Applied-Field Magnetoplasmadynamic Thrusters, Part 2: Analytic Expressions for Thrust and Voltage

Abstract

The new visualization of applied-eld magnetoplasmadynamic thruster operation offered by numerical simulations with the MACH2 code is used to develop an analytic model. This model provides simple expressions for the thrust and voltage drop across the plasma that capture all of the trends and in most cases the magnitudes of a wide range of experimental data including tests at multiple laboratories on three propellants: argon, hydrogen, and lithium. It establishes that the thrust scales as the square root of the product of the applied-eld strength, discharge current, and mass-ow rate. Voltage scales linearly with applied-eld strength and is independent of discharge current and mass-ow rate. This model also provides additional insights that can be used to improve applied-eld magnetoplasmadynamicthruster performance. NomenclatureA = atomic weight, amu a = cathode radius to electrode length ratio, r c / L B = magnetic induction, T I = discharge current, A j = current density, A/m 2 L = electrode length, m Çm = mass-ow rate, kg/s p = pressure, N/m 2 Q = cross section, m 2 R = electrode radius ratio, r a / r c R = speci c gas constant, m 2 /s 2 -K Rm = magnetic Reynolds number r a = anode radius, m r c = cathode radius, m T H = heavy particle temperature, K U = characteristic speed, IB/ l , m/s V = discharge voltage, V V emf = electromotive voltage, V V f = fall voltage, V V p = plasma voltage, V V RH = resistive + Hall voltage, V v = axial velocity, m/s w = azimuthal velocity, m/s Z = charge number a = degree of ionization g F = ow ef ciency k = mean free path, m l = viscosity coef cient, kg/m-s q = mass density, kg/m 3 ¾ = stress tensor, N/m 2 } = ionization factor, i [a i / j a j Z 2 i Z 2 j ] X = Hall parameter Subscripts r, h , z = physical dimensions: radial, azimuthal, axial

Study of applied magnetic field magnetoplasmadynamic thrusters with particle-in-cell code with Monte Carlo collision. I. Computation methods and physical processes

“…The PIC thrust prediction trend was in good agreement with experimental data and MACH2 computations, 11 although agreement was not apparent in the analytic results presented in Ref. 10. The detailed consideration of the plasma acceleration has been more completely evaluated and discussed in an accompanying article (II).…”

Study of applied magnetic field magnetoplasmadynamic thrusters with particle-in-cell and Monte Carlo collision. II. Investigation of acceleration mechanisms

“…One way is using the above formulas and Eq. (11) or (12), which is based on the energy conversion assumption. The other way to compute the total thrust is…”

High Power MPD Thruster Performance Measurements

“…Prior analysis has shown that the proper application of axial and radial magnetic fields can increase thermal contributions to the total thrust through viscous heating of the propellant gas, which is anticipated to result in an improvement in thruster efficiency. 27,28 Previous research at Princeton University demonstrated quasi-steady self-field thruster operation up to several megawatts with hydrogen propellant, reaching efficiencies of 50% and specific impulse values in excess of 10000 s. 26 Although preliminary, the results indicate efficient high power operation of MPD thrusters can be achieved at specific impulse values of interest for future deep space exploration missions.…”

“…12,13,27,28 Although not used in the self-field performance data reported below, this option is available through the use of an un-cooled magnet consisting of insulated 4-AWG copper cabling wound on a 0.2-m (8") OD pvc pipe. The insulated cabling is continuously wound in 7 layers, with 18 turns per layer.…”

“…[19][20][21][22][23][24][25] Although gas-fed MPD thruster efficiencies have typically been lower than devices operated with lithium, 12,13,26 recent numerical models indicate that significantly improved performance can be achieved through the use of modified electrode geometries and the proper application of expansion nozzles and/or applied magnetic fields. 7,27,28 The use of non-condensable gas propellants mitigates possible ground handling and spacecraft contamination issues associated with lithium propellant, and may provide efficient thruster performance over a wide range of operating conditions. The NASA GRC effort is focused on the development and refinement of these high power gas-fed thruster technologies.…”