Trapped Gyro-Landau Fluid (TGLF) Model

• TGLF is a quasilinear, local gyro-fluid transport model that reduces the five-dimensional gyrokinetic system into a finite set of fluid-moment equations for predicting tokamak turbulence.
• It employs moment truncation with Landau-fluid closures and bounce averaging of trapped particles to convert linear eigenmode spectra into empirical particle, heat, and momentum fluxes.
• Recent surrogate models like TGLF-SINN leverage neural networks to achieve full differentiability and significant speedups, enabling integrated, real-time simulations of tokamak transport.

The Trapped Gyro-Landau Fluid (TGLF) model is a quasilinear, local gyro-fluid transport model for tokamak turbulence. It projects the five-dimensional gyrokinetic system onto a closed set of fluid-moment equations for each species, incorporates trapped-particle bounce averaging and Landau-fluid closures, and converts linear eigenmode spectra into turbulent particle, heat, and momentum fluxes through empirically calibrated saturation rules. In practical integrated modeling, TGLF is used to predict local anomalous transport from local gradients, geometry, collisionality, and finite-$\beta$ parameters; a typical TGLF call takes $\mathcal O(1\text{--}10)\,\mathrm{ms}$, but whole-device simulations requiring thousands of evaluations remain computationally expensive (Cao et al., 7 Sep 2025).

1. Foundational formulation and ordering assumptions

TGLF is described as a quasilinear, local gyro-fluid transport model whose basic assumptions include drift ordering, small-amplitude perturbations, a slab-like ballooning representation of toroidal geometry, and moment truncation with Landau-fluid closure. In the ST40 study, these assumptions are listed as

$$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$

together with $|\delta f| \ll f_0$ (Tzanis et al., 7 Feb 2025).

A complementary derivation writes the perturbed distribution for species $s$ as

$f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$

with $F_{0s}$ a Maxwellian background depending on $n_s(r)$ and $T_s(r)$, and introduces the non-adiabatic response

$h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$

Under the standard drift ordering $\mathcal O(1\text{--}10)\,\mathrm{ms}$0, with $\mathcal O(1\text{--}10)\,\mathrm{ms}$1 the cyclotron frequency and $\mathcal O(1\text{--}10)\,\mathrm{ms}$2, the gyrokinetic dynamics are reduced to a fluid-moment hierarchy in which trapped particles are bounce averaged and passing populations are closed by Padé-type operators (Cao et al., 7 Sep 2025).

The significance of these approximations is operational rather than merely formal. TGLF is not a nonlinear gyrokinetic solver; it is a reduced-order model that retains the microinstability drives and transport-channel structure needed for transport prediction while remaining fast enough for repeated calls inside profile-evolution or flux-matching workflows.

2. Moment hierarchy, trapped-particle physics, and Landau-fluid closure

The model’s central reduction is from gyrokinetic phase space to a finite set of fluid moments. In the ST40 summary, TGLF is described as truncating at density, parallel momentum, and temperature moments, closed by Landau-fluid (“Hammett–Perkins”) operators. In the NSTX application summary, the retained state is described more explicitly as including density $\mathcal O(1\text{--}10)\,\mathrm{ms}$3, parallel velocity $\mathcal O(1\text{--}10)\,\mathrm{ms}$4, parallel and perpendicular temperatures $\mathcal O(1\text{--}10)\,\mathrm{ms}$5, $\mathcal O(1\text{--}10)\,\mathrm{ms}$6, and the corresponding parallel and perpendicular heat fluxes $\mathcal O(1\text{--}10)\,\mathrm{ms}$7, $\mathcal O(1\text{--}10)\,\mathrm{ms}$8, giving up to eight moments for each species (Lestz et al., 4 Sep 2025).

A compact expression of the linear system is

$\mathcal O(1\text{--}10)\,\mathrm{ms}$9

where $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$0, $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$1 contains diamagnetic drives proportional to $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$2 and $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$3, $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$4 encodes curvature and geometric couplings such as $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$5, $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$6, and $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$7, and $$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$8 incorporates finite-$$\omega \lesssim \omega_*, \qquad k_\parallel \ll k_\perp, \qquad \rho\,k_\perp \lesssim 1,$$9 electromagnetic effects (Lestz et al., 4 Sep 2025).

