Stabilizing plasma instabilities cast as PDE-constrained optimization
Qin Li
University of Wisconsin-Madison
Mathematics
PDE-constrained optimization has become a powerful framework for addressing inverse and control problems in systems governed by partial differential equations (PDEs). Kinetic theory encompasses a broad class of equations that describe the non-equilibrium dynamics of interacting particles, and applying PDE-constrained optimization to these systems reveals a variety of unique and intriguing behaviors.
In this talk, I will discuss two representative cases. In the first, we explore the use of PDE-constrained optimization for stabilizing plasma instabilities—a challenge central to achieving controlled fusion. Dispersion-relation-based linear analysis and landscape analysis are employed to identify optimal stabilization strategies. In the second case, we highlight an essential yet often overlooked adjustment required for gradient computation when PDEs are solved using particle methods.