Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

TL;DR

This paper introduces a spectrally accurate, differentiable bounce-averaging algorithm for stellarator optimization, enabling efficient, gradient-based improvements in stellarator performance metrics, including neoclassical ripple transport.

Contribution

It presents the first differentiable bounce-averaging algorithm integrated into stellarator optimization, allowing direct gradient-based reduction of neoclassical ripple transport.

Findings

Efficient optimization of stellarator performance metrics.

First direct optimization of neoclassical ripple transport.

Algorithm achieves spectral accuracy and automatic differentiation.

Abstract

We present a fast, spectrally accurate, automatically differentiable bounce-averaging algorithm implemented in the DESC stellarator optimization suite. Using this algorithm, we can perform efficient optimization of many objectives to improve stellarator performance, such as the $\epsilon_{\mathrm{eff}}^{3/2}$ proxy for the neoclassical transport coefficient in the $1/\nu$ (banana) regime. By employing this differentiable approximation, for the first time, we optimize a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the cost of differentiation is independent of the number of controllable parameters.