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

The influence of cross-phase on turbulent transport of toroidal momentum

W. Tian1,2, T. Long1, P. H. Diamond3, M. Xu1, R. Ke1, L. Wang4, Z. Gao2
1Southwestern Institute of Physics, 2Department of Engineering Physics, Tsinghua University,
3CASS and Department of Physics, University of California, San Diego
4
School of Electrical and Electronic Engineering, Huazhong University of Science and Technology
e-mail (speaker): tianwj19@mails.tsinghua.edu.cn
Previous works indicate that intrinsic rotation is ofsignificant importance for the next generation devices
like ITER, where external momentum input is not
sufficient to drive large enough toroidal rotation tostabilize MHD instabilities such as the resistive wallmode [1]. Plasma intrinsic rotation is believed to be thesynthesized result of multiple effects, such as effects ofMHD, neoclassical and turbulent fluctuation and so on.
Results in DIII-D ohmic L mode and ECH H-mode
plasma show a clear disagreement in neoclassicalprediction and measured velocities [2]. In this case,influence of turbulence must be taken into account.
The key physics quantity related to intrinsic rotation isturbulent momentum flux, which can be showed asequation (1)[3]:(1)
tur  n Vr  V   V  n Vr  n Vr  V The three terms on the right-hand side are Reynolds
stress term, convective term and triplet term,respectively. The Reynolds stress could be decomposed
as follows, VrV    PVrV ( w) cos  ( w)w

 Im( PVrV ( w))  Re( P  ( w)) VrV ( w)  arctan (2)(3)

The Reynolds stress relies on fluctuation intensity as
well as the cross phase between Vr and V  .
A shot-by-shot density ramp-up experiment isoperated in J-TEXT tokamak. The plasma is ohmicly
heated, with no external toroidal momentum source. Tensof discharges are operated with line averaged density
among 0.32-0.55 nG , the Greenwald density limit. A setof reciprocating Langmuir probe array which is capableof measuring all terms in equation (1), provides
significant parameters for the experiment.
The edge toroidal rotation V  is in co-Ip direction in
low density and reverses to counter-Ip direction in highdensity. The predicted neoclassical V  is in counter-Ip
direction. The deviation from neoclassical prediction isanalyzed by direct measurement of the turbulent
momentum flux and its three components. The former
two terms both contribute to momentum transport.
Reynolds stress term provides a strong co-Ip torque inlow density, which becomes weak in high density inwhich case the convective term kicks in with a minor
counter-Ip torque. Cross-phase dynamics for Reynolds
stress and particle flux are analyzed. The varied
contribution of Reynolds stress term in varied densities isfrom the change of cross-phase behavior. In low density,
the cross-phase shows a phase slip characteristic andprovides a large radial gradient to the Reynolds stressand thus a strong torque. While in high density, thecross-phase concentrates around  in the whole profile,giving rise to a flat profile. These trends can be clearlyseen in figure 1. As a comparison, the cross-phase inparticle flux has a flat profile around 0 rad. The
counter-Ip torque from convective term in high density is
the result of synthetic effects of V  gradient andincreased density fluctuation gradient.
References[1] E.J. Doyle et al Nucl. Fusion 47 (2007) S18–S127[2] Grierson B.A. et al., 2013 Nucl. Fusion 53 063010[3] Diamond P.H. et al 2009 Nucl. Fusion 49 045002

Figure 1. Left: profiles of the components in equation (1) in three different densities. Right: the cross phase ofReynolds stress in 0.34 nG and 0.52 nG .