Wave trapping and E × B staircases

Abstract

A model of E × B staircases is proposed based on a wave kinetic equation coupled to a poloidal momentum equation. A staircase pattern is idealized as a periodic radial structure of zonal shear layers that bound regions of propagating wave packets, viewed as avalanches. Wave packets are trapped in shear flow layers due to refraction. In this model, an E × B staircase motif emerges due to the interaction between propagating wave packets (avalanches) and trapped waves in the presence of an instability drive. Amplitude, shape, and spatial period of the staircase E × B flow are predicted as functions of the background fluctuation spectrum and the growth rate of drift waves. The zonal flow velocity radial profile is found to peak near its maxima and to flatten near its minima. The optimum configuration for staircase formation is a growth rate, that is, maximum at zero radial wave number. A mean shear flow is responsible for a preferential propagation speed of avalanches. It is not a mandatory condition for the existence of staircase solutions, but has an impact on their spatial period.