Measurement of the Applied-Field Component of the Thrust of a Lithium Lorentz Force Accelerator

Abstract

The operation of an inverted-pendulum thrust stand designed to directly measure the applied-field thrust component of a steady-state applied-field magnetoplasmadynamic thruster is presented. This measurement, which is necessary for improving and validating thrust models, is achieved by mechanically isolating the solenoid from the thruster so that the solenoid can move independently. The deflection of the solenoid is compared to deflection by known forces to determine the applied-field thrust component. The thrust stand is found to be accurate to ±9 mN over a total range of 1200 mN. Two measurement methods are implemented to account for tare forces resulting from azimuthal currents to the thruster electrodes and are shown to agree with one another. As a proof-of-concept, the first direct measurements of the applied-field component of the thrust from a 30 kW lithium Lorentz force accelerator operating at 400 A, 8 mg/s lithium mass flow rate, and 0.056 T applied-field strength give a measured force of 108 ± 14 mN. This measurement agrees with the value predicted by measuring the total thrust and subtracting out all other thrust components. Nomenclature a 0 Ion sound speed, m/s A Area, m 2 B A Applied magnetic field, T J Current, A k Thrust coefficienṫ m Mass flow rate, kg/s p Pressure, N/m 2 r Electrode radius, m T Thrust, N Subscript ae Anode exit plane AF Applied-field c Cathode GD Gasdynamic SF Self-field

MPD Thruster Technology and Its Limitations

“…There is a power regime for each component when that component MPDTs, and it is caused by the current's interaction with its own self-induced magnetic field. In AF-MPDTs, the SF thrust component is often dominating at high power [12]. Brittany Lee Ilardi in their report found that current runs radially from the anode toward the cathode in a classic self-field MPDT, then axially down the cathode.…”

“…Self-Field MPD (William J. Coogan et al, 2016) studied that in an MPDT, there are three thrust generating mechanisms: Self-field (SF), Gas dynamic (GD), Applied-field (AF). There is a power regime for each component when that component MPDTs, and it is caused by the current's interaction with its own self-induced magnetic field.…”

“…The speed of sound of representative points in the flow will scale like −1 (M is the molecular mass of gas) and from equation (12) we see that Mach number must vary like the quantity,…”