How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence

This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps” and “steps,” which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

Figure 1

(a) Contour plot of the time evolution of $\left|\nabla n\right|$ along the plasma radius for $\mathrm{\Lambda }=4000,c_{\chi }=0.95,\alpha =6,{\varepsilon }_c=6.25,\beta =0.1,{\mu }_c=D_c=0.78,a_u=1,g_i=5.1,{\varepsilon }_i=0.002$. Horizontal axis is the log of time; vertical is the scaled radius. Different stages of evolution are as follows: a, fast merger of microsteps and formation of mesosteps; b, coalescence of mesosteps to barriers; c, barriers propagate along gradient, condense at boundaries; and d, stationary profile. (b) Evolutionary landscape of the vorticity profile $u$ (i.e., the shearing profile), as a function of position $x$ and time $t$.

Figure 2

(a) Upward, escalator-like migration of the step at times $t=700$ and $t=1300$. (b) Detachment of shearing pattern from the location of formation, and migration towards the boundary.

Figure 3

Transformation in the profiles of (a) density, (b) vorticity, (c) turbulent PE, and (d) turbulent particle flux. Forward transition is from A to B, and backward transition is from C to D.

Figure 4

Global particle flux versus density gradient, showing hysteresis behavior.