Microtearing Mode in Fusion Plasmas

• Microtearing mode (MTM) is an electromagnetic instability driven by the electron temperature gradient, characterized by tearing-parity eigenfunctions that localize magnetic reconnection at rational surfaces.
• Diagnostic methods include evaluating electron diamagnetic frequencies, rational-surface alignment, and clustering criteria, which clarify MTM identification and regime-dependent behavior.
• MTMs play a key role in fusion plasmas by generating magnetic fluctuations and stochastic fields that substantially enhance electron heat transport in both core and pedestal regions.

Microtearing mode (MTM) denotes an electromagnetic, tearing-parity microinstability driven primarily by the electron temperature gradient, with fluctuations in the parallel vector potential $A_\parallel$ that imply perturbed magnetic field-line reconnection at micro-scales. In linear structure, $A_\parallel$ is even across the resonant surface and localized there, while $\phi$ is odd; the mode propagates in the electron diamagnetic direction and is important because it can generate magnetic fluctuations, magnetic islands, stochastic magnetic fields, and predominantly electron heat transport in both core and pedestal plasmas (Predebon et al., 2013, Hatch et al., 2020, Cu-Castillo et al., 22 Oct 2025).

1. Defining characteristics and diagnostic criteria

Two formulas recur across MTM studies. The electron diamagnetic frequency is written as

$$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$

and the electron-temperature-gradient contribution as

$$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$

Modes resonate at rational surfaces satisfying

$q(r) = \frac{m}{n}.$

Because MTM frequency is close to $\omega_{e*}$, sharp radial localization of $\omega_{e*}$ can localize the instability to a narrow region of the plasma (Hatch et al., 2020).

Tearing parity remains the defining structural signature. In gyrokinetic eigenfunctions, $\phi$ is odd-symmetric and elongated, while $A_\parallel$ is even and localized near the resonant layer; in slab formulations, the corresponding boundary conditions are $A_\parallel$0 and $A_\parallel$1 (Predebon et al., 2013). Reactor-oriented STEP calculations identify the subdominant electromagnetic branch as MTM using tearing parity, propagation in the electron diamagnetic direction, $A_\parallel$2-dominated structure, and an “ion-scale in $A_\parallel$3, electron scale in $A_\parallel$4” radial character (Kennedy et al., 2023).

Pedestal studies have also formalized practical classification criteria. In a DIII-D pedestal ensemble, k-means clustering over six linear features strongly favored two classes, and the adopted MTM criteria were

$A_\parallel$5

These criteria agreed with the clustering classification in $A_\parallel$6 out of $A_\parallel$7 simulations, including $A_\parallel$8 simulations mutually identified as MTM (Hatch et al., 24 Mar 2026). In spherical-tokamak CGYRO studies, tearing character was also quantified by

$A_\parallel$9

with MTMs identified by $\phi$0 (Patel et al., 2024).

These diagnostics matter because parity alone does not isolate the transport channel. MTMs are usually identified not just by tearing parity, but by the conjunction of tearing parity, electron-diamagnetic propagation, and predominantly electromagnetic electron heat transport.

2. Linear drive physics and collisionality dependence

The classical collisional picture treats MTM as an electron-temperature-gradient-driven electromagnetic instability in which velocity-dependent electron–ion collisions create a phase lag between the parallel inductive electric field and the perturbed magnetic field. In slab theory with a comprehensive collision model, the essential destabilization mechanism is the lag of the parallel inductive electric field behind the magnetic field owing to the time-dependent thermal force and inertia force induced by the velocity-dependent electron–ion collisions (Yagyu et al., 2022). A simple pedestal MTM dispersion relation used for comparison with gyrokinetics is

$\phi$1

In JET pedestal calculations, this formula captured the collisionality threshold quantitatively and major qualitative features, especially a peak in growth rate around $\phi$2 followed by stabilization at larger $\phi$3, while not reproducing the absolute growth-rate magnitude well (Hatch et al., 2020).

The collisional picture is not universal. A central revision came from studies showing that the collisionless limit is not unique. If non-ideal electron mechanisms remain active—most importantly electron inertia and magnetic-drift-induced non-ambipolar currents—linearly unstable collisionless or nearly collisionless MTMs can exist (Predebon et al., 2013). In collisionless low-$\phi$4 toroidal plasmas, the derived gyrokinetic dispersion relation shows that MTMs remain driven by the electron temperature gradient and that this instability drive is mediated by magnetic drifts (Chandran et al., 2022). This implies that statements such as “MTMs are stabilized as $\phi$5” depend on which non-ideal physics is retained.

