Properties of the FRX-L Field Reversed Configuration (FRC) inferred from density profile measurements assuming MHD equilibrium

A laser interferometer probes the line integrated time history of plasma density along eight chords of the FRX-L high-density ($\sim 10^{17} $ cm$^{-3}$) FRC. The data is Abel and tomographically inverted to provide density profiles. The FRC is roughly in an axisymmetric rotational MHD equilibrium for a $3$ $\mu $s interval between the initial implosion that produces the FRC and an $n=2$ rotational instability that terminates confinement. $B_{z}(r,t)$ may then be inferred, given an external magnetic field measurement. The period during which its area integral\ approximates an independent axial flux measurement self-consistently identifies the equilibrium interval. Basic FRC properties such as temperature, poloidal flux, and $\alpha $ (rotational to ion diamagnetic drift frequency ratio) are then inferred. Results indicate that poloidal flux estimates based on magnetic and axial flux measurements alone are conservative, and that the critical $\alpha $ for $n=2$ instability (estimated two ways) is roughly between 0.5 and 1.0.