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

TL;DR

The paper addresses how microturbulence in ITG-TEM plasmas drives energy exchange between electrons and ions, an effect often neglected in transport modeling. It develops an entropy-balance framework and decomposes turbulent energy transfer into parallel heating, perpendicular drift heating, and field-line coupling, then tests a quasilinear model against nonlinear gyrokinetic simulations using a CBC tokamak configuration. The key findings show that TEM dominates energy transfer from electrons to ions, ITG drives the opposite transfer, and in mixed ITG-TEM the direction aligns with the net entropy production; a simple ΔEF-based method can predict the sign of energy transfer even when the quasilinear model struggles. The results have practical implications for including turbulent energy exchange in fusion-relevant transport simulations and for guiding reduced models of turbulence in reactor-scale plasmas.

Abstract

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.

Figures (13)

• Figure 1: The linear growthrate $\gamma$ (left) and frequency $\omega_r$ (right) at $k_x\rho_{ti}=0$. The most unstable mode transitions between ITG and TEM around $(R_0/L_{Te}, R_0/L_{Ti})=(5.0, 3.0)$.
• Figure 2: Time evolution of instantaneous turbulent energy transfers $\breve{Q}^{\rm turb}_{a} (a=e, i)$ in pure TEM turbulence. Red and blue dashed lines indicate energy transfer averaged over time in a steady state turbulence for ions and electrons, $Q^{\rm turb}_{i}$ and $Q^{\rm turb}_{e}$, respectively.
• Figure 3: Comparison of all terms in the entropy balance equation, Eq. (\ref{['eq:EBequation_real']}), in a steady state of the pure TEM turbulence for $(R_0/L_{Te}, R_0/L_{Ti})=(7.0, 1.0)$. All terms in Eq. (\ref{['eq:EBequation_real']}) for electrons (left) and ions (right) are normalized by $q_e^{\rm turb}/(T_eL_{Te})$ and $q_e^{\rm turb}/(T_iL_{Te})$, respectively.
• Figure 4: The wavenumber spectra of turbulent energy transfer terms in Eqs. (\ref{['eq: parallel_heating']})--(\ref{['eq:collision_psi']}) for electrons (left) and ions (right) in the case of $(R_0/L_{Te}, R_0/L_{Ti}) =(7.0, 1.0)$. The spectra are given as functions of $k_y \rho_{ti}$ obtained by summing over $k_x$. The electron cooling due to the $\nabla B$-curvature drift denoted by $Q_{eB}^{\rm turb}<0$ and the ion heating due to the parallel field denoted by $Q_{i\parallel}^{\rm turb}>0$ are dominant mechanisms in the turbulent energy exchange between electrons and ions in TEM turbulence.
• Figure 5: The turbulent particle flux $\Gamma^{\mathrm{turb}}_i(=\Gamma^{\mathrm{turb}}_e)$, electron and ion heat fluxes, $q^{\mathrm{turb}}_e$ and $q^{\mathrm{turb}}_i$, and energy transfer $Q^{\mathrm{turb}}_i(=-Q^{\mathrm{turb}}_e)$ as functions of $(R_0/L_{Te}, R_0/L_{Ti})$. Square and circular markers in Figs. \ref{['fig:PF_HF_EE_LTi_ITGTEM']} (a-c) indicate nonlinear results and results calculated by Eq. (\ref{['eq:QuasilinearFluxes']}), respectively. Diamond and triangle markers in Fig. \ref{['fig:PF_HF_EE_LTi_ITGTEM']} (c) represent the results of Eq. (\ref{['eq: delta EF']}) and Eq. (\ref{['eq:DeltaEF']}), respectively.