Edge and spherical-tokamak studies add further nuance. In the shallow-gradient region just inside the MAST pedestal top, the dominant edge MTM does not show the familiar finite-collisionality maximum; instead, the study suggests a collisionless trapped-particle mechanism that is sensitive to magnetic drifts and enhanced by high magnetic shear and high trapped-particle fraction (Dickinson et al., 2012). In MAST core calculations, the instability is still driven by the electron temperature gradient, but is not substantially affected by either of the destabilising mechanisms proposed in previous theoretical models; instead the instability is destabilised by interactions with magnetic drifts, and the electrostatic potential (Applegate et al., 2011).

A recurring misconception is that tearing parity alone identifies canonical MTM physics. That is not generally valid. In steep-gradient collisionless gyrokinetics, the $\phi$6 high-order KBM eigenstate has the same mode structure parity as the micro-tearing mode, while remaining pressure-gradient-driven even without collisions and electron temperature gradient (Xie et al., 2017). In slab geometry, a collisionless fine-scale tearing-parity instability can survive down to $\phi$7, but is best interpreted as a tearing-parity harmonic of the slab ETG mode rather than as the standard collisional slab MTM (Geng et al., 2020). This suggests that MTM identification requires parity, propagation, transport signature, and parameter dependence to be considered together.

3. Pedestal localization, rational-surface selection, and global structure

Pedestal MTMs differ from many core MTMs because radial profile variation across the mode width becomes decisive. In the JET pedestal, the observed high-frequency “washboard” fluctuations appear as separated toroidal-mode-number bands rather than a continuous unstable sequence. For JET pulse $\phi$8, the lower band lies at roughly $\phi$9 with dominant $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$0, and the higher band at roughly $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$1 with dominant $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$2; the authors summarize this as two bands centered on $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$3 and $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$4 (Hatch et al., 2020). Global gyrokinetic simulations showed that only those $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$5 whose rational surfaces align with the local maximum of $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$6 become strongly unstable. In the modified case with a $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$7 reduction in $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$8 and a $$\omega_{e*} = k_y \rho_s c_s \left(\frac{1}{L_n} + \frac{1}{L_{Te}}\right),$$9 increase in electron temperature gradient, the relevant rational surfaces shifted so that $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$0 and $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$1 aligned with the $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$2 peak, and unstable MTMs appeared at $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$3, matching the spectrogram much better (Hatch et al., 2020).

This rational-surface picture makes global treatment essential. In the same JET study, local calculations incorrectly predicted instability at intermediate $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$4 and produced a strongly unstable MHD-like mode that disappeared in global calculations. The point is not merely numerical. The pedestal drive region is so narrow that neighboring rational surfaces can sample very different values of $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$5, so toroidal mode selection becomes a genuinely global profile effect rather than a local dispersion-curve property.

A related experimental demonstration was carried out in the DIII-D pedestal. There the expected laboratory-frame frequency was constructed as

$$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$6

with the Doppler shift determined by the radial electric field, and fast vertical jogs of about $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$7 cm in $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$8 ms were used to move edge rational surfaces independently of the natural inter-ELM profile evolution. Edge-localized magnetic fluctuations with $$\omega_{T*} = k_y \rho_s c_s \left(\frac{1}{L_{Te}}\right).$$9 then exhibited inverted chirping when the jog displaced candidate rational surfaces away from the local $q(r) = \frac{m}{n}.$0 peak, providing a perturbative validation of the resonant-surface MTM model (Nelson et al., 2021).

A more recent DIII-D pedestal survey of $q(r) = \frac{m}{n}.$1 equilibria from three discharges placed this behavior in a broader stability map. MTMs were found primarily in the mid-pedestal steep-gradient region, often in the high-$q(r) = \frac{m}{n}.$2, low-$q(r) = \frac{m}{n}.$3 ballooning second-stable region where KBMs are weakened or absent. In that ensemble, MTMs exhibited threshold behavior near pre-ELM conditions, and their mixed parity, appreciable electromagnetic heat flux, and non-negligible particle transport motivated the interpretation that they can constrain pedestal pressure rather than electron temperature alone (Hatch et al., 24 Mar 2026).

