Ashley K. Hallock

Optimization of Electrodynamic Energy Transfer in Coilguns With Multiple, Uncoupled Stages

A 1-D model for inductive electromagnetic acceleration of projectiles using a coilgun has been nondimensionalized to find relevant scaling parameters. The dynamic impedance parameter, representing the ratio of the resonant period of the unloaded electrical circuit to the time the projectile is electromagnetically coupled to the coil, is the scaling term that can be adjusted to optimize the electromagnetic energy transfer process. The mutual inductance profile, which represents the ability to convert potential electromagnetic energy into projectile kinetic energy, was modeled for a specific geometry using a semi-empirical function previously found suitable for cylindrical pulsed inductive plasma accelerators. Contour plots representing coilgun efficiency were generated for varying initial projectile velocity across a range of dynamic impedances. The contour plots show that below a given initial velocity a dynamic impedance parameter can be selected to maximize energy transfer to the projectile. This optimum varies as a function of the initial velocity a projectile possessed when it enters the coilgun stage. Once the contour plot is generated for a geometry it can be used to optimize the acceleration process for any stage in a coilgun if the individual coils comprising the stages are electromagnetically uncoupled from each other and the velocity of the projectile as it exits the previous stage is known.

Effect of Inductive Coil Geometry and Current Sheet Trajectory of a Conical Theta Pinch Pulsed Inductive Plasma Accelerator

Results are presented demonstrating the e ect of inductive coil geometry and current sheet trajectory on the exhaust velocity of propellant in conical theta pinch pulsed induc- tive plasma accelerators. The electromagnetic coupling between the inductive coil of the accelerator and a plasma current sheet is simulated, substituting a conical copper frustum for the plasma. The variation of system inductance as a function of plasma position is obtained by displacing the simulated current sheet from the coil while measuring the total inductance of the coil. Four coils of differing geometries were employed, and the total inductance of each coil was measured as a function of the axial displacement of two sep- arate copper frusta both having the same cone angle and length as the coil but with one compressed to a smaller size relative to the coil. The measured relationship between total coil inductance and current sheet position closes a dynamical circuit model that is used to calculate the resulting current sheet velocity for various coil and current sheet con gura- tions. The results of this model, which neglects the pinching contribution to thrust, radial propellant con nement, and plume divergence, indicate that in a conical theta pinch ge- ometry current sheet pinching is detrimental to thruster performance, reducing the kinetic energy of the exhausting propellant by up to 50% (at the upper bound for the parameter range of the study). The decrease in exhaust velocity was larger for coils and simulated current sheets of smaller half cone angles. An upper bound for the pinching contribution to thrust is estimated for typical operating parameters. Measurements of coil inductance for three di erent current sheet pinching conditions are used to estimate the magnetic pressure as a function of current sheet radial compression. The gas-dynamic contribution to axial acceleration is also estimated and shown to not compensate for the decrease in axial electromagnetic acceleration that accompanies the radial compression of the plasma in conical theta pinches.

Effect of inductive coil geometry on the operating characteristics of an inductive pulsed plasma thruster

Summary form only given. The effect of inductive coil geometry on the operating characteristics of an inductive pulsed plasma thruster [1,2] is investigated analytically and experimentally. Model results indicate that the introduction of radial current sheet motion caused by a conical inductive coil geometry (versus a flat circular plate) increases the axial dynamic impedance parameter at which thrust efficiency is maximized and generally decreases the overall achievable thrust efficiency. Operational characteristics of two thrusters with inductive coils of different cone angles are explored through thrust stand measurements and time-integrated, unfiltered photography. Trends in impulse bit measurements indicate that, in the present configuration, the thruster with the inductive coil possessing a smaller cone angle produced larger values of thrust, in apparent contradiction to results of the model.

Single- and Repetitive-Pulse Conical Theta-Pinch Inductive Pulsed Plasma Thruster Performance

Impulse bits produced by conical theta-pinch inductive pulsed plasma thrusters possessing cone angles of 20°, 38°, and 60°, were quantified for 500-J/pulse operation by direct measurement using a hanging pendulum thrust stand. All three cone angles were tested in single-pulse mode, with the 38° model producing the highest impulse bits at roughly 1-mN-s operating on both argon and xenon propellants. A capacitor charging system, assembled to support repetitively pulsed thruster operation, permitted testing of the 38° thruster at a repetition rate of 5 Hz at power levels of 0.9, 1.6, and 2.5 kW. For similar conditions, the average thrust measured during repetitive-pulse operation exceeded the value obtained when the single-pulse impulse bit is multiplied by the repetition rate, suggesting that a greater impulse bit per pulse was produced when operating in the repetitive-pulse mode.

Effect of Inductive Coil Geometry on the Operating Characteristics of an Inductive Pulsed Plasma Thruster

Operational characteristics of two separate inductive thrusters with conical theta pinch coils of different cone angles are explored through thrust stand measurements and timeintegrated, unfiltered photography. Trends in impulse bit measurements indicate that, in the present experimental configuration, the thruster with the inductive coil possessing a smaller cone angle produced larger values of thrust, in apparent contradiction to results of a previous thruster acceleration model. Areas of greater light intensity in photographs of thruster operation are assumed to qualitatively represent locations of increased current density. Light intensity is generally greater in images of the thruster with the smaller cone angle when compared to those of the thruster with the larger half cone angle for the same operating conditions. The intensity generally decreases in both thrusters for decreasing mass flow rate and capacitor voltage. The location of brightest light intensity shifts upstream for decreasing mass flow rate of propellant and downstream for decreasing applied voltage. Recognizing that there typically exists an optimum ratio of applied electric field to gas pressure with respect to breakdown efficiency, this result may indicate that the optimum ratio was not achieved uniformly over the coil face, leading to non-uniform and incomplete current sheet formation in violation of the model assumption of immediate formation where all the injected propellant is contained in a magnetically-impermeable current sheet.

Recommended Practice for Use of Inductive Magnetic Field Probes in Electric Propulsion Testing

Inductive magnetic field probes (also known as B-dot probes and sometimes as B probes or magnetic probes) are often employed to perform field measurements in electric propulsion applications where there are time-varying fields. Magnetic field probes provide the means to measure these magnetic fields and can even be used to measure the plasma current density indirectly through the application of Ampere’s law. Measurements of this type can yield either global information related to a thruster and its performance or detailed local data related to the specific physical processes occurring in the plasma. The available literature is condensed into an accessible set of rules, guidelines, and techniques to standardize the performance and presentation of future B-dot probe measurements.