James Clerk Maxwell Prize for Plasma Physics: Adjoint Methods in Plasma Physics and Charged Particle Dynamics

Physicists and engineers frequently encounter situations where calculations of the governing equations of a system of interest appear to need to be repeated many times to describe or optimize the system. This is the case when a particular state dependent quantity or metric needs to be determined in a large space of parameters. In this case a computational savings can be achieved if an "adjoint problem" can be found that produces the desired information without requiring multiple computations. A simple example is the design of a receiving antenna. One wishes to know and optimize the signal received as a function of the incident angle and polarization of incoming waves. It might appear that solution of Maxwell's field equations would have to be repeated for each possible incident direction and polarization. However, due to the reciprocal property of the governing equations, the desired information is obtained by treating the antenna as a transmitter and calculating the far field radiation pattern. Thus, one computation replaces many. The adjoint approach has previously been applied in circuit theory, electromagnetics, aerodynamics, plasma physics, as well as in other fields. In this talk I will review some problems from the areas of plasma physics and charged particle dynamics where adjoint methods have proven useful or possibly can be applied. These include calculating the efficiency of RF current-drive in tokamaks, the level of shot noise in gyrating electron beams, the sensitivity of 3D MHD equilibria to changes in confining magnetic fields, the sensitivity of charged particle sources and accelerator lattices to the shape of electrodes and the placement of guiding magnets, the sensitivity of beam driven microwave sources to changes in the dimensions of their RF structures. Challenges remain in many of these applications, and I hope to present these as well.