Internal Transport Barrier Broadening through Subdominant Mode Stabilization in Reversed Field Pinch Plasmas

The reversed field pinch (RFP) device RFX-mod features strong internal transport barriers when the plasma accesses states with a single dominant helicity. Such transport barriers enclose a hot helical region with high confinement whose amplitude may vary from a tiny one to an amplitude encompassing an appreciable fraction of the available volume. The transition from narrow to wide thermal structures has been ascribed so far to the transport reduction that occurs when the dominant mode separatrix, which is a preferred location for the onset of stochastic field lines, disappears. In this Letter we show instead that the contribution from the separatrix disappearance, by itself, is marginal and the main role is instead played by the progressive stabilization of secondary modes. The position and the width of the stochastic boundary encompassing the thermal structures have been estimated by applying the concept of a 3D quasiseparatrix layer, developed in solar physics to treat reconnection phenomena without true separatrices and novel to toroidal laboratory plasmas. Considering the favorable scaling of secondary modes with the Lundquist number, these results open promising scenarios for RFP plasmas at temperatures higher than the presently achieved ones, where lower secondary modes and, consequently, larger thermal structures are expected. Furthermore, this first application of the quasiseparatrix layer to a toroidal plasma indicates that such a concept is ubiquitous in magnetic reconnection, independent of the system geometry under investigation.

Figure 1

Temperature profile (triangles) measured along a horizontal diameter, featuring a thermal structure overplotted to the magnetic surfaces. The vertical lines mark the structure width $W_{T_e}$. The red surface is $S_{\mathrm{QSL}}$, defined in the text.

Figure 2

(a) Thermal structure width $W_{T_e}$ versus the dominant mode amplitude $b_T^{1,-7}$. (b) Ensemble-averaged amplitude of selected secondary modes versus $b_T^{1,-7}$.

Figure 3

Resonance positions of the $n=-8$, $-9$ modes, ${\rho }_8$ (red triangles) and ${\rho }_9$ (green diamonds), plotted versus the position ${\rho }_{\mathrm{T}\mathrm{H}}$ of the ITB outermost points. Full symbols refer to DAx and ${\mathrm{SHAx}}_n$ states, whereas empty symbols pertain to ${\mathrm{SHAx}}_w$ states.

Figure 4

(a) Depiction of variables used in Eq. (1). Magnetic surfaces of (b) a SHAx and (d) a DAx case. The red line is the collection diameter of $r_c$ and $r_s$, the red full segment is the array of $r_c$ values. The two red surfaces bound the QSL. (c),(e) $r_s$ and $D$ versus $r_c$. The horizontal red line indicates the $D=D_{\text{th}}$ values of $S_{\mathrm{QSL}}$, the innermost red surface of (b) and (d). The highest value of $D$ (blue diamonds) identifies (b) the blue quasiseparatrix surface and (d) the separatrix.

Figure 5

$W_{\mathrm{QSL}}$ plotted (a) versus $b_T^{1,-7}$ and (b) versus $W_{T_e}$.