23P072-P
Numerical MHD Analysis of LHD Plasmas in Magnetic Axis Swing Operation
磁気軸スイング放電におけるLHDプラズマのMHD数値解析
Katsuji ICHIGUCHI1,2, Satoru SAKAKIBARA1,2, Satoshi OHDACHI1,2, B. A. CARRERAS3
市口勝治1,2, 榊原 悟1,2，大舘 暁1,2，B. A. CARRERAS3
National Institute for Fusion Science, Oroshi-cho 322-6, Toki, Gifu, 509-5292 Japan1
The Graduate University for Advanced Studies, Oroshi-cho 322-6, Toki, Gifu 509-5292, JAPAN2BACV Solutions Inc., Oak Ridge, Tennessee 37831, USA3
核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-61
総合研究大学院大学、〒509-5292 岐阜県土岐市下石町322-62
BACV Solutions Inc., Oak Ridge, Tennessee 37831, USA3
In the magnetic axis swing operation of Large Helical Device experiments, local pressure collapse wasobserved. In the operation, the background magnetic field was controlled during the discharge so that thecorresponding vacuum magnetic axis should be shifted inwardly. The collapse phenomenon is analyzed
numerically. The equilibria calculation with the pressure profile assumed as the shape of the square ofparabola show that the magnetic hill is formed and the magnetic shear is reduced at the resonant surface inthe change of the magnetic field. This property can enhance the driving force of the pressure driven modes,
such as interchange modes and infernal modes.

1. Introduction
MHD Stability is one of the crucial issues inthe design of future reactors. Coil arrangement
has to be determined so that collapse phenomena
should be avoided. In the heliotoron
configurations, pressure driven modes are themost dangerous instabilites which can cause thecollapses. Therefore, the determination of thecollapse boundary due to the pressure driven
mode is inevitable to construct a heliotron typemachine. In the design of the Large HelicalDevice (LHD), linear stability limit against theideal interchange mode was employed for theestimation of the collapse boundary. The linearstability analysis shows that the LHD
configuration with Rax < 3.75 m is unstable,
where Rax denotes the horizontal position of thevacuum magnetic axis. In the LHD experiments,
however, good confinement has been obtained in
the configuration with Rax=3.6m. Particularly,
the highest beta vale of <β>=5.1% is achieved[1]in the configuration. This result indicates thediscrepancy between the linear stability results
and the experiments.
Recently, so-called magnetic axis swing
experiment was carried out to find out thecollapse boundary concerning with the position of
the vacuum magnetic axis[2]. In this experiment,
the currents in the poloidal field coils are changed
during each shot so that the corresponding
vacuum magnetic axis position should be shifted
inwardly. In the case where the corresponding
vacuum magnetic axis position is changed from

Rax=3.60m to Rax=3.50m, plasma collapse isobserved after the corresponding vacuum axis
position is about Rax=3.55m. The collapse islocalized around the magnetic surface with therotational transform of 1/2 in the core region.
This result indicates the collapse boundary may
exist around Rax=3.55m. Thus, in the presentwork, we investigate the mechanism of thecollapse with numerical MHD approach.
2. Numerical Method
To analyze the results of the magnetic axis swing
experiment, we have to treat the time evolution of
the background equilibrium as well as theperturbations, because the equilibrium quantities
vary depending on the change of the coil currents.
However, there is big difference between the timescales in the change of the equilibrium and theperturbed quantities. The equilibrium quantities
changes in the order of 10ms, while the perturbed
quantities changes in the order of 1μs.Therefore, in
the analysis of the axis swing experiment, we haveto solve a multi-scale problem.
We have already established a numerical scheme
to treat such multi-scale problems [3-6]. In thescheme, time-dependent nonlinear dynamics
calculation and update of the static equilibrium isiterated. The NORM code[7] and the VMEC
code[8] are used for the dynamics and theequilibrium calculations, respectively. The NORM
code follows the dynamics based on the reduced
MHD equations. In the equilibrium calculation, thedeformation of the average part of the pressure isincorporated. This scheme is applied to the LHD
plasma in the configuration with Rax=3.6m toinvestigate the stability mechanism in the plasma.
The result indicates a stable scenario to high beta
regime with self-organization of the plasma.
In the present work, we utilize this scheme in thenumerical analysis. Particularly, we incorporate thechange of the magnetic field due to the change ofthe poloical coil currents in the VMEC equilibrium
calculation.
3. Equilibrium Property
Before the nonlinear dynamics calculation, we
examine the Rax dependence of the equilibrium
quantities. We calculate the free boundary
equilibria with the VMEC code under the nonet-current condition. The pressure profile of
P=P0(1-s)2 is employed and the beta value at theaxis is fixed to β0=4.2%, where s denotes thenormalized toroidal magnetic flux. In the freeboundary calculation, a virtual limiter is set at
R=4.2m. We change the vacuum magnetic fieldfrom that of Rax=3.6m to that of Rax=3.5m.

well region in the case of Rax =3.5m.
As a result, in the change of the magnetic fieldfrom Rax=3.6m to 3.5m, there is a tendency that themagnetic shear is reduced and the magnetic wellchanges to the magnetic hill. This tendency
indicates that an interchange mode is more easily
destabilized for smaller Rax. Since the position ofthe ι=1/2 surface is located near the magnetic axis
and the magnetic shear is weak at the surface, anon-resonant mode like an infernal mode can beunstable in these configuration. Based on theknowledge, we study the nonlinear behavior of theunstable modes and investigate the collapse
mechanism by applying the multi-scale scheme.
V'' R ax=3.6m-3.5m,B q=100% ,γ=1.196

1.0

P=P 0 (1-s) 2
β 0 =4.2%
rlim =4.6m

ι0.80
0.70

00.60
0.50

Rax=3.6m-3.5m,Bq=100%,γ=1.196

β(%)

3322
1
102.53.0

3.5

4.0

4.5

rotational transform

P=P0(1-s)2
β0=4.2%
rlim=4.6m

40
5.0

R (m)

Fig.1. Rax dependence of pressure profile and rotationaltransform profile as functions of major axis R. Solid,
dashed, and dot-dashed lines correspond to Rax=3,60m,3,55m and 3.50m, respectively.

As shown in Fig.1, the magnetic axis is locatedmore inward as Rax decreases. The rotationaltransform at the magnetic axis is slightly smaller
than 1/2 in all cases. As shown in Fig.2, the Raxdependence of the profile is not necessarily
monotonic, however, the position of the ι=1/2
surface approaches to the magnetic axis. The
magnetic shear becomes weak at the surface
simultaneously. The profile of the magnetic wellcorresponds to the property of the position of themagnetic axis. In the case of Rax=3.6m, themagnetic well spreads from ρ=0 to ρ=0.42 and thesurface of ι=1/2 exists in the well region. As Rax
decreases, the well region shrinks and there is no-1.000.5ρ

0.40
1.0Fig.2. Rax dependence of V’’ profile and rotationaltransform profile as functions of ρ. Solid, dashed, anddot-dashed lines correspond to Rax=3,60m, 3,55m and3.50m, respectively.

Acknowledgments
This work is supported by a budget
NIFS11KLTT001 of the National Institute forFusion Science, and Grant-in-Aid for Scientific
Research (C) 22560822 of JSPS Japan.
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