23D08
On the Radial Electric Field in High Electron Temperature
CERC Plasmas in LHD
LHD高電子温度CERCプラズマにおける両極性径電場について	 1)

Seikichi Matsuoka, 1,2)Shinsuke Satake, 3)Arimitsu Wakasa, 1)Hiromi Takahashi,
Masayuki Yokoyama, 1,2)Takashi Shimozuma, 1)Takeshi Ido, 1)Akihiro Shimizu,
3)
Sadayoshi Murakami and 1)LHD Experiment Group
1)
1,2)
松岡清吉, 佐竹真介，3)若狭有光，1)高橋裕己，1,2)横山雅之，1,2)下妻	  隆，1)井戸	  毅，
1)清水昭博，3)村上定義，1)LHD実験グループ
1,2)

1)

2)

National Institute for Fusion Science, 322-6, Oroshi-cho, Toki, Gifu 509-5292, JapanThe Graduate University for Advanced Studies (SOKENDAI), 322-6, Oroshi-cho, Toki, Gifu 509-5292, Japan
3)
Kyoto Univ., Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan1)
核融合科学研究所 〒509-5292	  岐阜県土岐市下石町322-6
2)
総合研究大学院大学 〒509-5292	  岐阜県土岐市下石町322-63)
京都大学 〒606-8501	  京都市左京区吉田本町
The neoclassical transport analyses are carried out for LHD CERC (Core Electron-Root Confinement)
plasmas. The CERC plasmas are characterized by their high electron temperature (Te), its steep gradient,and the strong positive (electron-root) radial electric field (Er) at the core region. The poloidal rotation,
which is related to the ambipolar Er through the radial force balance, is also investigated. The poloidal
rotation of the CERC plasma increases in the negative direction with the formation of the electron-root Er
at the core region, where the flat Te profile still exists.

1. Introduction
To investigate the neoclassical (NC) transport
and the radial electric field (Er) is still an
important issue in helical devices such as LHD
withthethree-dimensional
magnetic
configuration. This is due to the so-called 1/ν
nature of the NC transport, which increases in thehigh temperature, or low collisional plasma,
where ν is the collision frequency. The radial
electric field, which is determined by theambipolar condition of the electron and ion NC
particle flux in helical devices, also plays a keyrole since it affects not only the NC transport but
also the anomalous transport arising from theturbulence through the Er shear.
In recent LHD experiments, high electron
temperature (Te) plasmas called CERC (CoreElectron-Root Confinement) [1,2] are intensively
explored with the ECH heating. The characters ofCERC are; high Te and its steep gradient of theelectron internal transport barrier (eITB) in thecore region, and the electron-root, or strong
positive Er with the strong shear in the coreregion. The eITB in a CERC plasma in LHD isformed by introducing the ECH heating [2]. As
the Te at the core region increases, the foot pointof the eITB moves outward. The region where theflat Te profile is observed becomes narrower.
Finally, the flattening of Te disappears andpeaked, or steep Te gradient, or eITB is formed,
which is followed by the formation of theelectron-root Er with the strong shear there.
The poloidal and toroidal rotations of plasma
are strongly related to the Er formation as driving
terms in the radial force balance equation [3].
Especially, in the ITB formation, the close
relationship between the poloidal rotation and Er
has been pointed out from the experimental
observations in JET [4]. (In [4], a significant
discrepancy between experimental Er and NC one
has also reported.)
However, the radial force balance of thepoloidal rotation and Er in LHD CERC (eITB)
plasmas has not been fully investigated yet. It isrequired to understand the underlying mechanismof the transport barrier from the viewpoint of theradial force balance in LHD. Thus, in this study
we focus on the behavior of the local flattening
region of Te and the formation of the NC
ambipolar Er and the poloidal rotation there inthis work. Also the particle orbit near the local
flattening region and its effect on Er and rotation
is investigated.
2. NC transport analysis by FORTEC-3D
We apply a numerical NC drift kinetic equation
solver, FORTEC-3D [5,6] to CERC plasmas.
FORTEC-3D follows the orbit of the hugenumber of particles and determines the NC
transport flux based on δf Monte-Carlo method.
The advantage of the code is that it involves thedynamics of many particles including the finite
orbit width (FOW) effect, which comes to affect
the NC transport and Er in a low collisional
plasma [4]. Since Te of the CERC plasma is highand its gradient is steep, it is appropriate toinvestigate the ambipolar Er with the electron
FOW effect.
In FORTEC-3D, the electron particle flux, Γe isdetermined from the solution of the drift kineticequation, δfe. At the same time, the  poloidal  and  toroidal   rotations   are obtained. The radial
electric field is now obtained by two ways; one isfrom the balance equation, and the other is fromthe ambipolar condition in which Er satisfies!e = !i as usually done in the transport analyses
in helical devices.

Er of the plasma w/o eITB is approximately zero atthe core region where the local flattening of Te
exists and does not rotate poloidally there. Theseresults suggest that the formation of Er and thespin-up of Vθ precede the resolution of the local
flattening.
In the presentation, we will show morecalculation results of LHD CERC plasmas. The
radial force balance of Er and the poloidal andtoroidal flows is discussed in more detail. The
particle orbit in the local flattening region is alsodiscussed.

3. Calculation results
FORTEC-3D is applied to LHD high Te plasmas.
As an example, calculation results for two cases
are shown in Fig. 1. One is the typical CERC
plasma with eITB at the core region but has thelocal flattening region at 0.2 < ! < 0.4. The otheris that without eITB and has the broad local
flattening region at ! < 0.4. The magnetic axis is3.53 m and the magnetic field strength is 2.70 T.

References[1] e.g., M. Yokoyama, et al., Fus. Sci. Tech. 50 (2006)
327.
[2] H. Takahashi, et al., IAEA Fus. Energy Conf. (2010)
pp.EXC/p8-15.
[3] K. Ida, et al., Plasma Phys. Contrl. Fus. 40 (1998)
1429.
[4] Crombé, et al., Phys. Rev. Lett. 95 (2005) 155003[5] S. Satake, et al., Plasma Fus. Res. 1 (2006) 002.
[6] S. Matsuoka et al., Phys. Plasmas 18 (2011) 032511.

Fig.1. Radial profiles of the poloidal rotation Vθ and Er.
Plasmas with and w/o eITB are shown respectively.

It is clearly shown in Fig. 1 that the CERC
plasma with eITB has the strong electron-root Er(up to 8 kV/m) at the core region and the poloidal
flow increases in the poloidal negative direction. Itshould be pointed out that the finite  Er and thus thefinite Vθ are observed at 0.2 < ! < 0.4 except
near ! = 0.3, although the local flattening of Te
does exist there. On the other hand, the ambipolar

Acknowledgments
One of the authors (S. M.) would like toacknowledge Prof. Katsumi Ida (NIFS) for his
useful comments on this research. This work is
partly supported by NIFS Collaborative Reserch
Programs, Grant No. NIFS11KNST014.