Simultaneous inference of multiple stagnation performance metrics in Magnetized Liner Inertial Fusion Experiments using Bayesian Data Assimilation*

The Magnetized Liner Inertial Fusion (MagLIF) concept being explored on the Z machine at Sandia National Laboratories is a promising route to achieving high fusion yields (>>1 MJ) on a future pulsed power generator.  MagLIF uses the current supplied by Z to compress a preheated and pre-magnetized cylindrical beryllium liner containing fusion fuel.  A pre-imposed axial magnetic field (B_z,o) acts to insulate the hot fuel from the cold liner, allowing PdV work to raise the fuel temperature via compression by the magnetically driven liner.  This concept has shown exciting performance gains in recent years demonstrating Gbar pressures and confinement of charged fusion products at stagnation.  However direct experimental measurement of critical performance metrics has remained elusive.  Here we demonstrate a Bayesian data assimilation technique that is able to simultaneously infer these key metrics (e.g., stagnation pressure, mix, confinement properties, etc.) with rigorously defined uncertainties by self-consistently matching x-ray power, x-ray imaging, x-ray spectral, neutron yield, and neutron spectral diagnostics through a reduced model of the system.  Extensive testing using analytic models as well as 1D and 3D MHD calculations is shown.  We apply this tool to a large suite of MagLIF experiments and examine trends in performance and stagnation properties with input conditions such as laser energy, magnetic field strength, fuel density, among others.  We analyze these trends in the context of analytic scaling theory, exploring the impacts of multiple different potential degradation mechanisms.  Finally, we examine the effects of three-dimensional structure on performance and provide a path towards better constraint of three-dimensional stagnation properties using synthetic experiments to guide diagnostic investments.