23P136-B
Numerical Measurements of Plasma Turbulent Structures Using theTurbulence Diagnostic Simulator
乱流計測シミュレータを用いたプラズマ乱流構造の数値計測
Naohiro Kasuya, Masatoshi Yagi, Kimitaka Itoh and Sanae-I. Itoh糟谷直宏, 矢木雅敏1,2), 伊藤公孝, 伊藤早苗1)
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-61) Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-kouen, Kasuga, Fukuoka 816-8580, Japan
九州大学応用力学研究所 〒816-8580 福岡県春日市春日公園6-12) Japan Atomic Energy Agency, 2-166 Omotedate, Obuchi, Rokkasho-mura, Aomori 039-3212, Japan
日本原子力研究開発機構 〒039-3212 青森県六ヶ所村尾駮表舘2番166
Turbulence Diagnostic Simulator is an assembly of simulation codes to clarify the formation mechanism of
turbulent structures by numerical diagnostics in magnetically confined plasmas. Global simulations arecarried out using a reduced MHD model of drift-interchange mode in helical plasmas, and time series dataof 3-D fluctuation fields are produced. Magnitudes of linear contribution and nonlinear couplings from theconvective derivative and the parallel derivative are evaluated in the nonlinear saturated states. It is shownthat the nonlinear couplings with higher m modes in the middle radius contribute to the pressure profile
modification, and the toroidal coupling induces the potential oscillation.

1. Introduction
Turbulence in toroidal plasmas forms
meso-scale structures, such as a zonal flow, and it
is important to clarify their role on anomaloustransport [1]. Numerical simulations can give
three-dimensional (3-D) turbulent fields, which
represent fundamental phenomena in plasmas, sothe simulation data are suitable as a test field tocarry out detailed analyses for comparison withexperimental results [2]. We have beendeveloping Turbulence Diagnostic Simulator(TDS), which is the combination of fluid
turbulence codes and numerical diagnosticmodules to simulate experimental measurementsof plasma turbulence [3]. Several kinds ofanalyses are possible corresponding to research
objects. In this paper, drift-interchange modes inhelical plasmas are analyzed, using TDS. The
contributions to energy evolutions from nonlinear
couplings are evaluated to clarify the formation
mechanism of turbulent structures.
2. ModelTo provide turbulence data, a simulation code
has been developed to calculate the drift-interchange turbulence in helical plasmas with acircular cross-section [3]. The averaging methodwith the stellarator expansion [4] is applied to givea set of model equations for stream function u, 
component of the vector potential A and totalpressure P. The model in [3] is extended to include
the magnetic curvature term in the pressure

evolution equationconservation.

tosatisfy

theenergy

3. Nonlinear Simulation
Three kinds of simulations are carried out; i) one
without the parallel dynamics of electrons, which
only includes the interchange mode, ii) one with theparallel dynamics of electrons but without themagnetic curvature term in the pressure evolutionequation, and iii) one including all terms in themodel. Here we analyze one of the set of turbulence
data from simulation ii), because the simulation
gives the most dynamical saturation.
The nonlinear simulation is performed, using thefollowing parameters: magnetic field B = 2.0 [T],electron temperature Te = 1 [keV], minor radius a =0.6 [m], major radius R0 = 3.75 [m], viscosities = 1  10-4, pole number l = 2, pitch
number M = 10. Rotational transform  is given by amonotonically increasing function with the radiusfrom  (0) = 0.31 to  (a) = 0.88, so rational surfaces
with m / n = 2 / 1 and 3 / 2 are included, but 1 / 1 is
not in the plasma, where m and n are the poloidal
and toroidal mode number, respectively. 1024 grids
in the radial direction and Fourier modes -32  m 32, -8  n  8 are taken.
Spatio-temporal data of turbulent fields aregenerated by this global simulation [5]. The
calculation with a fixed pressure source, whichforms a pressure profile peaked at r = 0, is carriedout. Low m, n modes whose rational surfaces exist

