J. Plasma Fusion Res. SERIES, Vol.1 (1998) 84-87

Electric Field Bifurcation and Transition in CHS
Heliotron/Torsatron
FUJISAWA Akihide*, IGUCHI Harukazu, IDEI Hiroshi, KUBO Shin, LEE Seishu, MATSUOKA Keisuke,
OKAMURA Shoichi, TANAKA Kenji, MINAMI Takashi, MORITA Shigeru, OHDACHI Satoshi,
OSAKABE Masaki, AKIYAMA Ryuichi, YOSHIMURA Yasuo, TOI Kazuo, SANUKI Heiji,

ITOH Kimitaka, TAKAHASHI Chihiro, KOJIMA Mamoru, HIDEKUMA Shigeru, IDA Katsumi,NISHIMURA Shin, EIIRI Akira, HAMADA Yasushi, ITOH Sanae-L1, INOUE Noriyuki,SAKAMOTO Ryuichi and FUJMARA Masami
National Institute for Fusion Science, Toki 509-5292, JapanlRIAM, Kyushu University, Kasuga 816-8580, Japan(Received: 30 September t997/Accepted: 20 January 1998)

Abstract
Transition in radial electric field has been observed in CHS plasmas during a combined heatingphase of ECH+NBI, using a heavy ion beam probe. The transition occurs in a timescale of a few dozen

or a hundred microseconds. Radial current to induce the transition is evaluated by high temporal resolution of the heavy ion beam probe. Neoclassical dependence of radial electric field on a plasma parameter will be discussed to clarifv the nonlinearitv to allow the transition.

Keywords:
transition, bifurcation, radial electric field, potential, nonlinear relation, multiple steady state,
heavy ion beam probe, toroidal helical plasma

experimentally confirmed and reported[4]. In thispaper, we will present two examples of the transition
phenomena. Neoclassical dependence of radial electricfield on electron temperature will be presented to discuss the nonlinearity to allow the transitions.

1. Introduction
In toroidal helical plasmas, the helical ripple transport is strongly dependent on the radial electric field,
particularly in collisionless regime[ 1-3]. The neoclassical theory predicts that the toroidal helical plasmas cantake multiple steady states in the radial electric field
when a certain condition for plasma parameter is satisfied. In the neoclassical framework, the plasma with thepositive electric field should have better confinement
property than that with the negative one. This nonlinear
dependence of the property in toroidal helical plasmas
on radial electric field can give birth to dynamic structural reformation between these steady states.
In fact, a transition in the radial electric field has
been observed in the CHS plasma, using a heavy ion
beam probe. The nonlinear relationship between radial

2. Experimental Setup and Background
The CHS is a medium size heliotron/torsatron device; the major and minor radii are 1.0 m and 0.2 m,
respectively[5]. In order to measure the potential
profiles, the CHS has an HIBP which adopts a uniquemethod to control the beam trajectory. In this method,which is denoted as 'active trajectory control'[6,7], theobservation location can be changed by sweeping bothprimary and secondary beams. The advantages of thismethod are (1) the accessible region of plasmas iselectric field and radial current has been alreadv
01998 by The Japan Society of Plasma*Corres ponding author's e -mail : fuj isawa@ nifs. ac.j p

Science and Nuclear Fusion Research84

Fujisawa A. et al., F,lectic Field Bifurcation and Transition in CHS Heliotron,/Torsatron

In a combined ECH*NBI heated plasmas, thetransition has been observed to occur around the corewhen the potential profile has such a prominent peak.

extended widely for several different configurations, (2)potential measurement errors can be reduced by keeping the beam injection angle into the energy analyzer
constant. High temporal and spatial resolution of theHIBP allows us to investisate the transition nature of

The plasma parameters are as follows. The central electron temperature is approximately 1 keV from a Thomson scattering system. The ion temperature is expected
to be 300 eV. The electron density has a flatter profile,and the line averaged electron density ranges fromn":3 - 5x1018 m-3. The heating powers of ECH andNBI are usually 300 kW and 800 kW, respectively.

the electric field.
The experiments we will present here were performed on the magnetic field configuration whose axis
is located on R*:0.921 m with field strength of 0.88
T. In this configuration, the necessary beam energy is72 keY when cesium is used. Initial results of potential
profile measurements have been already reported forthis configuration[8]. The plasma with ECH heating
feature shows a positive electric field (electron root),
while the plasma of NBI feature does a negative electricfield (ion root). The plasma is found to show various
characteristics in potential according to different heating scheme, or different plasma parameter regimes.
In low density plasma n:3 - 5x1018 m-3, where
higher ECH heating (200 - 300 kW) is applied with theresonance on the magnetic axis, the potential profile
has exhibited a remarkable feature. The potential
profile has a sharp peak around the core, and the steep
change in radial electric field exists at p:9.3 - O.O.
Figure 1. shows a potential profile of an ECH heated

3. Observation of Bifurcation Phenomenon
Here we will present two examples of transition
phenomenon. The first one is shown in Fig. 2(a). In thiscase, the electron density is n" = 5119t8 m-3. A pair oftransitions occurs around t:88 ms. The potential at
the plasma center exhibits abrupt drop by - 400 V,

being followed by the second transition to the initialstate in a few microseconds. The detail of this change
can be also analytically obtained by fitting a function oftanh ((t-to)/ z) to the slopes. The analysis shows thatthe timescale parameters are r:16 ps and r:59 ps forthe drop and rise, respectively.
The second one is shown in Fig. 2(b). The electron
density of this case is n" = 3 - 4x1018 m-3 A pair oftransitions is also observed around r:55 ms. In thiscase, the plasma stays shortly in a steady state for - L
ms after the first transition. The central potentialchanges by - 200 V and by - 400 V in the first andsecond transition, respectively. The fitting procedure ofplasma with 300 kW input power, together with apotential profile of 100 kW case. These profiles show
clear difference around the core region of p ( 0.3.

tanh ((/- fo)/ z) gives the timescale parameters ofz:60 ps and t:220 pls to the first and second transition, respectively. Note that the scales of the horizontal
axes in Figs. 2(a) and 2(b) are different. For both cases,
no significant change can be seen outside of the radiusof p> 0.4.

