S6-3

On the Physics of Vortex Formation in Plasmas
プラズマ渦形成の起源と構造の解明
M. Y. Tanaka, S. Yoshimura, K. Nagaoka, A. Okamoto*, M. Kono**
田中雅慶，吉村信次，永岡賢一，岡本 敦*，河野光雄**
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
核融合科学研究所，〒509-5292 土岐市下石町322-6*High Temperature Plasma Center, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan東京大学高温プラズマ研究センター，〒113-8656 東京都文京区弥生2-11-16**Faculty of Policy Studies, Chuo University, Hachioj, Tokyoi 192-0393, Japan
中央大学総合政策学部，〒192-0393 東京都八王子市東中野

Since the drift of ions is likely to generate vortical motion, magnetized plasma is a mine of vortex physics.
We have observed a variety of vortices such as a plasma hole and a tipolar vortex, in a magnetized
cylindrical plasma. An overview of vortex dynamics for these vortices is presented with emphasis on theformation mechanism and the physical significance.

604020y (mm)1. Plasma Hole
Figure 1 is the end view image of a plasma hole.
The central dark region in the figure indicates thedensity hole, the sizes of which are 6 cm indiameter and more than 100 cm in axial length. Thedensity in the hole region is about one tenth of thatin the ambient plasma, and the width of transition
layer between the hole and ambient plasma is about
1.2 cm, which corresponds to several ion Larmor
radii.

0-20-40-60-60-40-20

02040

60x (mm)Fig.2 Velocity field of a plasma hole.

Fig.1 End view image of a plasma hole.
The flow velocity field of the plasma holeexhibits a monopole vortical structure with a sink in
its center (see Fig.2). When the direction of themagnetic field is inversed, the azimuthal velocity
also changes its direction of rotation, indicating thatthe azimuthal rotation is due to E x B drift. The
remarkable characteristic of the plasma hole is theexistence of radial flow, which remains unchanged
under the field inversion. It is found that the radialflow is a F x B drift, F being the viscous force due
to shear in the azimuthal rotation. The vorticity
distribution indicates a Gaussian shaped
localization as shown in Fig.3 and is identified as aBurgers vortex [1-3], which is intrinsic in viscous
fluids. The mechanism of central localization ofvorticity is the balance between the inward
transport and the viscous diffusion. The
characteristic scale length of vorticity localization
determines the effective viscosity, exhibiting ananomalously high value 10 6 cm 2 / sec , which isthree orders of magnitude higher than the classicalvalue due to atomic collisions.
When we consider the interaction of viscous
vortices, the existence of radial flow is of essential
importance since it causes an attractive interaction
between vortices. Consequently, the dynamicalbehavior of a system of viscous-vortices isqualitatively different from that of point vortices

ions, which dominates the electric field. The visible
spectroscopy of ArI and ArII revealed that thetripolar vortex always accompanies a steep density
cave in the background neutrals (see Fig. 5). In thiscircumstance there exists an inward flow of neutrals
due to the steep density gradient. Through the
charge-exchange process, the directed motion(momentum) of neutrals is transferred into the ion
fluid, producing an effective force and thesubsequent vortical motion of ions. In this case, thelogarithm of neutral density, log nn, acts as apotential, and should be included in the fluid
equation for ions. The theoretical analysis gives a
tripolar solution, showing a quite well agreementwith the experimental result [6].

Fig.3 Vorticity localization of a plasma hole.

2. Tripolar Vortex
Tripolar vortex consists of three aligned vortices
with alternate signs of polarity of rotation, and isregarded as a novel coherent structure in ordinary
fluids and ocean. It was first observed in laboratory
experiment and then in the Bay of Biscay [4].
Figure 4 shows a tripolar vortex in a plasma [5].
The bright regions are high density regions (densityclump), and the potential profile is similar to that ofthe plasma density, indicating the existence of
localized electric field and the resultant vorticalmotion due to the E×B drift.

Fig.5. Neutral density profile with atripolar vortex

The observation of anti-ExB tripolar vortex
shows that the dynamical behavior of the plasma
may be modified through the coupling of ions to theflow of background neutrals. Hence, we may saythat the plasma is coexistent with the flow ofbackground fluid.
REFERENCES[1]
Fig.4. End view image of a tripolar vortex

The vorticity distribution determined from thevelocity field shows a tripolar structure; a centervortex with positive polarity (counterclockwiserotation) and two satellites in both sides withnegative polarity (clockwise rotation).
All the polarities of component vortices are
surprisingly opposite to that of the E×B drift. This
result means that there exists a new force acting on

[2]
[3]
[4]
[5]

[6]

K.Nagaoka, A.Okamoto, S.Yoshimura, M.Kono
and M.Y.Tanaka, Phys.Rev.Lett. 89 (2002) 075001
J.M.Burgers, Adv.App.Mech. 1 (1948) 171
T.Kambe, J. Phys. Soc. Jpn. 53 (1983)13G. J. F. van Heijst and R. C. Kloosterziel, Nature338 (1989) 569.
A. Okamoto, K. Hara, K. Nagaoka, S. Yoshimura,
J. Vranješ, M. Kono, and M. Y. Tanaka,Phys. Plasmas, 10 (2003) 2211.
J. Vranješ, A. Okamoto, S. Yoshimura, S. Poedts,
M. Kono, and M. Y. Tanaka, Phys. Rev. Lett., 89(2002) 265002.