Scaling laws for the cutoff wavenumber of the short-wavelength ion-temperature-gradient mode in a Z-pinch

We use a heuristic fluid model to predict the dependence of the cutoff wave number for the short-wavelength ion temperature gradient (SWITG) mode on ion density gradient, ion temperature gradient (ITG) and ion-electron temperature ratio. In particular, we predict that the cutoff wave number increases linearly with increasing ITG for sufficiently large values of the ITG. Direct numerical solutions of the gyrokinetic dispersion relation using a purpose-built solver confirm the predicted scalings at large ITG values and find a weaker power-law scaling for intermediate ITG values. Combining these wave number scalings with a simple diffusive estimate for turbulent fluxes produces a scaling prediction for the ITG heat flux in SWITG-driven turbulence. Applying the critical balance conjecture additionally provides scalings for the aspect ratio of the SWITG turbulent eddies.