400

Figure 2(c) shows the radial electric field andradial current to induce the transition for the case ofFig. 2(b). Here, the measured potential is transformed

I ,oointo the average radial electric field, which is defined as

E,:- (Q(0.3a)- Q(0\)/0.3a. The thin line indicates

00.5

the time averaged electric field using a wavelet analysis
with an assumption ot ((0.3a):const. The bold line
represents radial current deduced by use of the following formula, e,eo)E,/ 0t:-7., where €0 represents thevacuum dielectric constant. The perpendicular dielectric
constant e_. is given by er:Mro,(lIc2/u2s) with the1p

toroidal enhancement factor being Mro, = l*2q2,
where q is the safety factor, and c and oa the light andFig. 1 Potential profiles of ECH plasmas. The open andclose circles show the plasmas with ECH input

Alfv6n velocities, respectively. Here, e, =2.7X104
with q:3 and T.r^:$y106 m/s, which corresponds

powers of 100 kW and 300 kW, respectively.
85

Fujisawa A. et al., Electric Field Bifurcation and Transition in CHS Heliotron,/Torsatron

to n":3;1gta --'.
(a)

4. Nonlinear Dependence of Radial ElectricField on Plasma Parameter in Neoclassical600Theorye 400Transition phenomenon is generally caused bynonlinearity of the system. For our case of the CHS
plasmas, nonlinear dependence of radial electric fieldtilh [{Fro) il6psi\tilh [(t-lo) /59Ps]/200 L87t (ms)(b)

on a parameter or parameters (e.9., control parameter),should be responsible for the observed transitions. In
neoclassical theory, the radial electric field is deter-tsh (t-b) /6oFsl400)

mined by equating nonambipolar fluxes of ions andelectrons as at(E ):4(E,). This equation can yield
multiple roots to the radial electric field when plasma

e 200tilh (t-lo) /:2mFslt (ms)(cl6r

Figure 3(a) shows a neoclassical nonlinear depend-E

ence of radial electric field on a control parameter,
which is chosen to be the electron temperature. The dependence is obtained using a formula derived by Hastings[2]. The calculation is performed with plausible-,-t-tt\Dlul- oAT-_-€ -ql<-l_A+-54.5
I

plasma parameters for the present experiments;

57

56.5

55.5

54.5

54

satisfies a certain condition.

(AE55.5t (ms)

4:350 eV, n":5X1018 m-3, and dn"/dp:O. The heli-Fig.2 Examples of transition phenomenon observed in a
combined heating phase of ECH+NBl in CHS heliotron/torsatron. (a) An example of transitions in aplasma with its electron density of 5'1018 m-3. (b)The other example of transition in a plasma with its
density of 3 -4"1018 m-t. (c) Time evolution ofcal ripple and toroidal coefficients are €h:0.023 ande,:0.16, respectively. This corresponds to the radial
position of p:0.3. If another plasma parameter, suchas density, ion temperature, etc., is chosen as the control parameter, a similar diagram can be obtained.
The state represented by the point A (or C) is unstable, therefore, the transition should occur from A toB (or C to D). The transition from A to B (C to D) inFigs. 3 corresponds to the observed first and second
transitions in Figs. 2(a) and 2(b). The electric field cantake multiple steady states when the electron temperature ranges from 650 eV to 690 eV. The temperature
range to allow the multiple roots tends to become larger
as the density gradient becomes larger in the calculation. The calculation also shows the neoclassical radialcurrent to induce the transition is a few A/m2. T\eorder of neoclassical current is within the experimentalvalue. This fact suggests that nonambipolar parts ofanomalous fluxes may be less dominant than those ofneoclassical fluxes. For the precise comparison between

radial current and electric field during the transition

for the case of (b).

4stable (electronqroot)

I\EeA/I|

unstableir

JIJ.J

I

0

experiments and theories, more accurate measurements,la,,,

IIta-|--att'B rrr|'C

stable (ion root)of plasma parameters are essential.

6906605. Summary
We have presented two examples of transitionT" (eV)phenomena which were observed in the CHS heliotron,/Fig.3 A neoclassical calculation. Dependence of radial

torsatron plasmas. The transition occurs in a few dozen
microseconds order. According to a neoclassical calculation, the radial electric field can have multiple steadyelectric field on a control parameter. Here, the con-trol oarameter is chosen to be the electron temperature.

86

Fujisawa A. et al., F,lectric Field Bifurcation and Transition in CHS Heliotron./Torsatronstates and satisfy bifurcation conditions for the plasmas
where we have observed transition phenomena.

tsl

K. Matsuoka, S. Kubo, M. Hosokawa et al-,Plasma Physics and Controlled Nuclear Fusion Research, 1988 (Proc. 12th Int. Conl, Nice, 1988),

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