Determination of poloidal mode numbers of MHD modes and their radial location using a soft x-ray camera array in the Wendelstein 7-X stellarator

Abstract

A forward modeling technique is developed for determining the characteristic features of observed MHD modes from the line-of-sight data of the soft x-ray (SXR) tomography diagnostics in the Wendelstein 7-X (W7-X) stellarator. In particular, forward modeling is used to evaluate the poloidal mode numbers m, radial location, poloidal rotation direction and ballooning character of the MHD modes. The poloidal mode structures have been modeled by the radially localized Gaussian-shaped emission regions rotating along the magnetic surfaces. In the present study the cases of rigid-shape emission regions and flexible emission regions are modeled. Various mode phase velocity dependences on the magnetic surface position are simulated. The modeled phase dynamics of line-integrated oscillations and the distribution of oscillation amplitudes are compared with the experimental signals of the SXR cameras which observe the plasma at various viewing angles in the poloidal cross-section. Application of this technique enables describing of the 1–50 kHz modes. In particular, in the discharge W7X-PID 20180918.045 three identified branches with the poloidal mode numbers m= 8, m= 10 and m= 11 localized at ρ ≈ 0.3 are rotating in the clockwise poloidal direction. The present paper reports the first application of the forward modeling technique to the data from the SXR diagnostics in W7-X. The high m-modes are identified by forward modeling in W7-X.

Determination of MHD mode structures using soft x-ray diagnostics in TCV

“…In order to extract the information about the mode numbers and direction of the rotation from line-integrated SXR measurements, we first use a simplified eigenmode model for the mode pattern in the poloidal plane of the location of the MPX camera (cf figure 3(a)). This model is adopted from the model described in detail in [15]. It is possible to perform 'virtual measurement' along the lines-of-sight across the modeled xray radiation distribution.…”

“…Thus, the path of the mode perturbation in the 'far away' and the 'near plasma' parts with respect to the camera cannot be distinguished from the SXR data. The significant difference in the paths can be caused by the closer location of the SXR camera [15] or by the asymmetry of the magnetic flux surfaces [13]. So, the sign of m cannot be experimentally determined in TCV, and only the absolute value of m can be determined.…”

“…The path along the magnetic flux surface is used in our calculations for the poloidal mode velocity modeling. We use the normalized path l n in our calculations [15]. The l n = 1 value corresponds to the single poloidal turn of the mode.…”

“…Figure 3(c ballooning modes. An analysis of multiple-m modes is difficult for the high-m mode case [15]. As seen from figure 5, such analysis is rather simple for the low-m TCV case.…”

“…The poloidal mode number and radial location can be determined using a singular value decomposition technique [8,10]. Forward modeling [8,[13][14][15][16][17][18] can be used for this purpose as well.…”