indicate a transition from a low-confinement operation mode, in which a majority of the plasma diffuses to the solid walls of the plasma source before emerging from the thruster, to a highconfinement operation mode, in which the plasma preferentially exhausts downstream through the MN. This transition is shown to be governed by the anisotropic Péclet number, Pean, which is defined as the ratio of the advective (field aligned) to diffusive (cross field) mass transport rates. Experimental estimations of the mass utilization efficiency of the plasma source for various magnetic field strengths and plasma source lengths are shown to support an analytically derived scaling law, and suggest Pean ≫ 1 as a design criterion for MN plasma sources.

Propulsive performance of a finite-temperature plasma flow in a magnetic nozzle with applied azimuthal current

The plasma flow in a finite-electron-temperature magnetic nozzle, under the influence of an applied azimuthal current at the throat, is modeled analytically to assess its propulsive performance. A correction to the nozzle throat boundary conditions is derived by modifying the radial equilibrium of a magnetized infinite two-population cylindrical plasma column with the insertion of an external azimuthal body force for the electrons. Inclusion of finite-temperature effects, which leads to a modification of the radial density profile, is necessary for calculating the propulsive performance, which is represented by nozzle divergence efficiency and thrust coefficient. The solutions show that the application of the azimuthal current enhances all the calculated performance parameters through the narrowing of the radial density profile at the throat, and that investing power in this beam focusing effect is more effective than using the same power to pre-heat the electrons. The results open the possibility for the design of a focusing stage between the plasma source and the nozzle that can significantly enhance the propulsive performance of electron-driven magnetic nozzles.

Influence of the Applied Magnetic Field Strength on Flow Collimation in Magnetic Nozzles

The influence of the magnetic field strength on the collimation of the plasma flow in an electron-driven magnetic nozzle is investigated experimentally. A collimated plasma flow is required for efficient plasma propulsion to minimize plume divergence losses. Faraday probe measurements are used to estimate the ion streamlines in the diverging field of the magnetic nozzle. It is found that decreasing the strength of the applied magnetic field invokes a transition from a collimated plume to an under-collimated plume, where an under-collimated plume is defined such that the plume divergence is greater than the magnetic field divergence. Langmuir and emissive probe measurements reveal that the transition to an under-collimated plume is accompanied by anomalous deceleration of the ion beam along the nozzle centerline, broadening of the transverse density profile, and the disappearance of an ion-confining potential well at the plasma periphery. This transition offers a guideline for reducing the plume divergence of an electron-driven magnetic nozzle.

Experimental Verification of Plasma Focusing by Azimuthal Current in a Magnetic Nozzle

The theoretically predicted ability of an applied azimuthal current to focus the plasma in a magnetic nozzle (MN) was investigated experimentally. The azimuthal current was induced through the Hall effect by applying a radial electric field with a pair of concentric electrodes upstream of the throat of an electron-driven magnetic nozzle fed by an RF plasma source. Spatially resolved probe measurements of plasma density and plasma potential inside the plasma source and in the external plume show that the induced azimuthal current leads to significant focusing of the plasma on the center axis, and is a far more efficient way to enhance the centerline density than increasing the RF power in the source. This opens the door to the potential use of a focusing stage to increase the thrust efficiency of magnetic nozzles by decreasing beam divergence.

Electric propulsion system scaling for asteroid capture-and-return missions

The requirements for an electric propulsion system needed to maximize the return mass of asteroid capture-and-return (ACR) missions are investigated in detail. An analytical model is presented for the mission time and mass balance of an ACR mission based on the propellant requirements of each mission phase. Edelbaum’s approximation is used for the Earth-escape phase. The asteroid rendezvous and return phases of the mission are modeled as a low-thrust optimal control problem with a lunar assist. The numerical solution to this problem is used to derive scaling laws for the propellant requirements based on the maneuver time, asteroid orbit, and propulsion system parameters. Constraining the rendezvous and return phases by the synodic period of the target asteroid, a semiempirical equation is obtained for the optimum specific impulse and power supply. It was found analytically that the optimum power supply is one such that the mass of the propulsion system and power supply are approximately equal to the total mass of propellant used during the entire mission. Finally, it is shown that ACR missions, in general, are optimized using propulsion systems capable of processing 100 kW – 1 MW of power with specific impulses in the range 5,000 – 10,000 s, and have the potential to return asteroids on the order of 10 − 10 tons.

An analytical model for the ow of collisionless plasma along magnetic elds

ow-averaged plasma parameters from their spatial non-uniformities. The result gives analytical solutions for the spatial variation of the potential, plasma density, and ion Mach number. Application of the model to the problem of supersonic plasma expansion from a magnetic nozzle shows good agreement with both numerical simulations and experimental measurements. Notably, the development of a downstream radial electric eld to preserve quasi-neutrality is the main factor that drives non-uniformities within the plasma. This result is used to explain experimentally observed focusing of the plasma exhaust with respect to the applied magnetic eld. Finally, the competition in the expansion process, between the conversion of thermal energy into kinetic energy and the loss to plume divergence of the kinetic energy useful for propulsion yields an expression for the maximum thrust coecient of a magnetic nozzle in terms of the parameters of the plasma source.