How the propagation of heat-flux modulations triggers E×B flow pattern formation

We propose a novel mechanism to describe E×B flow pattern formation based upon the dynamics of propagation of heat-flux modulations. The E×B flows of interest are staircases, which are quasiregular patterns of strong, localized shear layers and profile corrugations interspersed between regions of avalanching. An analogy of staircase formation to jam formation in traffic flow is used to develop an extended model of heat avalanche dynamics. The extension includes a flux response time, during which the instantaneous heat flux relaxes to the mean heat flux, determined by symmetry constraints. The response time introduced here is the counterpart of the drivers' response time in traffic, during which drivers adjust their speed to match the background traffic flow. The finite response time causes the growth of mesoscale temperature perturbations, which evolve to form profile corrugations. The length scale associated with the maximum growth rate scales as Δ2∼(v _thi/λT_i)ρ_i√χ _neoτ, where λT_i is a typical heat pulse speed, χ_neo is the neoclassical thermal diffusivity, and τ is the response time of the heat flux. The connection between the scale length Δ2 and the staircase interstep scale is discussed.