The dynamics of long wavelength electrostatic turbulence in tokamaks*

From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, it is found that conventional notions concerning directions of cascades, locality and isotropy of spectral transfer, frequencies of fluctuations, and stationarity of saturation do not hold for moderate to long wavelengths (kρs≤1). In particular, at long wavelengths, where spectral transfer of energy is dominated by the E×B nonlinearity, energy is carried to short scale (even in two dimensions) in a manner that is anisotropic and highly nonlocal (energy is efficiently passed between modes separated by the entire spectrum range in a correlation time). At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed (i.e., energy to high k) and are nonconservative in enstrophy and energy similarity ranges (but conservative overall). In regions where both nonlinearities are important, cross-coupling between the nonlinearities gives rise to large nonlinear frequency shifts which profoundly affect the dynamics of saturation by modifying the growth rate and nonlinear transfer rates. These modifications produce a nonstationary saturated state with large amplitude, long period relaxation oscillations in the energy, spectrum shape, and transport rates. Methods of observing these effects are presented.