Magnetothermodynamics: measuring the equations of state of a compressible magnetized plasma.

Magnetothermodynamics (MTD) is the study of compression and expansion of magnetized plasma with an eye towards identifying equations of state for magneto-inertial fusion experiments. We present recent results from SSX experiments on the thermodynamics of compressed magnetized plasmas. In these experiments, we generate twisted flux ropes of magnetized, relaxed plasma accelerated from one end of a $1.5~m$ long copper flux conserver, and observe their compression in a closed conducting boundary installed at the other end. Plasma parameters are measured during compression. The instances of ion heating during compression are identified by constructing a PV diagram using measured density, temperature, and volume of the magnetized plasma. The theoretically predicted MHD and double adiabatic (CGL) equations of state are compared to experimental measurements to estimate the adiabatic nature of the compressed plasma. Since our magnetized plasmas relax to an equilibrium described by magnetohydrodynamics, one might expect their thermodynamics to be governed by the corresponding equation of state. However, we find that the magnetohydrodynamic equation of state is not supported by our data. Our results are more consistent with the parallel CGL equation of state suggesting that these weakly collisional plasmas have most of their proton energy in the direction parallel to the magnetic field.