THE DYNAMICS OF LONG-WAVELENGTH ELECTROSTATIC TURBULENCE IN TOKAMAKS

From extensive simulation of simple local fluid models of long wavelen gth drift wave turbulence in tokamaks, it is found that conventional n otions concerning directions of cascades, locality and isotropy of spe ctral transfer, frequencies of fluctuations, and stationarity of satur ation do not hold for moderate to long wavelengths (kp(s) less-than-or -equal-to 1). In particular, at long wavelengths, where spectral trans fer of energy is dominated by the E X B nonlinearity, energy is carrie d to short scale (even in two dimensions) in a manner that is anisotro pic and highly nonlocal (energy is efficiently passed between modes se parated by the entire spectrum range in a correlation time). At short wavelengths, transfer is dominated by the polarization drift nonlinear ity. While the standard dual cascade applies in this subrange, it is f ound that finite spectrum size can produce cascades that are reverse d irected (i.e., energy to high k) and are nonconservative in enstrophy and energy similarity ranges (but conservative overall). In regions wh ere both nonlinearities are important, cross-coupling between the nonl inearities gives rise to large nonlinear frequency shifts which profou ndly affect the dynamics of saturation by modifying the growth rate an d nonlinear transfer rates. These modifications produce a nonstationar y saturated state with large amplitude, long period relaxation oscilla tions in the energy, spectrum shape, and transport rates. Methods of o bserving these effects are presented.