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

Zonal Flow Generation in the Presence of Fast Ions

T. S. Hahm1, G. J. Choi2, S. J. Park2, Y.-S. Na2
1
Nuclear Research Institute for Future Technology and Policy, Seoul National University
2
Department of Nuclear Engineering, Seoul National University
e-mail (speaker): tshahm@snu.ac.kr
Fast ions’ effects on turbulence-driven zonal flow
generation are investigated in the context of a simple
reduced model based on the Hasegawa–Mima equation.[1]Fast ions’ much higher characteristic frequency ofparallel motion in comparison to the drift wave’s phasevelocity along the magnetic field facilitates a derivationof the reduced model equations. Nonlinear mode
coupling analyses show that the threshold amplitude ofdrift wave required for the zonal flow modulational
instability is significantly reduced, making its generationeasier. This occurs as both a down-shift of the drift
wave’s frequency and a reduction of dispersion in thepresence of the fast ions cause a decrease in themismatch between the primary drift wave frequency andthe zonal flow modulated sideband drift wave’s
characteristic frequency.
Specifically, in the long wavelength regime, satisfying𝑘⊥ 𝑞𝑠 ~𝑞𝑥 𝜌𝑠 ≪ 𝑘⊥ 𝜌𝑇𝑓 ~𝑞𝑥 𝜌𝑇𝑓 ≪ 1 ( 𝑘⊥ and 𝑞𝑥 arewavenumbers of drift wave and zonal flow, and 𝑞𝑠 and𝑞𝑇𝑓 are the Larmor radius of main ion at electron
temperature and of fast ions), fast ions do not contributeto the vorticity of drift waves, while they do for thevorticity of zonal flows. Consequently, the reductions of
the drift wave frequency and its dispersion due to thedilution of main ion density lead to the reduction offrequency mismatch from the sideband induced drift
wave’s characteristic frequency. As a result, the thresholdof drift wave amplitude is reduced, making the zonal
flow generation easier as shown in the below equation
and Figure 1-a.[2] for zonal flow growth rate.

and time are normalized to 𝜌𝑠 and 𝐿𝑛𝑒 /𝑐𝑠 .
In the intermediate wavelength regime, 𝑘⊥ 𝑞𝑠 ~𝑞𝑥 𝜌𝑠 ≪1 ≪ 𝑘⊥ 𝜌𝑇𝑓 ~𝑞𝑥 𝜌𝑇𝑓 , the fast ions’ contribution tovorticity is negligible for both drift waves and zonal
flows due to unmagnetized fast ion density response topotential fluctuation. Therefore, the zonal vorticity
equation is not affected. However, the dilution of mainion density and the reduction of its gradient decrease thethreshold value of the primary drift wave amplitude
required for the zonal flow generation via the reductionsof the drift wave frequency and its dispersion. Its
dependence on the main ion dilution factor is stronger
compared to the long wavelength case as shown in the𝐿𝑛𝑒 2Γ ≈ √1 − 𝑓ℎ 𝑘𝑦 𝑞𝑥 √2|𝜙DW0 |2 − (1 − 𝑓ℎ )3 ( ) 𝑞𝑥2𝐿𝑛𝑖References[1] A. Hasegawa and K. Mima, Phys. Fluids 21, 87 (1978)[2] T.S. Hahm et al, Phys. Plasmas 30, 072501 (2023)[3] H. Han et al, Nature 609, 269 (2022)[4] S. Mazzi et al, Nat. Phys. 18, 776 (2022)[5] S. H. Kim et al, Nucl. Fusion 56, 126002(2016)

Here, Γ is a growth rate of zonal flow, 𝑓ℎ ≡ 𝑍𝑓 𝑛𝑓0 /𝑛𝑒0 ,𝜙DW0 = (𝐿𝑛𝑒 /𝜌𝑠 )(|𝑒|𝛿𝜙DW0 /𝑇𝑒 ) where 𝛿𝜙DW0 is an
primary electrostatic potential fluctuation, and the length

below equation and Figure 1-b.[2] for zonal flow growth
rate.
𝐿𝑛𝑒 2
Γ ≈ 𝑘𝑦 𝑞𝑥 √2|𝜙DW0 |2 − (1 − 𝑓ℎ )4 ( ) 𝑞𝑥2
𝐿𝑛𝑖
This finding could be a common nonlinear physics
mechanism behind numerous recent results on tokamak
plasma confinement enhancement caused by the fastions.[3,4] Our long wavelength approximation for zonal
flows are reasonable for the case with 100 keV range fast
ion temperature with 𝑇𝑓 /𝑇𝑒 ~10 as shown in an example
in Ref [3]. Regarding the ITER parameters with𝑇𝛼 /𝑇𝑒 ~10 [5] and an example dealing with 1 MeV rangefast ions with 𝑇𝑓 /𝑇𝑒 ~30,[4] our results for the moderate
wavelength regime can be tested.

Figure 1. Normalized zonal flow growth rate Γ/k y 𝜌𝑠 in the unit of cs /𝐿𝑛𝑒 (a) for qx 𝜌𝑠 = 0.2 in the long wavelength𝑠regime and (b) for qx 𝜌𝑠 = 0.4 in the intermediate wavelength regime.