Comparative studies of cross-phase dynamics in turbulent momentum flux and particle flux at the tokamak edge
Authors: Long Ting , Diamond P. H. , Hong Rongjie , Tian Wenjing , Ke Rui , Zhou Yongkang , Wang Zhanhui , Nie Lin , Xu Min , Wang Zhe , Li Bo , Hao Guangzhou , Li Jiquan , Xiao Guoliang , Shi Zhongbing , Chen Wei , Zhong Wulyu 
Published: February 2025

Abstract
Turbulent transport events, including turbulent transport flux of momentum (i.e., turbulent momentum flux or Reynolds stress) and turbulent transport flux of particle (i.e., turbulent particle flux), have important effects on the confinement performance of magnetic confinement fusion devices. Poloidal Reynolds stress is the ensemble average of the product of radial velocity fluctuations and poloidal velocity fluctuations, i.e.,

$$\langle {\widetilde{v}}_{r}{\widetilde{v}}_{\theta }\rangle$$

⟨

v
~

r

v
~

θ

⟩

. Turbulent particle flux is the ensemble average of the product of radial velocity fluctuations and density fluctuations, i.e.,

$$\langle \widetilde{n}{\widetilde{v}}_{r}\rangle$$

⟨

n
~

v
~

r

⟩

. Changes in either amplitude of fluctuations or cross phase between fluctuations can cause changes in turbulent transport. In this paper, cross-phase dynamics in the Reynolds stress and turbulent particle flux at the tokamak edge are studied in detail. Reynolds stress and turbulent particle flux are, respectively, written as the product of fluctuation amplitudes and an average cross-phase factor. The mathematical expressions of the average cross-phase factors are derived. The average cross-phase factors and the power spectra of cross phase are obtained using experimental measurement data. It is found that the cross-phase dynamics in Reynolds stress and particle flux are very different. Reynolds stress is found to be more sensitive to cross phase than particle flux is. In the strong

$$E\times B$$

E
×
B

shear layer, spatial slips of cross phase lead to the obvious radial gradient of Reynolds stress. In the no/weak

$$E\times B$$

E
×
B

shear region, the cross phase in Reynolds stress tends to lock. Here, phase locking refers to that the power spectra of phase tend to distribute around a fixed phase which does not change with radial position, while phase slip means that the power spectra of cross phase tend to distribute around a phase that varies with radial position. Phase slip or locking mainly describes the central phase weighted by the power spectra, while the phase scattering mainly describes the dispersion of the power spectrum distribution of the phase. The increased scattering of cross phase, which indicates the power spectra distribution of the phase is more dispersed, contributes to the decreased Reynolds stress for higher collisionality. The cross phase in particle flux tends to lock in both strong and no/weak shear regions. The degree of scattering of cross phase in the particle flux does not change obviously as collisionality increases. For higher collisionality, it is the increased density fluctuation amplitude rather than cross-phase dynamics that leads to the increased particle flux. The underlying physical mechanism that causes Reynolds stress and particle flux to exhibit different phase dynamics is discussed.