25F08
Simulation Study of Energetic Particle Driven Geodesic Acoustic Mode in LHD
Plasma高エネルギー粒子駆動測地音響モードのシミュレーション研究	 
Hao Wang1), Yasushi Todo1,2)王	  灏1）, 藤堂	  泰１、２）
1)

The Graduate University for Advanced Studies
Oroshi-Chou 322-6, Toki 509-5292, Japan
2)
National Institute for Fusion Science
Oroshi-Chou 322-6, Toki 509-5292, Japan１）
総合研究大学院大学	  〒509-5292	  土岐市下石町３２２−６２）
核融合科学研究所	  〒509-5292	  土岐市下石町３２２−６The energetic particle driven geodesic acoustic modes (GAM) in the Large Helical Device are investigatedusing a hybrid simulation code for magnetohydrodynamics (MHD) and energetic particles. It is found thatthe mode frequency is lower and the growth rate is higher for higher energetic particle β values. Both thechirped frequency and the constant frequency evolutions take place. The resonant particle distribution invelocity space is investigated, and the transit frequency of the resonant particles is in good agreement withthe mode frequency. In addition, both the inward propagating and the outward propagating modes areobserved in the simulation results.

2. Simulation ModelIn the MEGA code, the bulk plasma is describedby the nonlinear MHD equations and the energetic
ions are simulated with the δf particle method. Theenergetic ion contribution is included in the MHD
momentum equation as the energetic ion currentdensity. This model is accurate under the condition
that the energetic ion density is much less than thebulk plasma density.
The energetic particle distribution function in€thepresent simulation is anisotropic in pitch angle Λ,and it peaks at Λ=Λpeak. Here Λ=µB0/E, µ is
magnetic moment, B0 is magnetic field strength at
the magnetic axis, and E is particle energy.
Realistic LHD experimental parameters are used for

simulation whereas axisymmetric equilibrium withconcentric circular magnetic surfaces is employed.
The helical effect is not considered.
3. The Mode Linear Property
5040354030
2530202015101000.0001

fa0.0002`hgrowth rate [%]Frequency [unit: kHz]

1. Introduction
The GAM is an oscillation of toroidal plasma
for which the m = n = 0 electrostatic potential islinearly coupled (by toroidal effects) to the m = 1,n = 0 sideband density perturbation.[1] This mode
is normally driven by plasma micro-turbulence,but in these years, energetic particle driven GAM
is also observed in many tokamaks and helicaldevice.[2,3] The energetic particle driven GAM isimportant since it may enhance the radialtransport of energetic particles, and deteriorate
the performance of fusion reactors.[4] In thismanuscript, the energetic particle driven GAM issimulated with MEGA code, a hybrid simulation
code for MHD and energetic particles.[5]500.0003

Fig.1. The frequency and growth rateversus energetic particle β value.

The simulated energetic particle driven GAM is34kHz with energetic particle β value equals 0.2%.
For comparison, the theoretical (MHD) GAM
frequency
is37.5kHz
with
f = (γP / ρR 2 )(1+ ι 2 /8π 2 ) /2π , the measured GAM
frequency in LHD is 32kHz. These threefrequencies are close to each other.
The simulation is performed with different
energetic particle β value in order to clarify how thefrequency and growth rate are affected by energetic
particles. We see lower frequency and higher
growth rate for higher βh as shown in Fig. 1. The
simulated NBI energy is 40keV. In the case ofENBI=170keV, the results are similar with

ENBI=40keV case.

propagating case.

4. Frequency Evolution
In LHD, both the chirping frequency and theconstant frequency evolutions are observed. In thepresent work, with the parameters βh=0.03%,
Λpeak=0.3 and NBI energy equals 170keV, the mode
frequency chirps from 50kHz to 65kHz in a fractionof a millisecond, as shown in Fig. 2. Different
simulation conditions are compared to investigate
the energetic particle driven GAM frequency
evolution behavior, and the results are shown in
Table I.

Fig.3. The energetic particle dE/dt
distribution in E-Λ space.

Fig.2. The frequency chirps from 50kHz to 65kHz.

Fig.4. The mode amplitude evolution.

Table I. The frequency evolution is affected by energetic
particle energy ENBI and peak pitch angle Λpeak.	 

6. Summary
In summary, the energetic particle driven GAMin LHD was simulated. As the linear properties,
the mode frequency decreases and growth rateincreases with βh increases. Both the chirpedfrequency and the constant frequency evolutions
take place. The resonant particle distribution invelocity space was investigated, and the transit
frequency of the resonant particles is in good
agreement with the mode frequency. In addition,
both the inward propagation and the outward
propagation were observed in the simulation
results.

Λpeak=0.3
Λpeak=0.5

ENBI=40keV
constant
constant

ENBI=170keV
chirpedconstant

The time derivative of particle energy isinvestigated in velocity space. The result is shownin Fig. 3. We see two regions of strong energy
transfer around (E=60keV, Λ=0.4) and (E=40keV,Λ=0.15). The signs of the energy transfer are
different from each other. The region around
E=60keV (E=40keV) is destabilizing (stabilizing)
the GAM. The transit frequency ftr, is defined asf tr = 1− Λ v /(2πqR0 ) ,where v is the energetic particle velocity, q is thesafety factor and R0 is the major radius. The transit
frequencies€ of the two regions are close to the mode
frequency. The solid curve in Fig. 3 presents aconstant transit frequency ftr=fGAM≡52.6kHz. Theenergetic particles in the two velocity space regions
are resonating with the GAM.
5. Mode Propagation
The energetic particle driven GAM can propagate
inward and outward, and both of propagations areobserved in experiment. They are also simulated in
the present work. Figure. 4 shows the inward

References[1] P H Diamond, S-I Itoh, K Itoh and T S Hahm:
Plasma Phys. Control. Fusion 47 (2005) R35.
[2] R. Nazikian, G. Y. Fu, M. E. Austin, H. L. Berk, R.
V. Budny, N. N. Gorelenkov, W. W. Heidbrink, C. T.
Holcomb, G. J. Kramer, G. R. McKee, M. A.
Makowski, W. M. Solomon, M. Shafer, E. J. Strait,and M. A. Van Zeeland: Phys. Rev. Lett. 101 (2008)
185001.
[3] T. Ido, A. Shimizu, M. Nishiura, S. Nakamura, S.
Kato, H. Nakano, Y. Yoshimura, K. Toi, K. Ida, M.
Yoshinuma, S. Satake, F. Watanabe, S. Morita, M.
Goto, K. Itoh, S. Kubo, T. Shimozuma, H. Igami, H.
Takahashi, I. Yamada, K. Narihara and the LHD
Experiment Group: Nucl. Fusion 51 (2011) 073046.
[4] G. Y. Fu: Phys. Rev. Lett. 101 (2008) 185002.
[5] Y. Todo: Phys. Plasmas 13 (2006) 082503.