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Radial transport of electric current by electromagnetic microturbulence in tokamaks

Using nonlinear gyrokinetic simulations with newly implemented electromagnetic diagnostics in GENE and CGYRO, this study demonstrates that electromagnetic microturbulence, particularly through electron-driven Maxwell stress in microtearing modes, can generate sufficient turbulent current flux to potentially modify the safety-factor profile in high-beta tokamak plasmas.

Original authors: Haomin Sun, Toby Adkins, Justin Ball, Yann Camenen

Published 2026-08-05

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CC BY 4.0

Original authors: Haomin Sun, Toby Adkins, Justin Ball, Yann Camenen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, glowing donut made of super-hot gas, swirling faster than a jet engine. This is a tokamak, a machine designed to mimic the power of the sun and provide us with clean, limitless energy. Inside this donut, the gas is so hot that atoms break apart into a soup of tiny, charged particles called ions and electrons. To keep this soup from melting the walls of the machine, scientists use powerful magnetic fields to hold it in place, like an invisible cage. But here's the tricky part: the gas inside is never perfectly still. It's constantly churning and bubbling with tiny, chaotic storms called turbulence. These storms act like a leaky bucket, letting heat and particles escape, which cools the fuel and stops the fusion reaction.

To understand how to fix these leaks, scientists study how these tiny particles move. They look at how the "spin" of the gas (its rotation) and the flow of electricity (the current) move around the donut. Usually, they think the heavy ions (like tiny bowling balls) do all the heavy lifting in moving momentum, while the super-light electrons (like ping-pong balls) are too small to matter much. However, in these extreme conditions, the rules of the game change. The magnetic fields themselves can wiggle and shake, creating a new kind of interaction that might let those tiny ping-pong balls suddenly become the main players in the game. Understanding this is crucial because if the electricity flow changes unexpectedly, it could destabilize the whole machine, causing the fusion reaction to sputter out.

In this new study, researchers used powerful computer simulations to peek inside these turbulent storms and see exactly how the heavy ions and light electrons are moving the toroidal angular momentum (the spin) and the electric current. They built a brand-new "ruler" inside their computer codes to measure these movements, paying special attention to the invisible magnetic forces that usually get ignored. They focused on two specific types of magnetic storms: one driven by tiny tears in the magnetic field (microtearing modes) and another driven by the pressure of the gas pushing against the magnetic cage (kinetic ballooning modes).

The team found something surprising. In the storms driven by those tiny magnetic tears, the heavy ions contributed less to moving the spin. Instead, the light electrons took charge, but not by pushing with their own bodies. They moved the spin by tugging on the magnetic field lines themselves, creating a "Maxwell stress" that acted like a giant, invisible hand shoving the current around. Even though the electrons were less effective at moving the spin compared to how much heat they were moving, they were surprisingly good at moving the electric current. In fact, the amount of current they were shuffling around was big enough to potentially mess with the safety of the magnetic cage, changing the shape of the magnetic field in a way that could compete with the natural currents that keep the machine running.

When they looked at the other type of storm (the pressure-driven one), the story was a bit different. The heavy ions were still the main movers of the spin, doing the job they usually do. However, even in this case, the electrons were still quietly tugging on the magnetic field lines. If the scientists had ignored this magnetic tug-of-war, they would have completely missed the fact that the electrons were moving enough current to be a big deal. The study suggests that in future, high-performance fusion machines—especially the compact, donut-shaped ones designed for power plants—ignoring these electromagnetic electron effects could lead to wrong predictions about how the machine spins and how its magnetic safety net holds together. The researchers didn't prove this happens in a real machine yet, but their simulations strongly suggest that these invisible magnetic hands are a major player in the game of fusion energy.

Technical Summary: Radial Transport of Electric Current by Electromagnetic Microturbulence in Tokamaks

Problem Statement
In tokamak plasmas, turbulent transport of toroidal angular momentum dictates rotation profiles, which in turn influence confinement and stability. While the ion contribution to this transport is well-understood in the electrostatic limit, the electron contribution is often neglected due to the small electron mass. However, a radial flux of toroidal angular momentum is intrinsically linked to a radial flux of toroidal current. Because the current flux scales with the charge-to-mass ratio, a seemingly negligible electron momentum flux can correspond to a substantial turbulent current flux. The divergence of this current flux can redistribute the toroidal current density, potentially modifying the safety-factor ( $q$ ) profile. This effect is particularly critical in high-beta plasmas where electromagnetic fluctuations (specifically microtearing modes and kinetic ballooning modes) become dominant, yet the role of electromagnetic terms in momentum transport and their connection to current redistribution has not been fully explored.

