S6−4 Flows and Structural Formation in Macroscopic Fusion Plasma
マクロな核融合プラズマにおける流れと構造形成
A. Fujisawa
藤澤 彰英
National Institute for Fusion Science,Oroshi-cho, Toki, 509-5292, Japan
核融合科学研究所，〒509-5292 岐阜県土岐市下石町322-6
In a research field of toroidal plasmas, it is an interesting finding that the structure is able to bifurcate.
Examples include H-mode, internal transport barriers, and the other improved confinement modes.
Intensive studies of the phenomena over two decades have revealed that the bifurcation can be caused bynonlinearity of perpendicular flow (or radial electric field), an interplay between the flow and turbulence.
This paper presents structural bifurcation that has been observed in CHS as a good example to show
structural bifurcation and a role of flow (or electric field) in structural formation. In addition, a CHS
experiment to identify zonal flow -another substantial player in the structural formation in toroidal
plasmas- is introduced.

2. Structural Bifurcation in Toroidal Plasmas
A number of improved confinement modes have

1bell

0.5

φ (kV)

identified in toroidal plasmas, such as H-mode, VHmode, revised shear modes, RI-mode and so on.
Many of the improved confinement modes show thebifurcation characteristics deeply associated withthe bifurcation characteristics of radial electric field.
In particular, neoclassical theories have expectedthat the radial electric field should have bifurcation
properties in toroidal helical plasmas.

dome

01. Introduction
In toroidal plasmas, turbulence is driven bygradients in thermal variables, while the gradientsare determined by the turbulence-driven transports.
Therefore, the structure of the toroidal plasmas isgoverned by turbulence, and the research ofturbulence property is one of the key issues for thestructure formation of the plasma.
The research of improved confinement modes
over more than two decades has revealed that theturbulence can be regulated by shear of flow (orradial electric field) spontaneously generated in theplasma. Note that the radial electric field isconnected with the plasma flow through ExB driftin magnetically confined plasmas. Nonlinear
property of electric field itself can produce
sufficient shear to reduce plasma turbulence.
Besides, turbulent Reynolds stress can be amechanism to generate plasma flow and its shear[1].
Recently, a new member, zonal flow [2],comes into this community to determine the plasmatransport. The nonlinear links or interactions
between these members (e.g., turbulence, zonalflows, mean flows, thermal variables, and so on) areconsidered to make plasma structure bifurcate andproduce a number of interesting structures intoroidal plasmas.
The paper introduces i) the bifurcation
phenomena in CHS as an example [3], ii) therelationship between flow, turbulence and structureiii) the CHS experiment on the first identification of
zonal flow, and iv) several remaining problems ofstructural formation of toroidal plasmas.

hill
Mexican hat
well (NBI)

-1

-0.5

0ρ

0.5

1Fig. 1. Characteristic patterns of the CHS potentialprofile. In dome and bell patterns, the transport barrier iscreated at the radius where discrete change of thegradient (or electric field) occurs

In fact, potential profile in CHS helical deviceshows bifurcation properties caused by theneoclassical theories. As is shown in Fig. 1, five
representative patterns have been identified in CHS;
well, Mexican-hat, hill, dome and bell. In thesepatterns, the three patterns of hill, dome and bell
clearly shows bifurcation characteristics, andtransport barrier formation are confirmed at theradial positions where the strong electric field shear

1+ β (dE /dr)1

Coherence

1

2

E

3. Relationship between Flows and Turbulenceand electric field shear generation
A number of experiments have indicated thatsufficiently large electric field shear should
suppress the plasma turbulence and form transportbarriers. According to theories, the radial electricfield shear can be related to the fluctuation
amplitude or transport coefficient as follows,DL,D∝

confirmation of the zonal flow substantiates a newparadigm that zonal flow and turbulence should be asystem to determine the plasma transport.

P (V /kHz)

exist; the normalized radius of ~0.3 and ~0.6 fordome and bell patterns, respectively. Repetitivetransitions between these three states, dubbed
electric pulsation, have been observed todemonstrate the bifurcation nature.

P~f -0.60.10.5

noise levelαwhere dE/dr is radial electric field shear. Then, theinvestigation of barrier formation is focused on thegeneration€ mechanism for radial electric field shear.
For the two patterns in CHS, dome and bell, thefluctuation reduction has been confirmed in the Ershear layer experimentally.
In the formation of the internal transport barriers(ITBs) of CHS (bell and dome), the scenario of thestructural bifurcation is as follows. First, radial
electric field at a radial position can bifurcate owing
to neoclassical property, and Er-shear is formed
between the regions belonging to the two different
Er-branches. Then, the created Er-shear reduces thefluctuation and the fluctuation-driven transport atthe shear layer. A transport barrier is formed at theEr-shear layer. This scenario is exactly the concepet
initially proposed for H-mode transition.
4. Presence of Zonal Flows in a Toroidal Plasma
In theories and simulations, the zonal flow has
attracted attention as an element to determine theturbulence level and transport. However, the zonal
flow has not been identified in experiments.
The zonal flow is a rapidly varying radialstructure with poloidal and toroidal symmetry(m=n=0). Therefore, one of the essential points forzonal flow identification is to find fluctuation offlow or radial electric field with a long-range
correlation. Its presence has been recently haveconfirmed for the first time with dual HIBPs inCHS.
The system has found the existence of electricfield fluctuation (f< ~1 kHz) which shows longdistance correlation in low frequency range, as isshown in Fig. 2. The confirmed zonal flow has
characteristic radial length of ~1.5 cm and life timeof ~1.5 ms. This observation leads to the fact that ameso-scale structure should interfuse into the timeaveraged potential structure. The experimental

0.01

0.1

1 f (kHz) 100100Fig. 2: Power spectrum and coherence of electric field
fluctuations in two toroidal locations in CHS.

5.
Remaining
Problems
forStructuralFormation in Toroidal Plasmas
The formation mechanisms of ITBs in toroidal
helical devices are rather clear, as is seen in the CHS
case. However, a number of unsolved problems
remain for structural bifurcation for the otherimproved confinement modes, such as H-mode.
Although the Er-shear effect on the transport
reduction is involved in H-mode or edge transportbarrier (ETB) formation, a number of processes areexpected to be associated with Er-shear generation
for ETBs, such as parallel viscosity, turbulent
Reynolds stress, neutral drag, and so on.
Even in L-mode structure, many intriguing
phenomena are still unsolved in the physics
mechanisms, such as non-local nature of transport.
In other words, a change happening at a local point
can propagate to another point in a much fastertimescale than the diffusive one. A possible
candidate to explain the non-local nature could be
nonlinear interactions between different scale
fluctuations.
In summary, investigation of turbulence in termsof mulit-scale ranges is essential for further
understanding of structural formation in toroidal
plasmas, as well as Er-generation mechanisms toregulate and bifurcate the turbulence characteristics.
References[1] A. Fujisawa, Plasma Phys. Control. Fusion 45
R1(2003)[2] P. H. Diamond, K. Itoh, S. –I. Itoh, T. S. Hahm,Plasma Phys. Control. Fusion in press.
[3] A. Fujisawa, Phys. of Plasma, 7 4152(2000).