Neoclassical Transport in the Helical Reversed-Field Pinch

Test particle evaluation of the diffusion coefficient in a fusion plasma in the reversed-field pinch (RFP) configuration shows distinct similarities with stellarators when the plasma spontaneously evolves towards a helical shape. The almost total absence of superbanana particles at the levels of helical deformation seen in experiment ($B_h/B=10\%$) causes transport to be proportional to collision frequency (at low collisions). This fact excludes the possibility that the minimum conceivable transport could be inversely proportional to collision frequency, which is typical of unoptimized stellarators. This result strengthens the perspectives of the helical RFP as a fusion configuration.

Figure 1

(a)–(c) Poincaré plots on the poloidal section for a MH [discharge #23977, $t=24\mathrm{ms}$, (a)], DAx [# 21982, $t=125\mathrm{ms}$, (b)] and SHAx [#23977, $t=174\mathrm{ms}$, (c)] state; (d)–(f) corresponding toroidal sections.

Figure 2

(a) Safety factor (solid line) and helical ripple (dashed line) profiles in RFX-mod; (b) Diffusion coefficient $D$ of ${\mathrm{H}}^{+}$ ions as a function of $\nu {\tau }_{\mathrm{tor}}$, MH (black circles), DAx (red triangles), SHAx (blue squares) and [inset, (c)] schematic view of the neoclassical transport regimes: $\mathrm{AS}=\mathrm{\text{axisymmetric}}$ system, $\mathrm{HS}=\mathrm{\text{helically}}$ symmetric, $\mathrm{SB}=\mathrm{\text{superbanana}}$ (adapted from Ref. 13).

Figure 3

(a) Density distribution of deposited particles, as a function of the pitch $\lambda =v_{\parallel }/v$; (b) the same, at the end of the run; (c) pitch as a function of the flux coordinate ${\psi }_p$, showing that lost particles are mostly passing.

Figure 4

(a) Critical pitch ${\lambda }_c$ plotted on the poloidal section, in a case with a helical deformation 7.5 times the experimental value; (b) percentage of superbananas over the trapped population; (c) escape time of particles (runtime $\sim 70\mathrm{ms}$); (d) variation of the toroidal precession rate with respect to the unperturbed case, $\delta {\omega }_d/{\omega }_d$. In all panels, the Poincaré plot of the island is overplotted to the color contours.

Figure 5

(a) Critical pitch ${\lambda }_c$ plotted on the poloidal section, in the experimental case; (b) percentage of superbananas over the trapped population; (c) escape time of particles (runtime $\sim 70\mathrm{ms}$); (d) variation of the toroidal precession rate with respect to the unperturbed case, $\delta {\omega }_d/{\omega }_d$.