An Adjoint Formulation of Energetic Particle Confinement
Abstract
An adjoint formulation of energetic particle confinement in axisymmetric tokamak geometry is derived and evaluated using a physics-informed neural network (PINN). The PINN estimates the mean escape time of energetic ions by solving an inhomogeneous adjoint of the drift kinetic equation with a Lorentz collision operator, yielding predictions of fast ion loss in tokamak geometry due to direct ion orbit loss and collisional transport. To our knowledge, this is the first time a PINN has been used to solve the drift kinetic equation in tokamak geometry, a challenging problem due to the large time scale separation between the rapid transit time of energetic ions and their slow collisional time scale. It is shown that a careful and intentional design of a PINN is able to learn the mean escape time across the majority of the plasma volume, suggesting a path toward constructing a rapid surrogate for use within a broader optimization framework.
Keywords
Cite
@article{arxiv.2511.11968,
title = {An Adjoint Formulation of Energetic Particle Confinement},
author = {Christopher J. McDevitt and Jonathan S. Arnaud},
journal= {arXiv preprint arXiv:2511.11968},
year = {2026}
}