Transport Barrier inside the Reversal Surface in the Chaotic Regime of the Reversed-Field Pinch

Magnetic field lines and the corresponding particle orbits are computed for a typical chaotic magnetic field provided by a magnetohydrodynamics numerical simulation of the reversed-field pinch. The $m=1$ modes are phase locked and produce a toroidally localized bulging of the plasma which increases particle transport. The $m=0$ and $m=1$ modes produce magnetic chaos implying poor confinement. However, they also allow for the formation of magnetic islands which induce transport barriers inside the reversal surface.

Figure 1

Poincaré plot of magnetic field lines in the $(r,\varphi )$ plane (a) $m=0$ modes only, (b) $m=1$ modes without $m=0$ modes, (c) $m=0$ and $m=1$ modes together.

Figure 2

(a) Poincaré plot with random phases for the $m=0,1$ modes; (b) radial profile of loss times ${\tau }_{\mathrm{loss}}$ in two conditions (green=random, blue=locked phases). The dashed line in (b) corresponds to the reversal surface [orange line in (a)].

Figure 3

Diffusion plots of test particles: particles are deposited at $r/a=0.7$, and allowed for diffusing in the plasma (top to bottom corresponds to increasing time steps). (a)–(c) phases are random; (d)–(f) phases are locked.

Figure 4

(a) Poincaré map obtained with mode amplitudes scaled down to experimental values; (b) same map, obtained by multiplying the $m=0$ amplitude by 5; (c) ${\tau }_{\mathrm{loss}}$ evaluated at the edge, as a function of the normalized $m=0$ amplitude.