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

Oscillatory behavior of low-frequency fluctuations in gyrokinetic simulations
K. Fujii1 and M. Nunami1,2
1 Nagoya University,
2
National Institute for Fusion Sciencee-mail (speaker): fujii.kohtaro@nifs.ac.jp
One key barrier to realizing fusion power is the turbulent
transport in magnetized plasmas. Ion temperature
gradients induce micro-instability called ITG mode, andthe ITG mode drives plasma turbulence. The turbulencecauses the particle/heat transports while exciting zonalflows via nonlinear interactions. The gyrokinetic
simulation demonstrated turbulent transport reduction byzonal flows [1]. The flows are expected to be a clue incontrolling turbulent transport.
In our work[2], the functional relation was proposedusing the time-averaged values of the turbulencecomponent 𝑇 and zonal flow component 𝑍 ofelectrostatic potential fluctuation, as well as thenormalized ion heat diffusivity 𝜒̃i . Based on the relation,
we have applied it to time series data of gyrokinetic
simulations as,
𝐶1 𝑇(𝑡)𝛼𝜒̃iModel (𝑡) =.
1 + 𝐶2 √𝑍(𝑡)⁄𝑇(𝑡)Here the coefficients (𝐶1 , 𝐶2 , 𝛼) are the fitting
parameters. We have performed gyrokinetic simulations
by means of the GKV code[3], which is a local flux tube
code. In recent work, it has been found that the functional
relation for time series data has more precisely reproduced
simulation-generated data than the relation based on timeaveraged data[4].
Furthermore, we have artificially introduced time delaysof 𝑇 and 𝑍 from 𝜒̃i , respectively represented by ∆𝑡𝑇and ∆𝑡𝑍 , to understand the influence of the correlation
between 𝑇 and 𝑍,
𝐶1 𝑇(𝑡 − Δ𝑡𝑇 )𝛼𝜒̃iModel (𝑡, Δ𝑡𝑇 , Δ𝑡𝑍 ) =.
1 + 𝐶2 √𝑍(𝑡 − Δ𝑡𝑍 )⁄𝑇(𝑡 − Δ𝑡𝑇 )The contour map of the fitting error has indicated that theerror is minimized when 𝑍 follows 𝑇 , ∆𝑡𝑇 > ∆𝑡𝑍 . On
the other hand, the similarity of the contour map has
shown that the low-frequency components may dominate
the structure of the contour map by using low-pass filtered𝑇 , √𝑍 , and 𝜒̃i . The low-frequency components haveexhibited a high coherence between 𝑇 and 𝑍 . Theseresults imply that the interaction between 𝑇 and 𝑍 oflow-frequency imposes a constraint on the time series data,
and we should investigate that.
Since zonal flows grow by energy transfer fromturbulence components, the relation between zonal flows
and turbulence can make an interpretation with thepredator-prey relation [5]. Using 𝑇 and √𝑍, the LotkaVolterra equations represent the populations of thepredator and prey,d𝑇= 𝑎𝑇 − 𝑏𝑇√𝑍,d𝑡d√𝑍= 𝑐𝑇√𝑍 − 𝑑√𝑍.
d𝑡
From these simultaneous ordinary differential equations,we get the expressions for 𝑇 and √𝑍,
11 d√𝑍𝑇(√𝑍, d√𝑍/d𝑡) = (𝑑 +),𝑐√𝑍 d𝑡
11 d𝑇√𝑍 (𝑇, d𝑇/d𝑡) = (𝑎 −).
𝑏𝑇 d𝑡
If we choose a certain cut-off frequency, 0.1 [𝑅0 /𝑣𝑡i ], ofthe low-pass filter, these equations can reproduce thesimulation data with errors less than 20 %. Here 𝑅0 and𝑣𝑡i represent the major radius at the magnetic axis andthermal speed, respectively. This indicates that we canexpress the oscillatory behavior of turbulence and zonal
flow components as the Lotka-Volterra-like equations.
References[1] Z. Lin et al., Science 281, 5384 (1998)[2] M. Nunami et al., Phys. Plasmas 20, 092307 (2013)[3] T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24(2006)[4] K. Fujii and M. Nunami, Plasma Fusion Res. 17,2403030 (2022)[5] P. H. Diamond et al., Plasma Phys. Control. Fusion 47,
R35 (2005)

Figure: Comparison between simulation data andpredator-prey model with low-frequency components.