Geometric optimization of vacuum electronic devices using adjoint techniques

Using particle-in-cell (PIC) simulations, we calculate shape gradients (sensitivity of some cost function to arbitrary perturbations of the shape boundary) for the optimization of self-consistent charged-particle trajectories with field-dependent emission. The number of parameters required to define the geometry of a vacuum electronic device---e.g. an electron gun or a nanoscale vacuum-channel transistor---is typically large (i.e. N ~ 100). It is therefore challenging to find optimal designs within the high-dimensional parameter space. Gradient-based optimization algorithms can efficiently find minima in large parameter spaces; however, a finite-difference calculation of the shape gradient requires (N + 1) PIC simulations---far too expensive to be practical. Antonsen et al. have shown that adjoint methods can be used to efficiently compute the gradient of an arbitrary cost function with respect to the entire device geometry using only two simulations [1]. In this work, we generalize Antonsen's work to accommodate field-dependent electron emission due to the electric field imposed by the device geometry, and we demonstrate the geometric optimization of a nanoscale vacuum-channel transistor.

[1]: Phys. Plasmas 26, 013109 (2019)