Diffusion-Based MTMs in Pedestal Transport

• Diffusion-based MTMs are microinstabilities characterized by a reduced mixing-length ansatz and gyrokinetic calibration to quantify electron heat transport in tokamak pedestals.
• The approach identifies MTMs using specific markers like electromagnetic heat-flux fraction, frequency localization, and tearing parity, effectively distinguishing them from competing instabilities.
• Integration with transport solvers such as ASTRA validates the model by reproducing experimental temperature and density profiles, underpinning predictive core-edge simulations.

Diffusion-based Microtearing Modes (MTMs) play a pivotal role in setting transport limits in strongly shaped magnetic fusion edge plasmas, particularly in the pedestal region of H-mode tokamak discharges. These microinstabilities, characterized by their electromagnetic nature and tearing parity structure, are dominantly responsible for electron heat and particle transport within a specific range of pressure gradient and magnetic shear. The modern reduced modeling framework for MTM-induced pedestal transport employs quasilinear diffusion coefficients based on mixing-length arguments and leverages high-fidelity gyrokinetic simulations for calibration, ultimately enabling self-consistent core-edge predictive calculations in 1D transport solvers such as ASTRA (Hatch et al., 24 Mar 2026).

1. Theoretical Framework for Diffusion-Based MTM Transport

The electron thermal diffusivity associated with MTMs is modeled using a mixing-length ansatz expressed as

$$\chi_{e,\rm mix}(r) = c_0 \max_{k_y} \frac{\gamma(k_y, r)}{\langle k_\perp^2 \rangle(k_y, r)},$$

where $\gamma$ is the linear growth rate (normalized to $a/c_s$), $k_y$ is the binormal wavenumber, and $\langle k_\perp^2 \rangle$ represents the field-line-following, eigenfunction-weighted perpendicular wavenumber. The constant $c_0$ is a calibration parameter tuned to nonlinear simulation data, with $c_0 = 3.0$ found to yield quantitative agreement with global gyrokinetic simulations (Hatch et al., 24 Mar 2026). The approach generalizes readily to global (real-space) and local (flux-tube) representations, with the global form typically taking the dominant toroidal harmonic for maximizing $\gamma/k_\perp^2$.

2. Quantitative Characterization and Mode Identification

Diffusion-based MTM models require quantitative mode-identification according to:

• Electromagnetic heat-flux fraction,

$$\hat Q_{\rm EM} = \frac{Q_{e,\,\rm EM}}{Q_{e,\,\rm ES} + Q_{i,\,\rm ES}} > 0.2,$$

• Frequency localized near the electron diamagnetic direction,

$\omega/\omega_{*e} < -0.5,$

• Tearing parity, quantified by

$\gamma$0

These fingerprints ensure that transport is attributed strictly to MTM physics and not to competing modes such as kinetic ballooning modes (KBMs) or electron temperature gradient (ETG) turbulence. Typical MTM parameter ranges for the edge pedestal are $\gamma$1–$\gamma$2, $\gamma$3–$\gamma$4, and onset is controlled by a strong threshold in the normalized pressure gradient $\gamma$5, i.e., $\gamma$6 for $\gamma$7 and $\gamma$8 sharply for $\gamma$9.

3. Surrogate Model Construction and Calibration

The quasilinear surrogate $a/c_s$0 interpolates local gyrokinetic results over a grid of pressure and density gradient scalings ($a/c_s$1, $a/c_s$2) and poloidal wavenumbers $a/c_s$3. All other geometric and kinetic parameters—magnetic shear $a/c_s$4, safety factor $a/c_s$5, Shafranov shift, collisionality—are implicitly included by the construction of the simulation database. This surrogate is then applied in reduced transport models by evaluating the diffusion coefficient at each radius and applying Gaussian smoothing over a minor-radius width of a few percent to avoid numerical artifacts associated with pixel-by-pixel discontinuities (Hatch et al., 24 Mar 2026).

4. Transport Solver Integration and Experimental Consistency

When coupled to the ASTRA 1D transport code, the MTM $a/c_s$6 surrogate, together with neoclassical thermal transport (NCLASS), empirically fitted ETG transport ($a/c_s$7, $a/c_s$8), and interpretive particle sources, quantitatively reproduces experimental temperature and density pedestal profiles. Only two free parameters—the MTM mixing-length prefactor $a/c_s$9 and the smoothing width—are tuned. The simultaneous fit to $k_y$0 and $k_y$1 over confinement-time timescales validates the MTM diffusive paradigm and links edge-scale turbulence to macroscopic confinement observations.

5. Radial Structure, Nonlinear Sensitivity, and Separatrix Effect

The spatial profile of the MTM-driven transport is highly nonuniform, with $k_y$2 vanishing below the mid-pedestal $k_y$3, peaking in the high-gradient, low-magnetic-shear region ($k_y$4–0.975 minor radius), and decaying outside. Peak values range from $k_y$5–$k_y$6 m$k_y$7/s (pre-ELM to onset) to $k_y$8–$k_y$9 m$\langle k_\perp^2 \rangle$0/s (steepest equilibria). Raising the plasma separatrix density $\langle k_\perp^2 \rangle$1 at fixed pedestal-top identity doubles or triples the MTM $\langle k_\perp^2 \rangle$2 at mid-pedestal and triggers a $\langle k_\perp^2 \rangle$3 reduction in pedestal pressure, consistent with ITPA H-mode scaling database trends. This behavior traces to increased collisionality, raised $\langle k_\perp^2 \rangle$4, and weaker density gradients, making both MTM and ETG transport more virulent in the edge (Hatch et al., 24 Mar 2026).

6. Implications for Core-Edge Modeling and Predictive Fusion Transport

Diffusion-based MTM models supply the missing physical mechanism for coupling separatrix and pedestal conditions—magnetic shear, pressure gradient, density, and collisionality—to global confinement properties. The thresholded, first-principles-based $\langle k_\perp^2 \rangle$5 fills the “second-stability gap” between KBM-dominated and ETG-dominated regimes, enabling next-generation core-edge coupling and predictive modeling of the burning plasma scenarios. Extensions to integrate additional transport channels (e.g., $\langle k_\perp^2 \rangle$6 shear stabilization, KBM foot transport, advanced kinetic closures) are natural within the surrogate diffusion-based paradigm, providing a robust foundation for simulation-driven scenario optimization and control (Hatch et al., 24 Mar 2026).