# Current Sheet Physics for Pulsed Electromagnetic Accelerators

## Current Sheet Mass Leakage Study

One form of electric propulsion is a pulsed plasma thruster. A pulsed plasma thruster (PPT) is a device that accelerates a propellant in a pulsed manner, not steadily. By changing the pulse frequency one can change the thrust of these devices, therefore PPTs are useful for a wide range of applications. Gas-fed PPTs such as the one we are studying work in the following manner. A certain amount of propellant gas is introduced into a gap between positively and negatively charged electrodes. A switch then exposes the gas to high voltage, which breaks the gas particles down into ions and electrons, forming a plasma. This plasma forms in a thin sheet between the electrodes and it conducts current. This current sheet is accelerated out of the device by the force created from the interaction of the current and the induced magnetic field. As the sheet moves, it picks up the neutral gas like a snowplow, pushing all of the propellant out of the device at a very high velocity (~40 km/s), creating thrust to move the spacecraft.

We find in studying these current sheets that the sheet rarely acts as an ideal "snowplow" as described above. One way in which the operation of the device deviates from ideality is by allowing plasma to leak behind the sheet into a wake along the cathode. This means that a significant portion of the propellant is not accelerated to a high velocity. This has a serious impact on the efficiency of PPTs.

In a pulsed electromagnetic accelerator a current sheet accelerates a propellant gas through the $$j\times B$$ force. In the ideal case all of the gas is entrained and accelerated by the sheet. An observed departure from this ideality is current sheet mass leakage, a phenomenon through which a wake of plasma is left behind the sheet along the cathode. This leads to a decrease in sweeping efficiency, the percent of the available propellant mass that is contained in the sheet. The present work describes experiments and an analytical model designed to quantify and explain the effect of current sheet mass leakage on the performance of the accelerator. High speed photography, interferometry and magnetic field probing are employed to gain an understanding of the evolution of the sheet and the performance of the device. After an initial bifurcation phase, the current sheet in this device enters a steady-state phase of propagation during which the mass, velocity and canting angle are approximately constant. It is found that non-dimensional impulse and efficiency decrease with increasing propellant pressure for discharges using argon propellant, because of a decreasing sweeping efficiency. The performance of neon discharges stays constant with pressure because the loss of mass from the current sheet is made up for by a commensurate increase in wake mass. The performance of helium and hydrogen discharges increases with pressure, because while the sweeping efficiency stays constant, the wake velocity increases. The trends in the behavior of the sweeping efficiency have been explored with an analytical model of the current sheet. It is proposed that in the lighter propellants, which have a higher ion Hall parameter, the ions in the sheet are subject to a directed motion towards the cathode, causing a high degree of leakage of plasma into the wake. The heavier propellants, with low ion Hall parameters, are subject only to a diffusive leakage of ions at the cathode. However, these sheets are found to be highly permeable to the ambient propellant.

To view a movie generated from contour plots of the magnetic field taken in the accelerator, click here. The color scale is in Tesla.

To view a movie generated from contour plots of the current density taken in the accelerator, click here. The color scale is in kA/cm^3.

To view a movie generated from contour plots of the electron numbert density taken in the accelerator, click here. The color scale is in cm^-3. Note that due to the limitations of the measurement technique and the fact that the plasma density is less repeatable than the magnetic field, this movie appears much less smooth.

## Current Sheet Canting Study

This research effort (both experimental and theoretical) was aimed at gaining an understanding of the canting of propagating current sheets.

Click here to see a movie of a typical firing of the accelerator (or click here to see a close-up of the breech during the first few microseconds of firing); a current sheet is observed to propagate from the breech to exit at a speed of approximately 35 [km/s]. Two things, among others, are evident in the movie. The first is that the current sheet severely tilts, with the anode attachment leading the cathode. Also, a dense blanket of luminous plasma on the cathode is seen to trail behind the current sheet. Both of these phenomena have negative implications for the performance of pulsed plasma thrusters. The leakage phenomenon is explained above, and the canting phenomenon has been explored in detail. This project has been completed.

Former students:
• Jack Berkery
• Tom Markusic