# Adjoint Methods in Charged Particle Dynamics

**Speaker:** Thomas Antonsen, University of Maryland, College Park, USA

**Title:** Adjoint Methods in Charged Particle Dynamics

**Abstract:** 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. It is often the case that only a particular state dependent quantity or metric needs to be determined. 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. In this talk I will review some problems from the area of charged particle dynamics where adjoint methods have proven useful. A new example is the optimization of electron beam optics in beam sources used in microwave and millimeter wave amplifiers.