[Paper Review] Optimization of quasisymmetric stellarators with self-consistent bootstrap current and energetic particle confinement

Matt Landreman, S. Buller+1 more|arXiv (Cornell University)|May 5, 2022

Magnetic confinement fusion research60 references51 citations

TL;DR

This paper presents a computationally efficient method to optimize quasisymmetric stellarators with self-consistent bootstrap current and improved energetic particle confinement. By leveraging the isomorphism between quasisymmetric stellarators and tokamaks, it applies accurate analytic bootstrap current formulas from axisymmetric theory—dramatically reducing computational cost—while enforcing consistency between the MHD equilibrium current profile and kinetic theory predictions via a penalty in the objective function. The result is a new class of stellarator designs with significantly reduced alpha particle losses and excellent neoclassical confinement at high beta.

ABSTRACT

Quasisymmetry can greatly improve the confinement of energetic particles and thermal plasma in a stellarator. The magnetic field of a quasisymmetric stellarator at high plasma pressure is significantly affected by the bootstrap current, but the computational cost of accurate stellarator bootstrap calculations has precluded use inside optimization. Here, a new efficient method is demonstrated for optimization of quasisymmetric stellarator configurations such that the bootstrap current profile is consistent with the geometry. The approach is based on the fact that all neoclassical phenomena in quasisymmetry are isomorphic to those in axisymmetry. Therefore accurate formulae for the bootstrap current in tokamaks, which can be evaluated rapidly, can be applied also in stellarators. The deviation between this predicted parallel current and the actual parallel current in the magnetohydrodynamic equilibrium is penalized in the objective function, and the current profile of the equilibrium is included in the parameter space. Quasisymmetric configurations with significant pressure are thereby obtained with self-consistent bootstrap current and excellent confinement. In a comparison of fusion-produced alpha particle confinement across many stellarators, the new configurations have significantly lower alpha energy losses than many previous designs.

Motivation & Objective

• To develop a computationally efficient method for optimizing quasisymmetric stellarators that self-consistently include bootstrap current effects.
• To address the high computational cost of accurate stellarator bootstrap current calculations in optimization workflows.
• To improve energetic particle confinement by ensuring consistency between the MHD equilibrium current profile and neoclassical kinetic theory predictions.
• To demonstrate that analytic tokamak bootstrap current formulas can be reliably applied to quasisymmetric stellarators via the isomorphism with axisymmetric systems.
• To produce new stellarator configurations with low alpha particle losses and excellent neoclassical transport at high plasma pressure (beta).

Proposed method

• Utilizes the isomorphism between quasisymmetric stellarators and axisymmetric tokamaks, where neoclassical phenomena—including bootstrap current—are mathematically equivalent under coordinate transformation.
• Applies the recent analytic bootstrap current formula by Redl et al. (valid for any collisionality and aspect ratio) to quasisymmetric stellarator geometry, bypassing costly 3D drift-kinetic solves.
• Introduces a penalty term in the optimization objective function that enforces consistency between the MHD equilibrium current profile and the predicted kinetic parallel current.
• Treats the current profile as a free parameter in the optimization, allowing self-consistent solutions without iterative fixed-point schemes.
• Employs a flexible optimization framework (Simsopt) to explore parameter space and generate new quasisymmetric configurations with desired current and pressure profiles.
• Validates the method by comparing results against full 3D drift-kinetic calculations and benchmarking alpha particle confinement performance.

Experimental results

Research questions

• RQ1 Can analytic tokamak bootstrap current formulas be reliably applied to quasisymmetric stellarators via the isomorphism with axisymmetric systems?
• RQ2 How can self-consistent bootstrap current profiles be efficiently enforced in stellarator optimization without costly fixed-point iterations?
• RQ3 What is the impact of self-consistent bootstrap current on energetic particle confinement in high-beta quasisymmetric stellarators?
• RQ4 How do the new optimized configurations compare to previous designs in terms of alpha particle loss rates?
• RQ5 Can the isomorphism-based approach achieve accuracy comparable to full 3D drift-kinetic calculations while reducing computational cost?

Key findings

• The isomorphism-based method enables accurate bootstrap current calculation in quasisymmetric stellarators at a fraction of the computational cost of full 3D drift-kinetic solvers.
• The method achieves self-consistency between MHD equilibrium current profiles and kinetic predictions through a penalty in the objective function, avoiding unstable fixed-point iterations.
• New quasisymmetric stellarator configurations were generated with self-consistent current profiles and high beta (up to β ≈ 5%), demonstrating excellent energetic particle confinement.
• Compared to previous designs, the new configurations exhibit significantly reduced fusion-produced alpha particle energy losses, especially at high beta.
• The analytic formula by Redl et al. shows high accuracy when applied to quasisymmetric stellarators, with results closely matching full 3D kinetic calculations.
• The approach is scalable and suitable for use in large-scale optimization of next-generation stellarator reactors with stringent confinement and current profile requirements.