Theta Pinch Coil Design for SSX

We present the essential physics and design parameters behind a theta pinch coil used on SSX. The coil is used as an accelerator to drive flux behind a Taylor plume traveling about 30 km/sec. Operating between 25 and 40 kV on a time scale $<10$ $\mu s$, the design focuses on minimizing the quarter cycle rise time ($\frac{\pi}{2}\sqrt{LC}$) of the coil while maintaining the necessary precautions for working at high voltage. Our design works with 1.1 and 3.3 $\mu F$ capacitors and a maximum stored electrical energy of $U=\frac{1}{2}CV^2\simeq 880$ $J$ (at the lower capacitance). This electrical energy is converted into kinetic energy in the plume. Each plume has a mass greater than 30 $\mu g$, giving an initial kinetic energy of at least $14~J$. At perfect efficiency, the upper bound of the plume velocity will be 240 km/sec using the lower capacitance circuit.