in the plasma are excited in the linear growing
phase, and saturation is obtained. In the saturated
state, mode structures of low m, n modes, such as(m, n) = (1, 1) and (2, 1), spread broadly in theradial direction, and those of medium m, n modes,
such as (3, 2) and (8, 4), are localized near theirrational surfaces. Here, we assume that variable u
represents the normalized electrostatic potential .
4. Nonlinear Coupling Process
The 00 component, which gives a mean poloidal
flow, is produced in the saturated state. Figure 1
shows the frequency and radial wavenumber
spectrum of 00, which has a characteristicfrequency f ~ 0.02. The radial structure is rather
global, though there exists perturbations with kr = 3- 9 in some moments. Here we analyze its
generation mechanism by calculating the linear andnonlinear contributions to the energy evolution.
The evolution equation of the electrostatic
potential energy includes the contributions from thelinear term (LT), ballooning term to give a linear
coupling with neighboring modes (TC), nonlinear
terms from the convective derivative (NT1) and theparallel derivative (NT2). NT2 comes fromelectromagnetic fluctuations in the //J term. The
volume integration of each term shows that TC is
the largest, so the main cause of the 00 oscillationis the coupling between 00 and P10.
For P10, competition between negative LT andpositive NT1 determines the evolution, so both theprofile modification, which contributes to thevariation of LT, and the nonlinear couplings, which
contribute to NT1, must be taken into account.
Figure 2 shows the radial profile of the nonlinear
contribution to the P10 formation, where NT1 isdecomposed into ones with each poloidal mode
number. There is a region where the contributions
from modes with higher m mode numbers arestrong in r / a = 0.5 - 0.8. The profile modificationarises in this region, and propagates to the otherregions. In addition, the dominant mode changes
according to the radial position.
For 32, which has large amplitude, LT+TC andNT1+NT2 are comparable. Among the nonlinear
contributions, NT2 is larger than NT1, and bursts of
NT2 affect the evolution.
For P00, the radial profile of NT1 indicates thecharacteristic regions; r / a < 0.3: strong mode
excitation, 0.4 - 0.7: existence of various modes, >0.8: existence of small number of dominant modes,
corresponding to the different features shown in thetime evolution of the 2-D contour on the poloidal
cross-section in [5].

Numerical diagnostics to simulate experimental
measurements are also carried out, whose results
will be presented in the poster.
5. Summary
In summary, global simulations are carried out
using a reduced MHD model in helical plasmas,
and obtained time series data of 3-D fluctuation
fields are analyzed. Magnitudes of linear andnonlinear contributions are evaluated. It is shownthat the nonlinear couplings with higher m modesin the middle radius contribute to the P10modification, and the toroidal coupling between
00 and P10 induces the 00 oscillation. In this way,
the data analysis using TDS is effective to clarify
the structural formation mechanism.

Fig.1. (a) frequency spectrum at r / a = 0.5 and (b)radial wave number spectrum of 00.

Fig.2. Radial profile of the nonlinear contribution tothe P10 evolution, which is decomposed into
each poloidal mode number component.

Acknowledgments
This work is supported by the Grant-in-Aid forYoung Scientists (20760581) and for Scientific
Research (21224014) of JSPS, by the collaboration
program of NIFS (NIFS11KNST013) and of RIAM
of Kyushu University.
References[1] P. H. Diamond, et al., Plasma Phys. Control. Fusion
47 (2005) R35.
[2] N. Kasuya, et al., Phys. Plasmas 15 (2008) 052302.
[3] N. Kasuya, et al., Plasma Sci. Tech 13 (2011) 326.
[4] M., Wakatani, Stellarator and Heliotron Devices(Oxford University Press, Oxford 1998).
[5] N. Kasuya, et al., Proc. 38th EPS Conf. on Plasma
Phys., Strasbourg, 2011, P4.113.