Energy exchange between electrons and ions driven by ITG-TEM turbulence

In this study, the energy exchange between electrons and ions in ITG TEM turbulence is investigated using gyrokinetic simulations. The energy exchange in TEM turbulence is primarily composed of the cooling of electrons associated with perpendicular drift and the heating of ions moving parallel to magnetic field lines. TEM turbulence facilitates energy transfer from electrons to ions, which is opposite to the direction observed in ITG turbulence. In mixed ITG TEM turbulence, the relative magnitudes of parallel heating and perpendicular cooling for each species determine the overall direction and magnitude of energy exchange. From the viewpoint of entropy balance, it is further confirmed that energy flows from the species with larger entropy production, caused by particle and heat fluxes, to the other species in ITG TEM turbulence. The predictability of turbulent energy exchange in ITG-TEM turbulence by the quasilinear model is examined. In addition, an alternative method based on the correlation between energy flux and energy exchange is developed, and its validity is demonstrated.

💡 Research Summary

This paper investigates the turbulent energy exchange between electrons and ions in ion‑temperature‑gradient (ITG) and trapped‑electron‑mode (TEM) driven turbulence using gyrokinetic simulations performed with the GKV code. The authors first derive an entropy balance equation for the perturbed distribution functions and decompose the turbulent energy transfer Q_turb,a,k into four contributions: parallel Joule heating (Q_∥), perpendicular drift‑curvature heating (Q_B), a nonlinear interaction term (Q_ψ) that sums to zero, and a collisional term (Q_C) that is negligible in the weakly collisional regime considered. By focusing on Q_∥ and Q_B, they identify the physical mechanisms that dominate the energy exchange for each species.

In pure TEM turbulence (R₀/L_Te = 7.0, R₀/L_Ti = 1.0) the simulations show that electrons experience a negative Q_B (cooling) associated with the ⟂ ∇B‑curvature drift, while ions experience a positive Q_B (heating). Consequently, energy flows from electrons to ions. This direction is consistent with an entropy‑balance argument: the electron particle and heat fluxes generate larger entropy production than the ion fluxes, so the second law of thermodynamics is satisfied even though the turbulent exchange transfers energy from the cooler electrons to the hotter ions.

Conversely, in pure ITG turbulence (parameters near R₀/L_Te = 5.0, R₀/L_Ti = 3.0) the dominant contribution is parallel Joule heating. Ions are heated (positive Q_∥) and electrons are cooled (negative Q_∥), leading to an opposite energy flow (ions → electrons). Again, the direction follows the species with larger entropy production (here the ions) donating energy to the species with smaller entropy production (the electrons).

For mixed ITG‑TEM turbulence, where both instabilities are simultaneously unstable, the net energy exchange is determined by the relative magnitudes of parallel heating and perpendicular cooling for each species. The authors derive approximate relations (Eqs. 25‑27) that express the net exchange Q_e − Q_i in terms of the perpendicular energy fluxes E_turb,e and E_turb,i divided by the major radius R₀. Their nonlinear simulation data confirm that these approximations hold, indicating that the difference in ⟂ energy fluxes essentially sets the sign and magnitude of the turbulent energy exchange.

A central part of the study evaluates the applicability of a quasilinear model, which predicts turbulent fluxes and energy exchange by scaling linear‑simulation‑derived ratios (W_X,a,N) with the saturated electrostatic‑potential amplitude. By comparing these quasilinear predictions with fully nonlinear results, the authors demonstrate that the proportionality between Q_turb,a (or particle/heat fluxes) and |φ|² remains valid for both pure TEM and mixed ITG‑TEM cases. They also introduce a reformulated linear quantity Y_a,k (Eq. 34) that respects the condition Σ_a Y_a,k = 0 even in linear calculations, making it suitable for quasilinear modeling.

Finally, the paper proposes an alternative estimation technique that exploits the observed correlation between the perpendicular energy fluxes and the turbulent energy exchange. This method allows one to infer Q_turb,a from measured or simulated fluxes without performing costly nonlinear runs, which is especially valuable for future reactor‑relevant regimes where turbulent exchange can dominate over collisional processes.

In summary, the work establishes three key insights: (1) TEM turbulence drives electron‑to‑ion energy transfer, while ITG drives ion‑to‑electron transfer; (2) the direction of turbulent exchange is governed by the species with larger entropy production, not by temperature differences, thereby preserving the second law; (3) quasilinear models, when calibrated with linear ratios and the new Y_a,k formulation, can reliably predict turbulent energy exchange in both pure and mixed ITG‑TEM turbulence. These findings suggest that global transport simulations for next‑generation fusion devices must incorporate turbulent energy exchange to accurately predict temperature profiles and overall performance.