Dimits Shift in Realistic Gyrokinetic Plasma-Turbulence Simulations

In simulations of turbulent plasma transport due to long wavelength ($k_{\perp }{\rho }_i\le 1$) electrostatic drift-type instabilities, we find a persistent nonlinear up-shift of the effective threshold. Next-generation tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. The gyrokinetic simulations reported here are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron microinstability drive.

Figure 1

The locations of both the linear and effective nonlinear thresholds depend on collisionality, but the size of the Dimits shift is not affected by collisionality. Transport is reduced by increasing collisionality because the nonadiabatic electron response is diminished, providing less “amplification” of the ion temperature gradient turbulence. $Q_{\mathrm{tot}}$ is the average transported power per unit area, $v_D\equiv \sqrt{(}{T}_D/m_D)$, $n_D$, $T_D$, ${\rho }_D$ denote the deuterium thermal speed, density, temperature, and gyroradius.

Figure 2

Transport fluxes increase with collisionality when an adiabatic electron model is used.

Figure 3

Adding impurities changes the linear and nonlinear thresholds (but not the Dimits shift). “DeB” simulations include kinetic treatment of deuterium, electrons, and boron.

Figure 4

Normalized growth rates for the fastest growing modes in each of the conditions shown in Figs. 1, 2, 3.