Methodology
To investigate this, the authors implemented complete electromagnetic momentum-flux diagnostics in two local gyrokinetic codes: GENE and CGYRO. Previous implementations in these codes lacked contributions from perturbed electromagnetic fields ( $\delta A_\parallel$ and $\delta B_\parallel$ ). The authors derived the full expressions for the toroidal angular momentum flux, separating contributions from particle motion and electromagnetic fields (specifically the Maxwell stress and terms related to parallel current fluctuations).

The validity of these new diagnostics was established through rigorous linear and nonlinear cross-code benchmarks:

Linear Benchmarks: Simulations of single linear modes with non-zero ballooning angles were performed to break up-down symmetry. Results for particle flux and various momentum flux components showed agreement within 10% (improving to <5% at higher gradients) between GENE and CGYRO.
Nonlinear Benchmarks: Simulations were conducted in up-down asymmetric magnetic equilibria to generate momentum flux without relying on flow shear. Time-averaged steady-state fluxes for particles, heat, and momentum agreed within 5% between the two codes.

These validated diagnostics were then applied to nonlinear simulations of Microtearing Mode (MTM) and Kinetic Ballooning Mode (KBM) driven turbulence across a range of plasma beta ( $\beta_e$ ) values.

Key Results

MTM-Driven Turbulence:
- In MTM-dominated turbulence, the total momentum transport is inefficient relative to heat transport (low Prandtl number, $Pr \approx 0.04$ ).
- Contrary to electrostatic expectations, the momentum flux is dominated by the electron contribution to the turbulent Maxwell stress ( $\Pi^{\delta A_\parallel}_{a,EM}$ ).
- The electron momentum flux exceeds a reference scale derived from the bootstrap current ( $\Pi_{BS}$ ) for $\beta_e \gtrsim 0.025$ . This suggests that the associated turbulent current flux is large enough to compete with collisional processes maintaining the bootstrap current.
- This result holds regardless of whether the momentum flux is driven by rotation shear or toroidal Mach number.
KBM-Driven Turbulence:
- In the transition from Ion Temperature Gradient (ITG) to KBM-dominated turbulence, both heat and total momentum fluxes increase, accompanied by a significantly larger Prandtl number.
- The total transport remains dominated by the electrostatic ion contribution.
- However, the electron momentum flux rises sharply during the transition, almost entirely due to the Maxwell stress term.
- In the KBM-dominated case, the electron momentum flux also exceeds the bootstrap-based reference scale ( $\Pi_{BS}$ ).
- Crucially, retaining the Maxwell stress term is essential; without it, the electron momentum flux would be underestimated, and the potential for significant current redistribution would be missed.

Significance and Claims
The paper claims that electromagnetic fluctuations qualitatively alter turbulent momentum transport in tokamaks. The primary finding is that the electron contribution to the momentum flux, mediated by the Maxwell stress, can become substantial enough to drive a turbulent current flux that competes with the bootstrap current.

The authors assert that:

Neglecting electromagnetic momentum transport in high-beta plasmas (such as those in spherical tokamaks or future devices like STEP) could lead to incorrect predictions not only of rotation profiles but also of the leading-order evolution of current and safety-factor profiles.
This effect allows for a regime where total toroidal angular momentum transport is inefficient (preserving rotation gradients) while simultaneously causing significant redistribution of toroidal current.
The study establishes the numerical existence of this effect and verifies the diagnostics required to measure it, identifying specific parameter regimes (high $\beta_e$ , MTM/KBM dominance) where it becomes important.

The authors remain modest regarding the global implications, noting that while the local flux magnitude suggests importance, the actual modification of the current profile depends on the sign, radial variation, and global divergence of the flux, which cannot be determined from local simulations alone. They conclude that developing a physical theory for these dynamics and determining their global consequences are subjects for future work.

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