Literature And External Packages

Core Physics Reference

  • Javier Escoto, Fast monoenergetic neoclassical transport coefficients in stellarators, PhD thesis, 2025: arXiv:2510.27513

This is the primary reference for:

  • the monoenergetic formulation

  • the Legendre-space block-tridiagonal solve

  • Onsager symmetry in the monoenergetic setting

  • the derivative and optimization discussion

Neoclassical Transport Theory

  • Helander and Sigmar, Collisional Transport in Magnetized Plasmas: Cambridge University Press

  • Helander 2014, theory of non-axisymmetric confinement: Reports on Progress in Physics

  • Helander and Simakov 2008, intrinsic ambipolarity and stellarator rotation: Physical Review Letters, PubMed

  • Landreman 2011, monoenergetic approximation limits: PPCF, arXiv:1102.2508

  • Landreman, Smith, Mollen, and Helander 2014, trajectory and collision-operator comparisons: Physics of Plasmas, arXiv:1312.6058

  • Redl, Angioni, Belli, and Sauter 2021, analytic bootstrap-current and neoclassical-conductivity formulae: PDF

  • Landreman, Buller, and Drevlak 2022, quasisymmetric-stellarator use of the Redl bootstrap-current formula and comparison to a 4D drift-kinetic solver: arXiv:2205.02914

  • Ferraro et al. 2025, implementation of Redl-style bootstrap-current modeling in an extended-MHD workflow using trapped fraction, collisionality, effective charge, and geometry factors: JPP

  • Beidler et al. 2011, international monoenergetic coefficient benchmark: Nuclear Fusion

These are the main references for:

  • radially local drift-kinetic ordering

  • thermodynamic forces

  • the ambipolar radial-current condition that determines E_r in non-quasisymmetric stellarators

  • neoclassical transport matrix structure

  • bootstrap-current interpretation

  • expected limits of exact parity between reduced monoenergetic workflows and broader drift-kinetic solvers

  • why the Redl precise-QS comparison is a separate analytic bootstrap-current validation from the reduced NTX+NEOPAX closure stress metric

  • why the finite-beta closure-target audit ranks local drivers such as epsilon, trapped fraction, and collisionality instead of introducing a scalar fitted current correction

  • the required benchmark surface for D11, D31, and D33

Spectral Collocation And Aliasing

  • Orszag 1971, filtering and alias elimination for Fourier representations: Journal of the Atmospheric Sciences

  • Escoto et al. 2024, spectral spatial/velocity discretization and convergence studies for fast monoenergetic neoclassical coefficients: arXiv:2312.12248

  • Escoto 2025 thesis, low-collisionality angular and Legendre convergence: arXiv:2510.27513

The classical product rules motivate explicit aliasing checks, but NTX’s operator contains reciprocal and geometry-derived coefficients that are not strictly band limited by the retained input spectrum. The implemented policy therefore preserves the physical collocation operator, enforces the retained- mode Nyquist floor, measures oversampling error on several geometries, and retains successive-grid convergence as the final gate.

Differentiable And Optimization Workflows

  • Paul, Abel, Landreman, and Dorland 2019, adjoint derivatives for neoclassical stellarator optimization: JPP, arXiv:1904.06430

  • McGreivy 2024, differentiable programming for computational plasma physics: arXiv:2410.11161

  • Blondel et al. 2022, modular implicit differentiation from converged optimality or residual equations: arXiv:2105.15183

  • Lee, Lazerson, Smith, Beidler, and Pablant 2024, direct optimization of neoclassical ion transport in stellarator reactors: Nuclear Fusion, arXiv:2406.04147

These references anchor NTX’s autodiff tests:

  • direct automatic differentiation against centered finite differences

  • prepared implicit or adjoint derivatives for many controls

  • inverse-design recovery from generated targets

  • uncertainty propagation from Jacobians

  • profile and geometry optimization with explicit physical metrics rather than reduced-response-only validation

Geometry-Breadth And Future Benchmark Families

  • Plunk, Landreman, and Helander 2019, direct construction of omnigenous magnetic fields near the magnetic axis: JPP, arXiv:1909.08919

  • Rodríguez, Plunk, and Jorge 2025, second-order quasi-isodynamic near-axis construction: JPP

  • Bindel, Landreman, and Padidar 2023/2025, direct optimization of fast-ion confinement: PPCF, arXiv:2302.11369

  • Calvo, Velasco, Helander, and Parra 2025, piecewise omnigenous fields with zero bootstrap current: Phys. Rev. E, arXiv:2505.02546

  • Liu, Yu, Velasco, and Zhu 2026, combined omnigenity and piecewise-omnigenity optimization: arXiv:2603.12139

These papers motivate the planned geometry-breadth lane. NTX should not promote hidden-symmetry, quasi-isodynamic, or omnigenous validation claims until the corresponding reusable geometry inputs, normalization audits, and convergence ladders are owned by the repository.

Momentum-Restoring Closure Theory

These references matter for:

  • momentum restoration beyond Lorentz pitch-angle scattering

  • Sonine/Laguerre moment equations

  • bootstrap-current sensitivity to higher-order closure moments

  • physically justified validation gates for reduced closure models

JAX And Python Geometry Packages

  • JAX

  • JAX gradient checkpointing, including the warning that checkpointing an entire function can add recomputation without reducing saved state

  • vmex

  • booz_xform_jax

  • NEOPAX

  • Lineax for possible structured linear solves after profiling identifies a real solve bottleneck

  • Equinox for possible PyTree/module and filtered-transform ergonomics after the public API boundaries are settled

Use these packages conservatively. The current NTX performance profile says the near-term speed lane is stable shapes, reusable compiled functions, prepared geometry reuse, and clear compile-versus-steady-state accounting. New dependencies should follow a measured profile improvement, not precede it.

Independent Validation Ecosystem

NTX users often want to compare against other neoclassical tools or pipelines. The repository documentation refers to:

  • SFINCS-JAX when discussing independent consistency checks

These packages are useful for trust-building and application workflows, but NTX’s equations, numerics, and public interface are defined by its own source tree and the Escoto thesis.