J. Plasma Fusion Res. SERIES, Vol.1 (1998) 92-95

Application of the Soft X-Ray Tomography Analyses
in Heliotron-E Plasmas
HOSOTSUBO Moritaka*, ZUSHI Hidekir, WAKATANI Masahiro2
and the Heliotron-E Group2'3
Graduate School of EngineerinS, Kyoto IJniversity, Uii 611-0011, JapanlAdvanced Fusion Research Center, RIAM, Kyushu University,"Kasuga 816-8580, Japan
Graduate School of Energy Science, Kyoto University,

Uii 611-0011, JaPan
3Institute of Advanced Energy, Kyoto University, Uii 611-0011, Japan(Received: 30 September 1997/Aecepted: 22 October 1997)

Abstract
Soft X-ray tomography analysis is used to understand physical mechanisms during the internal disruption. An interrelation between the amplitude and growth rate of the coherent mode, and the driving
term is derived. The observed non-linear behavior is quite different from the physical picture based on
the linear stability analysis. This technique is also applied to clarify the sawtooth stabilization effects byECRH. Shafranov shift and power deposition profile are derived.

Keywords:
soft X-ray tomography, growth rate, hysteresis relation, sawtooth, internal disruption, ECRH

1. lntroduction
Stabilization of MHD activities and deep understanding for the physical mechanisms have been one of
the important subjects to the fusion plasma[l]. It has
been reported in JET that at an internal disruption ahelical instability is abruptly triggered[2]. Although ob-servation of these trigger phenomena stimulated us,
only the time evolution of the instability is shown andno relation between the mode growth and the driving
term is given. In currentless heliotron plasmas, pressure
driven instabilities have been investigated so far[3-5].
In this paper, using tomography we investigate the nonlinear dynamics of a coherent mode during the disruption phase. The another application of the tomography
analysis i:' performed to study the Shafranov shift andthe rf deposition profile for plasmas stabilized byFCRH.

2. Experimental Gondition
Four sets of SX array with each 20 detectors areused for tomography. From the energy sensitivity(0.1 - 1 keV) of the detector the signals reflect the dynamics in density. This system allows us to reconstructan image by the expansion up to m:3 component[6].
Here, m is the poloidal mode number used in FourierBessel expansion. The vacuum magnetic configurationis characterized by magnetic hill, the q:2 surface near
the magnetic axis, weak magnetic shear near the q:2
surface and the inward shift (2-4 cm) of the axis. The
range of plasma parameters are as follows: B:1.9 T,
PECH<0.5 MW, P*u,:3 MW, 0.5 kev< [(0)< 2keY,and B(0) <I "/o.

01998 by The Japan Society of Plasma*Corresponding author's e-mail: hosotub@ ppl. kyoto- u.ac.ip

Science and Nuclear Fusion ResearchHosotsubo M. et al., Application of the soft X-Ray Tomography Analyses in Heriotron-E plasmas

3. Explosive Growth of the Coherent Modeand a Hysteresis Relation

T*=r(4!91,;gg

We use the reconstructed emissivity e (r, t) to analyze the dynamics at the disruption. Especially, an in-terrelation between following quantities, E6_2, f6:2,and Ve is analyzed. Here we consider that d.:, is them:2 mode amplitude, y^_2 the growth rate derived
from the time derivative of ln (e._r(r)), and Ve thelocal gradient as the driving term. The growing processof the m:2 mode during the sawtooth oscillations isshown in Fig. 1. The non-rotating m:2 mode is abruptly enhanced just before the sawtooth crash. The
m:2/n:1 mode associated with the 4:2 surface is23€*=2

considered destabilized by the increased in the local
pressure gradient at the q:2 surface. Thus both f._,and y^-, are investigated as a function of Vel._,, at thedisruption, as shown in Fig. 2. Since the peak position

Fig.3 Functional dependence of y^-ron the mode amplitude.

of 6.-, is shifted outward during the crash, we trace
the peak value of 6.-r. Vel"-,, is taken at the fixed po-

not increase below Ve*. That is, a hysteresis relation

sition. The m:2 mode is abruptly triggered, when Ve
is Ve* (a critical value). T:he m:2 mode amplitude
reaches its maximum, and then decays as Ve decreases
during the crash phase. Finally the amplitude becomesnoise level. As Ve increases again, the amplitude does

exists in the mode growth and drive term. Another as-pect is that Ve is almost constant in the interesting time
period. That is, even if Ve reaches Ve* several ms before the crash, the occurrence of the jump in the growthrate seems to be random. In this sense this trigger event
is quite probabilistic[7]. Finally we also studied a relation between y^-, and 6._, in this non-linear phase.
The result is given in Fig. 3. When the mode is triggered abruptly, y--z increases with d._,, and then it
stops to increase and turns over, However, E._, continues to increase and reaches to the maximum. Thisobservation is quite different from the physical picture(a) RawSXdata

0.750
o. 6250.500
0. 3758.250

based on the linear stability analvsis.

