An Adjoint Formulation of Energetic Particle Confinement

TL;DR

This paper introduces a novel approach using physics-informed neural networks to solve the adjoint drift kinetic equation for energetic particle confinement in tokamaks, enabling efficient prediction of ion loss mechanisms.

Contribution

It is the first application of PINNs to the drift kinetic equation in tokamak geometry, providing a new method for rapid surrogate modeling of energetic particle confinement.

Findings

PINN successfully estimates mean escape time across plasma volume.

The approach captures ion loss due to orbit loss and collisional transport.

Potential for integration into optimization frameworks.

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.