Zonal flow and streamer generation in drift turbulence

The relative importance of poloidally extended zonal flows (k(theta) not equal 0, k(r) = 0) and radially extended streamers (k(theta) not equal 0, k(r) = 0) in regulating drift turbulent energy transport is a central question in tokamak physics. Both forms of nonlinear structure can be described within the framework of the Hasegawa-Mima equation, as extended by Smolyakov et al (Smolyakov A I, Diamond P H and Malkov M 2000 Phys. Rev. Lett. 84 491), although streamers have not previously been analysed in this context. Here we present results obtained by comparing analytical weak-turbulence calculations with numerical simulations using a spectral code. The analytical results are obtained with a four-wave model, incorporating a drift wave (k(2)) coupled to both sidebands (k(2) +/- k(1)) by a zonal flow or streamer (k(1)). Fully nonlinear studies of this four-wave system have been carried out, and we find that analytical expressions derived from wave coupling models provide a good guide to the spectral code results. Instability conditions are found and growth rates computed, showing that zonal flows are more unstable than streamers, at least at this level of description. Typically, we find that the streamer growth rate is lower than that of the zonal flow by a factor of order rho (s)k(1). Insofar as our Hasegawa-Mima model contains many of the core physics elements of more sophisticated approaches, these results are of wider importance to the numerical modelling of drift turbulence in tokamaks.