7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

MHD numerical analysis of global flow in 3D magnetic configurations

Katsuji ICHIGUCHI1,2, Yasuhiro SUZUKI3, Yasushi TODO1, Yuki TAKEMURA1,2,Satoru SAKAKIBARA1,2, Mikiro Yoshinuma1, Benjamin A. CARRERAS4
1
National Institute for Fusion Science, 2 The Graduate University for Advanced Study, SOKENDAI,
3Graduate School of Advanced Science and Engineering, Hiroshima University, 4 BACV Sol. Inc.
e-mail (speaker) : ichiguchi.katsuji@nifs.ac.jp
The global flow can affect the global stability of fusion
plasmas. In tokamaks, for example, the effects of theplasma rotation on the edge localized mode and resistive
wall mode are studied extensively. Also in stellarators, it
has been reported that collapse phenomena wereobserved in the phase of no plasma rotation in Large
Helical Device (LHD) [1,2,3]. However, in thetheoretical aspect, the flow has not been studied
systematically. One reason is that the evaluation of theglobal flow is not very easy in three dimensional (3D)
magnetic configurations numerically. For this point, wehave established a numerical scheme to calculate the 3D
profile of the global flow. We already showed theoriginal idea of the scheme and the preliminary results of
the application to the flow in the LHD plasma [4]. Also,
the effects of the obtained flow on the stability against
the interchange instability was examined by utilizing theHINT code [5] and the MIPS [6]. The preliminary resultthat the global flow has a stabilizing contribution on theinstability was obtained in the early nonlinear phase.
Recently, we have improved several points in the flow
calculation and in the stability analysis. In the flow
calculation, the incompressibility and the surface flow
are assumed in the formulation. The accuracy of thenumerical achievement of the assumption is improved
through the modification of the coordinate transform
procedure between Hamada, VMEC, and cylindricalcoordinates. As a result, the continuous streamlines of
the global flow are obtained. In addition, we haveremoved a kind of singularity at the magnetic axis
position by developing a new root-finding technique.
As the previous work on the evaluation of the 3D global
flow, Kumar et al. proposed another formulation [7].
They only treated so-called Pfirsch-Schluter (PS). On
the other hand, our formulation covers wider range of theflow including the PS flow. Thus, we have derived theformula corresponding to the PS component and haveshown that our formulation is identical to the Kumars’sone. We have also revealed that the condition assumed in
the Kumar’s formulation corresponds to no flow in thesurface average.
In the stability analysis we have made improvement
significantly. The viscosity has been made work only on
the perturbed component of the flow to keep theamplitude of the global background flow in the entire
time evolution. The linear growth rate of each toroidal
component of the instability can be evaluated from thekinetic energy component now, which was masked by

the big contribution of the global flow.
In the conference, we will discuss the numerical results
obtained by utilizing the updated numerical tools shown
above. In particular, we will focus on the dependence ofthe linear stability and the nonlinear saturation level ofthe instabilities on both the beta value and the flow
amplitude.
References[1] S. Sakakibara, et al., Nucl. Fusion, 55, 083020 (2015)[2] Y. Takemura, et al., Plasma Fusion Res., 12, 1402028(2017)[3] Y. Takemura, et al., Nucl. Fusion, 59, 066036 (2019)[4] K. Ichiguchi et al, Proc. of 44th EPS Conference on
Plasma Physics, 26 - 30 June 2017, P2.133, (2017).
[5] Y. Suzuki et al., Nucl. Fusion, 46, L19 (2006).
[6] Y. Todo et al., Plasma and Fusion Res., 5, S2062(2010).
[7] S. T. A. Kumar et al., Nucl. Fusion 57, 036030 (2017)