Characterizations of Low-Frequency Zonal Flow in the Edge Plasma of the HL-2A Tokamak

Abstract

A low-frequency (<4 kHz), poloidally and toroidally symmetrical potential structure that peaks near zero frequency is observed in the edge plasma of the HL-2A tokamak. The axisymmetry structure exhibits a radial coherence length less than 1 cm. These characteristics are consistent with the theoretically predicted low-frequency zonal flows (LFZF). The radial wave-number frequency spectra of the LFZF show that the LFZF packets propagate both outwards and inwards. The geodesic acoustic mode (GAM) is found to coexist with the LFZF, and the LFZF is found to modulate the GAM and ambient turbulence with in-phase and antiphase relations, respectively, through an envelope analysis.

Zonal flow energy ratio evolution during L-H and H-L transitions in EAST plasmas

“…The characteristic of H mode is that the turbulence level is reduced compared to L mode, a strong radial electric field  E r ( ) shear exists and the ion pressure gradient develops in the plasma edge region [5,6]. Zonal flows [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] must also be considered in regulating turbulence and triggering the L-H transition. Zonal flows include the low frequency zonal flow (LFZF) and the geodesic acoustic mode (GAM).…”

Dynamic transport regulation by zonal flow-like structures in the TJ-II stellarator

“…Experimentally, global, fluctuating flow patterns manifest themselves as electric potential structures exhibiting long-range correlation (LRC), and have been observed in different devices using Langmuir probes and Heavy Ion Beam probes [5,6,7,8]. These LRC potential structures oscillate but are constant on a flux surface (which amounts to having k ≈ k ⊥ ≈ 0), but to qualify as a zonal flow-like structure they must also be 'zonal' (i.e.…”

Stability analysis of Reynolds stress response functional candidates

“…With rðxÞ ¼ À1 for x 2 ½n 1 ; n 2 and rðxÞ ¼ 1 otherwise, where n 1 ; n 2 are the positions of the sign flips with @ x u n ðn 1 Þ ¼ @ x u n ðn 2 Þ ¼ 0 and n 2 À n 1 ¼ 2p=n, we obtain the functional derivative of the second variation in Eq. (8) with respect to p(x), dd 2 V½u n ; p dpðxÞ p¼p r ¼ 4b@ 2 x u n ðn 1 Þ½dðx À n 1 Þ À dðx À n 2 Þ; (11) where the second derivative generally does not vanish, meaning that slightly altering p at the position of the sign flips n 1 ; n 2 in the right direction will render the perturbation unstable and can be done without breaking the admissibility constraint Ð 2p 0 pdx ¼ 0. (The variation (11) has such a simple structure, because the Lyapunov functional is translation invariant.…”

“…For the case of fusion reactors, the flows are of eminent importance due to their dampening effect on the turbulence 5 and they arise in two flavors, stationary [6][7][8][9][10][11][12][13] and oscillating. 14-21 For sufficiently large system size, the timeevolution of the ZF becomes deterministic since they effectively average the turbulent forces over many eddies.…”