4. Stabilization by ECRH

Fig. 1 Time evolution of the line integrated raw signals

In particular case, mainly -3.5 cm shift case, it has
been observed that unstable plasmas are stabilized byand the reconstructed m=2 mode.

lrl "€^i(arbitrary r.ttil;
m=2ECRH[7I. The second harmonic off-ixis heating wasperformed with a 106 GHz gyratron. During the pulse,
the sawtooth oscillations are suppressed, but they appear again - 20 ms after ECRH turned-off. Within thistime-scale 4(0) is reduced to a previous level berbre
ECRH. The Te and ne profiles are shown in Fig. 4. Although B(0) is increased from 0.8 "io to 1.1 %, and-Yp"l,:," is also increased by a factor of 2, the observed

I (u) iplasma becomes stable. AlthoughE,*€ (arbitrary unit)-V&i.__,, is increas,eu,e(r) becomes hollow during the pulse. This is ascnbed
to that the SX signal is more sensitive to the densrty(impurity ions) change because of its energy window€(arbitrary unit)(0.1-1 keV). The change in e(r) reflects that the bothdensity and impurities are pumped-out [8] from theFig. 2 Hysteresis relation during a crash: the ratio ofE^-r/ e^-o tzs. Ve (a) and y^., vs. Ve(b).

heating zone except the very early phase of the pulse.
93

Hosotsubo M. et al., Application of the Soft X-Ray Tomography Analyses in Heliotron-E PlasmasT" (eV)

ne96091 9 ECH on off AV=-40i

3000IaIt4S33 841 tOH {{l74843 847 ECH oflf4rJ33 U{1 t CH o': 350.ns^802m0c)
NIoJa40aqitcFu rl -I TI

10000L0TiCRHl.witl

CH ofr 350msw: ;h E( RHIY\\rl r\s101520250

510152025<r> cmFig. 4 The profiles of l"(Thomson data) and nu(inverted\<r> cm
from the FIR interferometer profile) with and without ECRH.

In order to understand this stabilization effect thetomography technique is used from a different point ofview. It has been reported in Ref. [7] that a reductionof MHD activities is seen by decreasing resistivity, 4, at
the q:2 surface by ECRH. Although the reduced 4 is

Q:2 svface disappear due to additional shift, that is,
the minimum value of rotation transform is expected
above 0.5, the change of AR with ECRH is small. Preliminary calculations with a peaked profile at B(0):1 % support this observation. Qualitative comparison

favorable to stabilization, 7"-dependence (a( 3/2) otZ.-z is considered too weak to explain the observed
complete stabilization during the ECRH pulse. Thus
Shafranov shift is studied by this tomography technique. Concretely, the shift is checked by following thelocation of the peak emissivity. Figure 5 shows the trajectories of the peak and the time evolution of the horizontal displacement with respect to the axis in vacuum
for cases with and without ECRH. It is clear that thepeak position is shifted outward compared with thewith the theoretical prediction is under study.
It is an important issue to study how close theheating zone is the rational surface. The rf deposition
profile is simultaneously derived from the signals offset
at just ECRH turn-on time. Reconstructed profiles atAr( 1 ms are shown in Fig. 6. The results suggest thatthe deposition profile is hollow and generation of energetic electrons seems to be non-uniform within thereconstruction accuracy. The heating zone is just outside the Q:2 strface in vacuum. Systematic analysis isunder study to clarify the effective location of the de-case without ECRH. Although this suggests that the-<TEjcctorics of thc pcak
ooo,i:'..1E
Oi:,1oi001

6tlp(d.-t>iITime(total l2Omsec)
Rcd(gquarc) : EGRH on oaee

Bluc(circle) : ECRH off oaso

Fig.6 ECRH power deposition profiles at very beginningof the ECRH pulse (At< 1 ms). For comparison themagnetic surfaces including the q=2 surface are

Fig.5 Trajectories of the peak emissivity and the time
evolution of the horizontal displacement from theshown.

magnetic axis in vacuum.
94

Hosotsubo M. et al., Application of the Soft X-Ray Tomography Analyses in Heliotron-E plasmas

position zone with respect to the rational surface.

References
t1l B.B. Kadomtsev, Tokamak plasma: A Complex

5. Summary
Application of soft X-ray tomography method toMHD phenomena is described. The nature of explosivet6l

Physical System, Chap. 5 & 7, Institute of physics
Publishing (1992).
D.J. Campbell and JET TEAM, plasma phys. andControlled Nucl. Fusion Research (proc. l3th Int.
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M. Wakatani e/a/., Nucl. Fusion 24, L4O7 (1984).
H. Zushi e/a/., Nucl. Fusion 27,895 (1937).
M. Hosotsubo et al., Proc. on Int. Conf. on plasma

17l

H. Zushi et al., IAEA 16th Fusion Energy Con-I2l

growth of the coherent mode is investigated. It is foundthat there exists a hysteresis relation between the mode
amplitude and the local gradient. From this tomography technique, both Shafranov shift and rf power
profile are simultaneously deduced for the plasma stabilized by ECRH.

t3l
t4l

tsl

Physics, Nagoya, Vol. 1,530 (1996).

Acknowledgments
We acknowledge Dr. B. Carreras, profs. K. Itohand S.-I. Itoh for fruitful suggestions. We would like tothank Profs. K. Terumichi, T. Maekawa, and K. Ha-ference, Montr6al, (1996) IAEA-CN-64/CP4.
t8l H. Zushi etal., Nucl. Fusion 28, 1801 (1938).

nada for their advice on tomography technique andX-ray photo diode array. One of the authors (H.2.)
gratefully acknowledge Prof. S. Itoh for his continuousencouragement. This work was supported by theGrant-in-Aid for Scientific Research of ministrv ofEducation, Japan.

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