Toroidal coupling in the kinetic response to edge magnetic perturbations

Abstract

The magnetic topology of the stochastic edge of a helical reversed-field pinch, with helicity m/n, shows to be deeply influenced by higher harmonics (m ± 1)/n, with the same n, due to toroidal coupling. As a consequence, by measuring kinetic quantities in a particular θ, φ location, one can incur in substantial errors or mis-interpretations of the kinetic plasma response: only a full 3D coverage of θ, φ angles can reveal the real topology of the plasma. This can be a caveat for MP application in tokamaks, because it shows that toroidal and poloidal sidebands, though smaller than the base mode by a factor ∼ = a/R, can have a sizable effect on the kinetic response of the edge plasma, and thus on related issues (for example, ELM stabilization and suppression).

Helical plasma-wall interaction in the RFX-mod: effects of high-n mode locking

“…To characterize the different behavior between the locking region and the background, in black is plotted the average value along all the torus ‹L cw › and in red the value in the hole region around 120°, L cw , hole . In the same plot also the Kolmogorov length L k has been reported in blue for comparison, estimated as in [13]. The figure shows that ‹L cw › increases steeply for S k <0.3 with a threshold-like behavior, while the value in the hole L cw,hole shows a more regular behavior with S k , similar to the Kolmogorov length.…”

“…The reference simulation is shown in Fig.4. Panel (a) shows the toroidal behavior of L cw on the equatorial plane (=0°) and at r=43.92cm (~2cm from the wall).The toroidal shape reproduces the well-known n=7 topology [4,13], but with a strong decrease similar to a couple of "holes", in the region around =120°, with minimum value of L cw with respect to the average. In panel (b) the toroidal behavior of the magnetic shift  1/7 of the dominant mode (red) is shown, together with the interferential pattern Δ sec of the secondary modes (black).…”

“…In this section the relation between the phenomenological parameter S k , introduced in the previous section, and the detailed edge magnetic topology is analyzed. To this end, the magnetic connection length to the wall L cw (r,,) is evaluated [13]. In the reference simulation by ORBIT code (shot #37537 t=130ms), S k =0.51.…”

“…Two cases are studied: S k =0.3 (panel a) and S k =0.8 (panel b). It is possible to identify two topological magnetic structures responsible of the L cw behavior [4,13]: the stochastic layer between the 1/7 and 0/7 islands (blue band in the Poincaré plot) and the O-points of the 0/7 islands (more evident in panel b). The red arrow indicates the toroidal position of the phase locking and the white contour corresponds to the value of the Kolmogorov length L k .…”

“…In fact, due to toroidicity, an m/n mode always generates (m + k)/n higher harmonics, k = ±1, ± 2,….., with the same n. The k = −1 poloidal sideband, which is by far the dominant one, corresponds to the 0/7 mode which is resonating in the edge, where q = 0 (reversal surface). Its amplitude is a factor ε = a/R smaller than the base mode (see figure 1 in [4] and the theoretical description in [5]). The effect of these poloidal sidebands is a correction of the shape of the edge plasma as recently shown in [6], but with little impact on the absolute value of the PWI.…”