Trapped-particle physics enters through bounce averaging and an effective Landau-pole closure. In the ST40 description, trapped electrons are handled by replacing the true $|\delta f| \ll f_0$0 in the Landau closure with an effective, bounce-averaged parallel wavenumber $|\delta f| \ll f_0$1, so that the trapped response captures the essence of trapped-electron Landau damping and bounce-resonant drive of trapped-particle modes such as TEM and UM. The NSTX summary likewise emphasizes the split between passing and trapped electrons, noting that trapped electrons carry their own fluid moments and respond non-adiabatically to curvature and $|\delta f| \ll f_0$2 drifts (Tzanis et al., 7 Feb 2025).

The reduced hierarchy admits a quadratic free-energy description. One expression given for the decomposed free energy is

$|\delta f| \ll f_0$3

which identifies the density, parallel-flow, and temperature perturbations as the basic energetic content of the fluid reduction (Cao et al., 7 Sep 2025).

3. Quasilinear transport construction and computational workflow

TGLF computes transport from a linear eigenmode spectrum evaluated over binormal wavenumber. At each $|\delta f| \ll f_0$4, linear analysis produces mode eigenfunctions $|\delta f| \ll f_0$5 and growth rate $|\delta f| \ll f_0$6. The quasilinear particle and heat fluxes are then assembled as spectral sums,

$|\delta f| \ll f_0$7

with per-mode contributions

$|\delta f| \ll f_0$8

A diffusive–pinch form is also used,

$|\delta f| \ll f_0$9

where $s$0 and $s$1 are diffusivities and $s$2 and $s$3 are convective pinches obtained by projection of the quasilinear spectrum onto gradient directions (Cao et al., 7 Sep 2025).

In operational terms, a single native TGLF evaluation proceeds in three stages:

• Inputs: 31 variables, including local normalized gradient scale lengths $s$4 and $s$5, safety factor $s$6, magnetic shear $s$7, effective charge $s$8, elongation $s$9, triangularity $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$0, normalized collisionality $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$1, beta $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$2, geometry factors $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$3, and Shafranov shift.
• Linear analysis: solution of the bounce-averaged fluid eigenvalue problem for discrete $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$4-values to obtain $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$5, real frequencies $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$6, and quasilinear weight functions $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$7.
• Saturation and spectral summation: application of empirically calibrated saturation amplitudes $f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$8, specifically the “SAT2” rule in the surrogate study, followed by

$f_s = F_{0s}(v) + \delta f_s(\mathbf R,v_\|,\mu),$9

and summation over $F_{0s}$0 to return $F_{0s}$1 (Cao et al., 7 Sep 2025).

The NSTX study emphasizes that TGLF uses physics-based saturation rules denoted SAT0, SAT1, and related variants, while the ST40 and surrogate studies explicitly discuss SAT2. This saturation dependence is not a secondary detail: it is one of the principal knobs governing transport stiffness and channel balance in applications.

4. Coupling to integrated transport solvers

TGLF is routinely embedded in transport frameworks rather than used in isolation. In the ST40 predictive workflow, ASTRA is coupled to SPIDER, NUBEAM, NCLASS, and a reduced scrape-off-layer model for last-closed-flux-surface boundary conditions. TGLF supplies the local anomalous fluxes, NCLASS supplies neoclassical coefficients and pinch velocities, NUBEAM provides particle, heat, and torque source terms, and SPIDER fixes the magnetic boundary via EFIT (Tzanis et al., 7 Feb 2025).

The transport equations advanced by ASTRA are written in flux coordinates $F_{0s}$2 as

$F_{0s}$3

$F_{0s}$4

$F_{0s}$5

with total fluxes split into neoclassical and TGLF contributions. In the same workflow, the reduced SOL “two-point” model sets LCFS boundary conditions through relations for $F_{0s}$6 and $F_{0s}$7 in terms of the outgoing core fluxes (Tzanis et al., 7 Feb 2025).

Quantitatively, the ST40 study reports typical mid-radius TGLF-predicted fluxes at $F_{0s}$8 of $F_{0s}$9, $n_s(r)$0, and $n_s(r)$1. At the core, $n_s(r)$2, strong $n_s(r)$3 shear $n_s(r)$4 and fast-ion dilution yield near-neoclassical transport levels of $n_s(r)$5, whereas toward the edge, $n_s(r)$6, the anomalous $n_s(r)$7 and $n_s(r)$8 rise to a few $n_s(r)$9 $T_s(r)$0. The same study reports agreement in global quantities and kinetic profiles between predictive and interpretative modeling as well as experimental measurements, and summarizes the fully predictive coupled simulations as achieving global parameters and profiles within $T_s(r)$1 of the reference (Tzanis et al., 7 Feb 2025).