4. Nonlinear saturation, stochasticity, and transport

Nonlinear studies show that MTM saturation is not described by a single mechanism. In global JET pedestal simulations, MTMs saturated by locally relaxing the background electron temperature gradient. As the mode grew, it flattened $q(r) = \frac{m}{n}.$4 in a narrow radial region around the rational surface, which reduced $q(r) = \frac{m}{n}.$5 and stabilized the mode; the resulting nonlinear frequency downshift brought the simulated frequencies into much closer agreement with the measured bands (Hatch et al., 2020). The same simulations reported electromagnetic heat flux levels “quite close” to the inter-ELM power loss $q(r) = \frac{m}{n}.$6 MW, while earlier ETG calculations in the same pedestal had produced $q(r) = \frac{m}{n}.$7 MW, supporting the interpretation that MTMs and ETG together likely account for pedestal electron heat transport (Hatch et al., 2020).

In the MAST core, the first converged nonlinear MTM simulations showed that magnetic topology itself controls saturation. MTMs generated magnetic islands at rational surfaces, and the radial extent of the stochastic region caused by island overlap played an important role in determining the saturation level of the MTM-driven heat flux. The practical geometric indicator was the comparison of island width and resonant-surface spacing, with strong transport associated with

$q(r) = \frac{m}{n}.$8

At $q(r) = \frac{m}{n}.$9 with $\omega_{e*}$0, $\omega_{e*}$1 was negligible and ETG heat flux was comparable to the experimental electron heat flux, while at $\omega_{e*}$2 with $\omega_{e*}$3, $\omega_{e*}$4 became significantly larger and comparable to both $\omega_{e*}$5 and $\omega_{e*}$6 (Giacomin et al., 2023). In that study, saturation depended strongly on zonal magnetic fields: removing zonal $\omega_{e*}$7 caused a strong increase in heat flux, whereas removing zonal $\omega_{e*}$8 had little effect (Giacomin et al., 2023).

Equilibrium $\omega_{e*}$9 shear introduces a further nonlinear control parameter, but not a universal one. In local spherical-tokamak simulations, MTM-driven transport in a MAST case was more resilient to suppression via $\omega_{e*}$0 shear, while the corresponding NSTX case was significantly suppressed. The explanation was the magnetic-shear dependence of $\omega_{e*}$1: at low $\omega_{e*}$2, growth varied weakly with ballooning angle, whereas at higher $\omega_{e*}$3, growth peaked at $\omega_{e*}$4 and became stable at larger $\omega_{e*}$5, allowing sheared flow to advect the mode into linearly stable ballooning angles (Patel et al., 2024). This suggests that MTM control by flow shear depends strongly on the safety-factor and magnetic-shear profiles rather than on a universal decorrelation rule.

5. Device dependence: spherical tokamaks, conventional tokamaks, stellarators, and reactor studies

Comparative core studies show both shared MTM physics and strong device dependence. Local linear GYRO calculations for NSTX, ASDEX Upgrade, and JET found MTMs as the dominant linear instability for the selected core parameters in all three devices. In all three, finite collisionality was needed for MTMs to become unstable and the electron temperature gradient was the fundamental drive. At the same time, the dependence of growth rate on $\omega_{e*}$6 differed sharply: in NSTX it increased with the electron temperature gradient, while in JET and ASDEX Upgrade it varied weakly and non-monotonically (Moradi et al., 2013). The dominant MTM transport fingerprint in that comparison was strong electron heat flux via $\omega_{e*}$7, with small ion heat and particle fluxes (Moradi et al., 2013).

Spherical-tokamak studies emphasize the role of magnetic drifts and $\omega_{e*}$8. In MAST core calculations, the prevalence of MTMs in spherical tokamak plasmas was attributed primarily to the higher value of plasma $\omega_{e*}$9 and the enhanced magnetic drifts due to the smaller radius of curvature, while flux-surface shaping and the large trapped particle fraction were found not to be the primary destabilizing mechanisms (Applegate et al., 2011). Reactor-scale STEP calculations then found a different ordering: a collisional MTM branch at ion binormal scales but electron radial scales was linearly unstable, with tearing parity, electron-diamagnetic propagation, and strong $\phi$0 character, but it remained subdominant to a hybrid-KBM branch under the reference conditions. STEP also differed from some earlier burning-ST concepts by lacking the collisionless intermediate-scale MTM branch, apparently because the larger density gradient produced by pellet fuelling strongly stabilises the collisionless MTM (Kennedy et al., 2023).

