[Paper Review] A model for the fast evaluation of prompt losses of energetic ions in stellarators

J. L. Velasco, I. Calvo+5 more|arXiv (Cornell University)|Jun 10, 2021

Magnetic confinement fusion researchPhysics and Astronomy36 references22 citations

TL;DR

This paper presents a fast, radially-local model based on the bounce-averaged drift-kinetic equation to classify energetic ion orbits as confined or prompt-loss in stellarators. By computing a critical drift parameter Γα, the model predicts configuration-dependent prompt losses with high accuracy compared to full Monte Carlo simulations, enabling efficient integration into stellarator optimization workflows for minimizing energetic ion losses.

ABSTRACT

A good understanding of the confinement of energetic ions in non-axisymmetric magnetic fields is key for the design of reactors based on the stellarator concept. In this work, we develop a model that, based on the radially-local bounce-averaged drift-kinetic equation, classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators. Such a model could in turn be employed in the optimization stage of the design of new devices.

Motivation & Objective

• To develop a computationally efficient model for predicting prompt losses of energetic ions in non-axisymmetric stellarator magnetic configurations.
• To classify particle orbits as confined or prompt-loss based on bounce-averaged radial drift, enabling rapid assessment of magnetic configuration performance.
• To validate the model against high-fidelity full-orbit Monte Carlo simulations (ASCOT) across a range of W7-X equilibria with varying β, mirror term, and rotational transform.
• To enable integration of the model into stellarator design optimization pipelines by ensuring speed and accuracy for real-time configuration screening.
• To explore the generality of the model beyond W7-X, including applications to heliotron and quasi-symmetric stellarators, and to assess its potential for guiding global simulation setups.

Proposed method

• The model uses the bounce-averaged drift-kinetic equation to compute the radial component of the magnetic drift, focusing on the bounce-averaged radial drift velocity.
• It introduces a critical parameter Γα = (2/π) arctan(|∂αJ| / |∂sJ|), which quantifies the ratio of tangential to radial drift components and determines orbit confinement.
• The model classifies orbits as prompt-loss if Γα > 0.5, indicating significant radial drift due to non-zero bounce-averaged radial magnetic drift.
• The method is implemented in the KNOSOS code, which rigorously treats magnetic drifts tangent to flux surfaces and is integrated into the STELLOPT optimization suite.
• Model predictions are validated against ASCOT Monte Carlo simulations across 71 free-boundary VMEC equilibria of the KJM stellarator configuration with varying β (0–7%) and parabolic pressure profiles.
• The model is extended to include radial electric fields via vE in the drift calculation, allowing for future inclusion of E×B effects and collisional diffusion in velocity space.

Experimental results

Research questions

• RQ1 Can a radially-local, bounce-averaged model accurately predict prompt losses of energetic ions in stellarators without full orbit tracking?
• RQ2 How does the critical parameter Γα correlate with prompt loss fractions across different magnetic configurations and β values in W7-X-like stellarators?
• RQ3 To what extent does the model capture the dependence of prompt losses on radial location (s) and magnetic configuration parameters (mirror term, rotational transform, β)?
• RQ4 Can the model identify non-monotonic or threshold-like behavior in prompt loss dependence on β, such as a minimum loss region around 2–3%?
• RQ5 How does the inclusion of radial electric fields and collisional effects modify the model’s predictions for prompt losses in realistic configurations?

Key findings

• The model predicts prompt loss fractions with high accuracy across a range of W7-X equilibria, showing strong agreement with ASCOT Monte Carlo simulations for energetic ions born at s = 0.06, 0.25, and 0.50.
• Prompt losses decrease approximately linearly with increasing β, with a minimum slope observed around 2–3% β for innermost flux surfaces (s = 0.06), indicating a potential optimization sweet spot.
• The model correctly captures the detrimental effect of low β on prompt losses at s = 0.06, where diamagnetic effects may worsen confinement, a feature not observed at s = 0.25.
• The model’s predictions remain robust across different magnetic configurations, including variations in mirror term and rotational transform, demonstrating its configurational sensitivity and predictive power.
• The model reveals that superbanana orbits—characterized by large bounce-averaged radial drift—are the dominant source of prompt losses, and their onset is well predicted by Γα > 0.5.
• The model’s success suggests that bounce-averaged drift-kinetic equations can quantitatively describe neoclassical transport of energetic ions, enabling faster global simulations by focusing on initial trapped-orbit classification.