The role of TGLF in these workflows is therefore not limited to linear microstability assessment. It is a local transport closure used inside time-evolving, source-driven, geometry-constrained simulations.

5. Electromagnetic treatment, validation against higher-fidelity models, and reported shortcomings

A recurring issue in TGLF applications is the treatment of electromagnetic physics. The NSTX study distinguishes electrostatic (ES) and electromagnetic (EM) formulations: ES TGLF retains only $T_s(r)$2, whereas EM TGLF also includes parallel vector potential $T_s(r)$3 via Ampère’s law and perpendicular magnetic fluctuations $T_s(r)$4 in the curvature drift. The paper states that at NSTX’s high $T_s(r)$5, the ES model grossly overpredicts $T_s(r)$6 and $T_s(r)$7 by $T_s(r)$8, while the EM model saturates to a finite $T_s(r)$9-stabilized level (Lestz et al., 4 Sep 2025).

The device-specific assessments reported in the ST40 and NSTX studies are summarized below.

Regime	Reported TGLF behavior	Reported issue
ST40, $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$0	reproduces GS2 linear growth rates to $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$1 and nonlinear GS2 fluxes to $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$2	satisfactory for TEM/UM/ITG-dominated transport
ST40, $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$3	misses the KBM branch seen by GS2	$h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$4 effects omitted
NSTX, ES TGLF	$h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$5 overpredicted by $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$6; $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$7 overpredicted by $h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$8	high-$h_s=\delta f_s + (q_s\varphi/T_s)\,F_{0s}.$9 electromagnetic physics absent
NSTX, EM TGLF	$\mathcal O(1\text{--}10)\,\mathrm{ms}$00 overpredicted by $\mathcal O(1\text{--}10)\,\mathrm{ms}$01; $\mathcal O(1\text{--}10)\,\mathrm{ms}$02 underpredicted by $\mathcal O(1\text{--}10)\,\mathrm{ms}$03	persistent channel imbalance and saturation sensitivity

In the ST40 analysis, TGLF is described as reproducing GS2 within $\mathcal O(1\text{--}10)\,\mathrm{ms}$04 at $\mathcal O(1\text{--}10)\,\mathrm{ms}$05, but discrepancies grow in the core where fast-ion $\mathcal O(1\text{--}10)\,\mathrm{ms}$06 and electromagnetic stabilization matter. The same analysis reports that TGLF is somewhat less stiff in its sensitivity to $\mathcal O(1\text{--}10)\,\mathrm{ms}$07 shear and beam-ion dilution than GS2, and that mid-edge transport can be overpredicted by up to $\mathcal O(1\text{--}10)\,\mathrm{ms}$08 unless tuned (Tzanis et al., 7 Feb 2025).

In the NSTX database of 37 high-performance discharges, the time-dependent TRANSP study finds that MMM more consistently agrees with the observations than TGLF, despite TGLF requiring orders of magnitude greater computational cost. EM-TGLF predicts $\mathcal O(1\text{--}10)\,\mathrm{ms}$09, compared with experimental $\mathcal O(1\text{--}10)\,\mathrm{ms}$10, and the paper concludes that at NSTX’s high $\mathcal O(1\text{--}10)\,\mathrm{ms}$11 the electrostatic TGLF model is unusable and electromagnetic fluctuations must be included. Even then, the study emphasizes the need for careful calibration of the spectral-shift model, specifically SAT1geo and SAT2, to avoid systematic over- or under-prediction (Lestz et al., 4 Sep 2025).

These results delimit the present operating envelope of TGLF. The model is effective in many electrostatic or moderately electromagnetic regimes, but finite-$\mathcal O(1\text{--}10)\,\mathrm{ms}$12, KBM-sensitive, MTM-sensitive, and fast-ion-dominated cases remain strongly dependent on closure choices and saturation calibration.

