Physics-Based Estimation of Toroidal Momentum Transport in Tokamaks

This repository implements a physics-based method to estimate the effective toroidal momentum diffusivity ($χ_ϕ^\text{eff}$) in tokamak plasmas, with explicit treatment of ion–neutral interactions, applied to experimental rotation profiles from the TCABR tokamak.

The method relies on a Fourier–Bessel expansion of the measured toroidal velocity profile and on the ion–neutral collision frequency, enabling a direct estimation of $χ_ϕ^\text{eff}$ in plasmas with no external momentum input. The results are strictly validated against collisionality regimes (ν*) and compared with established neoclassical and semi-empirical transport models.

This code accompanies and reproduces the analysis presented in:

Novaes, D. O., Severo, J. H. F., Rizzato, F. B. et al.
Estimation of Effective Momentum Diffusivity and Its Correlation with Neutral Particle Density Based on Toroidal Rotation Profiles in the TCABR Tokamak.
Brazilian Journal of Physics, 55, 43 (2025).
DOI: 10.1007/s13538-024-01681-x

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Scientific Scope

Primary Output

• Radial profile of the effective toroidal momentum diffusivity $χ_ϕ^\text{eff}$.
• Quantitative comparison with neoclassical (Helander) and semi-empirical transport models.
• Collisionality-based regime validation (Pfirsch–Schlüter).

What this code is

• A reproducible analysis pipeline linking experimental rotation data to momentum transport coefficients.
• A tool for studying intrinsic rotation and ion–neutral momentum transport in medium-size tokamaks.

What this code is not

• A general-purpose transport solver.
• A predictive integrated modelling framework.

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Method Summary

The effective momentum diffusivity is computed following the derivation detailed in the reference article. The core estimator is:

$\chi_{\varphi}^\text{eff} = \sum_{j}\frac{1}{\lambda_{j}^{2}} \left( \frac{3}{4\epsilon} - 1 \right)\nu_\text{iH₀}$

where:

• the eigenvalues λⱼ, from a Helmholtz-like equation, are obtained from the zeros of a Fourier–Bessel expansion fitted to the experimental toroidal velocity profile,
• the ion–neutral collision frequency $ν_\text{iH₀}$ depends on the ion temperature and neutral density profiles,
• experimental uncertainties are propagated using a Monte Carlo approach.

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Code Structure

• main_analysis.m — main analysis pipeline.
• src/ — core physics and analysis routines.
• plotting/ — plotting utilities.
• data/ — experimental input profiles.
• results/ — cached outputs.

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Requirements

• MATLAB R2021a or newer
• Parallel Computing Toolbox
• Optimization Toolbox
• Curve Fitting Toolbox

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Licence

MIT Licence.

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Author

Douglas Oliveira Novaes
dougnovaes@alumni.usp.br