Gradient-based optimization of a multiphysics whole-device model of a fusion Z-Pinch

The sheared flow-stabilized Z Pinch has garnered much attention as a promising fusion energy device concept, and is favored for its compact size and high beta. The plasma current is a key parameter for fusion Z Pinches, since, assuming adiabatic compression, the fusion yield scales with the eleventh power of current. It is understood (Skolar et al., Physics of Plasmas (2023)) that the plasma current in a Z Pinch is affected by plasma-electrode interactions, including the Langmuir sheath on-axis, electron emission, and sputtering. To accurately model these effects requires a kinetic model of the plasma-electrode boundary. On the other hand, the plasma current is a function of the whole device circuit dynamics, which can be modeled as a series RLC circuit. In this work, we present an integration of these two models--a kinetic model of the plasma sheath at the electrodes and an ODE model for the device circuit--in an end-to-end differentiable multiphysics code. Flexible multiphysics modeling is further enabled by the use of Tesseracts, an open-source library for reusable, reproducible, differentiable software components. Our end-to-end differentiable methodology enables us to apply gradient-based optimization to the Z Pinch operating trajectory. We present results of gradient-based optimization studies for the Z Pinch circuit parameters and initial plasma parameters with respect to time-integrated fusion yield.