Stellarator results extend MTM physics beyond tokamak symmetry. In multiscale nonlinear GENE simulations of W7-X, electromagnetic ion-scale MTMs coexisted with ETG turbulence, but the isotropic nature of stellarator ETGs limited their suppressive effect, allowing MTMs to persist. In the dedicated electromagnetic case, the MTM-associated electromagnetic electron heat flux fell from $\phi$1 to $\phi$2 when ETG scales were included—significant weakening, but not full suppression (Merlo et al., 8 Aug 2025). A later W7-X study identified an NBI discharge in which MTM turbulence dominated transport in a high-density-gradient regime. There the simulated fluxes,

$\phi$3

were in close agreement with experimental estimates,

$\phi$4

and MTM dominance was attributed to the suppression of ITG and density-gradient-driven trapped-electron turbulence by low magnetic shear and the nearly max-$\phi$5 W7-X geometry (Cu-Castillo et al., 22 Oct 2025).

6. Reduced models, integrated pedestal frameworks, and open controversies

A substantial methodological development has been the use of reduced models and surrogates to interpret MTM observations rapidly. The SLiM reduced model for slab-like pedestal MTMs makes the rational-surface-to-$\phi$6-peak distance an explicit input, and its trained neural-network surrogate, SLiM$\phi$7, was reported to achieve about $\phi$8 accuracy and $\phi$9 s/mode, roughly a $A_\parallel$0 speedup over the optimized direct SLiM dispersion solver (Curie et al., 2023). In NSTX case studies, that speed enabled profile scans that matched observed $A_\parallel$1 to $A_\parallel$2 magnetic bands and constrained the pedestal $A_\parallel$3 profile through rational-surface alignment (Curie et al., 2023).

Pedestal-wide integrated workflows place MTM in a coupled transport–stability landscape. An approach combining OMFIT PRO_create equilibrium scans, ideal-MHD stability with ELITE and GATO, and local gyrokinetic transport from CGYRO/QLGYRO identified a recurring four-region structure: first-stable KBM, a KBM-unstable band, a KBM second-stable region, and an MTM-unstable region at high pedestal drive. In SPARC-like scans, KBM and MTM heat fluxes were found to increase strongly with toroidal field, suggesting that access to the KBM second-stability region may become significantly more difficult in high toroidal field devices (McClenaghan et al., 24 Jun 2026). A DIII-D reduced transport model went further by coupling quasilinear MTM and ETG transport to ASTRA; with tuned free parameters it reproduced experimental pedestal $A_\parallel$4 and $A_\parallel$5 profiles, and when the separatrix density was doubled from $A_\parallel$6 to $A_\parallel$7, it predicted an approximately $A_\parallel$8 reduction in pedestal-top pressure attributable to increased MTM and ETG transport (Hatch et al., 24 Mar 2026).

Several controversies remain active. The first concerns collisionality: JET pedestal work explicitly concluded that MTM growth rates may either increase or decrease with collision frequency depending on parameters, so slogans such as “MTMs require finite collisionality” or “growth always rises with collisionality” are too crude for pedestal conditions (Hatch et al., 2020). The second concerns identification: tearing parity is necessary but not sufficient, because the $A_\parallel$9 KBM has the same parity as MTM (Xie et al., 2017), and collisionless slab tearing-parity modes can be better interpreted as ETG harmonics whose electromagnetic component is actually stabilizing (Geng et al., 2020). The third concerns model hierarchy: local flux-tube or quasilinear MTM treatments can be highly informative, but global pedestal mode-number selection, stochastic magnetic-layer formation, and nonlinear frequency downshifts can depend on physics that those reduced descriptions do not capture. A plausible implication is that MTM will remain a multi-regime concept rather than a single universal dispersion relation.

In present usage, “microtearing mode” therefore denotes a family of tearing-parity, electromagnetic electron-driven microinstabilities whose common signatures are clear, but whose onset, saturation, and transport impact remain strongly regime dependent. Across core, pedestal, tokamak, and stellarator studies, the central questions are no longer whether MTMs exist, but which non-ideal mechanism is active, how rational-surface geometry selects the mode, and when the resulting magnetic fluctuations become transport-dominant.