6. Surrogate models, differentiability, and accelerated TGLF workflows

Because native TGLF remains costly in integrated simulations, recent work has focused on neural surrogates. The TGLF-SINN study replaces the spectral summation with a fully differentiable neural-network surrogate and identifies three key innovations:

• Feature engineering: an element-wise asinh transform followed by standardization applied to both the total fluxes and each per-wavenumber contribution,

$\mathcal O(1\text{--}10)\,\mathrm{ms}$13

which reduces target prediction range and permits negative predictions without clipping.

• Spectra-informed architecture: $\mathcal O(1\text{--}10)\,\mathrm{ms}$14 parallel branches, one per $\mathcal O(1\text{--}10)\,\mathrm{ms}$15, each taking the 31 physical features plus the scalar $\mathcal O(1\text{--}10)\,\mathrm{ms}$16, processed by a shared Encoder–ResNet–Decoder to predict

$\mathcal O(1\text{--}10)\,\mathrm{ms}$17

whose sum is inverted to recover the total flux.

• Physics-guided spectral regularization and Bayesian active learning: a combined loss

$\mathcal O(1\text{--}10)\,\mathrm{ms}$18

with

$\mathcal O(1\text{--}10)\,\mathrm{ms}$19

together with Expected Information Gain acquisition

$\mathcal O(1\text{--}10)\,\mathrm{ms}$20

estimated via Monte Carlo dropout and ensembling (Cao et al., 7 Sep 2025).

On the Major + Minor perturbation set of $\mathcal O(1\text{--}10)\,\mathrm{ms}$21 outlier-filtered points, TGLF-SINN achieves an average LRMSE of $\mathcal O(1\text{--}10)\,\mathrm{ms}$22 versus $\mathcal O(1\text{--}10)\,\mathrm{ms}$23 for the SOTA TGLF-NN, a $\mathcal O(1\text{--}10)\,\mathrm{ms}$24 relative reduction. In the BAL setting, using only $\mathcal O(1\text{--}10)\,\mathrm{ms}$25 of the data raises LRMSE by only $\mathcal O(1\text{--}10)\,\mathrm{ms}$26 above the full-data TGLF-NN and by $\mathcal O(1\text{--}10)\,\mathrm{ms}$27 above the full-data TGLF-SINN. In downstream flux matching within the FUSE suite for DIII-D L-mode and H-mode, replacing native TGLF with TGLF-SINN reduces end-to-end runtime from 15 min on 128 threads to 20 s, a $\mathcal O(1\text{--}10)\,\mathrm{ms}$28 speedup, while TGLF-NN in Julia takes 1.5 s, or $\mathcal O(1\text{--}10)\,\mathrm{ms}$29 faster than full TGLF. Both surrogates yield experimentally validated profiles with sub-$\mathcal O(1\text{--}10)\,\mathrm{ms}$30 relative errors (Cao et al., 7 Sep 2025).

The NSTX study reports a parallel surrogate effort in which TGLF-NN models are trained on $\mathcal O(1\text{--}10)\,\mathrm{ms}$31 TGLF runs from NSTX plasmas over $\mathcal O(1\text{--}10)\,\mathrm{ms}$32, reproducing TGLF transport coefficients with $\mathcal O(1\text{--}10)\,\mathrm{ms}$33 local flux error. Embedded in the FUSE flux-matching solver rather than TRANSP/PT, TGLF-NN is reported as $\mathcal O(1\text{--}10)\,\mathrm{ms}$34 faster than full TGLF per slice, and a transfer-learned GKNN surrogate to QLGYRO is reported as $\mathcal O(1\text{--}10)\,\mathrm{ms}$35 faster than QLGYRO, with $\mathcal O(1\text{--}10)\,\mathrm{ms}$36 RMSE $\mathcal O(1\text{--}10)\,\mathrm{ms}$37 and $\mathcal O(1\text{--}10)\,\mathrm{ms}$38 in a 700-case validation (Lestz et al., 4 Sep 2025).

A defining feature of TGLF-SINN is full differentiability with respect to the 31 transport inputs. The study explicitly connects this to gradient-based coupling to neoclassical, equilibrium, and control-system modules in whole-device simulation, adjoint-based optimization of magnetic configurations or heating profiles, and model-predictive schemes for real-time control of plasma turbulence. In that sense, the recent surrogate literature does not replace TGLF’s transport role; it re-expresses the TGLF mapping in a form that is faster, differentiable, and more data-efficient for integrated fusion workflows.