Extreme Heat Fluxes in Gyrokinetic Simulations: A New Critical $\beta$

A hitherto unexplained feature of electromagnetic simulations of ion temperature gradient turbulence is the apparent failure of the transport levels to saturate for certain parameters; this effect, termed here nonzonal transition, has been referred to as the high-$\beta$ runaway. The resulting large heat fluxes are shown to be a consequence of reduced zonal flow activity, brought on by magnetic field perturbations shorting out flux surfaces.

Figure 1

Transport levels $Q$ for $\beta =0.9\%$: the black solid, red dashed, and blue dotted lines correspond to the ion and electron electrostatic fluxes, and the electron electromagnetic flux, respectively. Both plots show the same data, the lower on a logarithmic axis, with black dotted lines of a slope twice the maximum linear growth rate, which is not exceeded by the $Qs$.

Figure 2

Impact of gradient variations $\Delta \omega$ on ${\beta }_{\mathrm{crit}}^{\mathrm{NZT}}$ (normalized to ${\beta }_{\mathrm{crit}}^{\mathrm{KBM}}$) for CBC and ITG case parameters. Different symbols and colors indicate different gradients. Vertical arrows signify that for a particular $\Delta \omega$, the NZT threshold lies above the ballooning threshold.

Figure 3

Half-turn radial field line displacement $\Delta r_{1/2}$ and $B_x$ correlation length ${\lambda }_{Bxx}$ as a function of $\beta$; linear fits indicate an intersection just above $\beta =0.8\%$.

Figure 4

Zonal flow decay in the presence of various values of a resonant and time-independent $A_{\parallel }\propto B_x$. Shown is the real part of the electrostatic potential $\Phi$ relative to the residual ${\Phi }_{\mathrm{R}}$ [with $\mathrm{Im}(\Phi )\ll \mathrm{Re}(\Phi )$]; time is measured relative to $t_{\mathrm{R}}$, where the residual had been reached ($B_x$ is turned on $t=t_{\mathrm{R}}$). The dotted red line shows an exemplary quadratic fit to the data, consistent with analytical theory.