Compression of an Accelerated Taylor State in SSX

In the Swarthmore Spheromak Experiment (SSX), compact toroidal plasmas are launched from a plasma gun and evolve into minimum energy twisted Taylor states. The plumes initially have a velocity $\sim40$ $km/s$, density $\sim0.4\times10^{16}$ $cm^{-3}$, and proton temperature $\sim 20$ $eV$. After formation, the plumes are accelerated by pulsed pinch coils with rise times $\tau_{1/4}=(\pi/2)\sqrt{LC}$ less than $1$ $\mu s$ and currents $I_{peak}= V_{0}/Z=V_0/\sqrt{L/C}$ on the order of $10^4$ $A$. The accelerated Taylor States are abruptly stagnated in a copper flux conserver, and over the course of $t<10$ $\mu s$, adiabatic compression is observed. The magnetothermodynamics of this compression do not appear to be dictated by the MHD equation of state $d/dt(P/n^\gamma)=0$. Rather, the compression appears to evolve according to the Chew-Goldberger-Low (CGL) double adiabatic model. CGL theory presents two equations of state, one corresponding with particle motion perpendicular to magnetic field in a plasma, the other to particle motion parallel to the field. We observe Taylor state compression most in agreement with the parallel equation of state: $d/dt(P_{\|}B^2/n^3)=0$.