Reversal of Simple Hydrogenic Isotope Scaling Laws in Tokamak Edge Turbulence

The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio dependence of turbulent ion and electron energy fluxes. The mass-ratio dependence arises from the nonadiabatic response associated with fast electron parallel motion and plays a key role in altering—and in the case of the DIII-D edge, favorably reversing—the naive gyro-Bohm scaling behavior. In the reversed regime hydrogen energy fluxes are larger than deuterium fluxes, which is the opposite of the naive prediction.

Figure 1

Total energy flux ($Q_e+Q_D$) comparing cgyro turbulence simulations with experimental DIII-D power balance. The rapid increase at $r/a=0.9$ (note the log scale) is driven by nonadiabatic electron physics and is highly sensitive to the electron-to-ion mass ratio, and also to the safety factor $q$.

Figure 2

Nonlinear ion energy flux comparing hydrogen, deuterium, and $50:50$ DT plasmas. Note that the normalization has fixed deuterium gyro-Bohm units. A favorable reversal of the naive scaling, Eq. (1), is observed in the TEM-dominated edge.

Figure 3

Nonlinear (a) electron and (b) ion energy flux in the edge at $r/a=0.9$ comparing deuterium and hydrogen plasmas versus the (artificial) scaling parameter $\lambda$ [see Eq. (11)] for the electron parallel motion. Naive gyro-Bohm scaling is recovered as $\lambda \to 0$. As $\lambda$ increases, the turbulence transitions from a weakly nonadiabatic regime ($Q_H<Q_D$) fit to Eq. (10) to first-order (gray dashed lines) to a strongly nonadiabatic regime ($Q_H>Q_D$) where the finite-$m_e/m_i$ corrections drive a reversal of the naive gyro-Bohm scaling.

Figure 4

Nonlinear ion energy flux in the ITG-dominated core at $r/a=0.7$ comparing hydrogen, deuterium, and $50:50$ DT plasmas. Shown are the components of the flux due to the naive gyro-Bohm scaling (yellow) and the weak nonadiabatic contribution (green). Also shown (in blue) is the Nakata-Garcia effect that arises from keeping the collision and shearing rates fixed in absolute units. When these shearing rates are kept fixed in ion units, as in Eq. (5), the Nakata-Garcia effect vanishes.