Vanishing Neoclassical Viscosity and Physics of the Shear Layer in Stellarators

The drift kinetic equation is solved for low density TJ-II plasmas employing slowly varying, time-dependent profiles. This allows us to simulate density ramp-up experiments and describe from first principles the formation and physics of the radial electric field shear layer. The main features of the transition are perfectly captured by the calculation, and good quantitative agreement is also found. The results presented here, that should be valid for other nonquasisymmetric stellarators, provide a fundamental explanation for a wealth of experimental observations connected to the shear layer emergence in TJ-II. The key quantity is the neoclassical viscosity, which is shown to go smoothly to zero when the critical density is approached from below. This makes it possible for turbulence-related phenomena, and particularly zonal flows, to arise in the neighborhood of the transition.

Figure 1

Plasma radial profiles for selected times: low (high) $n$ in open (closed) circles. The evolution is given through $\frac{1}{n}\frac{\partial n}{\partial t}=3{\mathrm{s}}^{-1}$, $\frac{1}{T_e}\frac{\partial T_e}{\partial t}=-1.5{\mathrm{s}}^{-1}$, and $\frac{\partial T_i}{\partial t}=0$.

Figure 2

Time evolution of the relevant quantities at $\rho =0.7$ during the density ramp-up.

Figure 3

Ambipolar equation at $\rho =0.7$ for several representative times.

Figure 4

Radial electric field profile for representative times. Lines are separated by 1 ms and thick lines by 5 ms. The starting ($t<t_{cr}$) $E_r(\rho )$ is positive.

Figure 5

Density dependence of the neoclassical poloidal viscosity during the transition. $n_{cr}$ is locally defined as the $n$ at which $E_r$ passes through 0 (inset: frequency dependence of the neoclassical damping for several values of ${\nu }_p$).