J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)134–138
000–000

Study of Electron Heat Pulse Propagation induced
by ECRH/on-off on T-10 and LHD
NEUDATCHIN Sergey1, INAGAKI Shigeru1, ITOH Kimitaka1, KISLOV Alexandr, KISLOV Dmitrii,
KRUPIN Vadim, KUBO Shin1, LYSENKO Sergei, OHKUBO Kunizo1, PAVLOV Yurii,
POZNYAK Valerii, SHIMOZUMA Takashi1, SUSHKOV Alexei,
YAKOVLEV Mikhail1 and IDA Katsumi1
Nuclear Fusion Institute, RRC “Kurchatov Institute”, 123182 Kurchatov sq.1, Moscow Russia
1
National Institute for Fusion Science, Toki 509-5292, Japan(Received: 9 December 2003 / Accepted: 29 July 2004)

Abstract
Internal Transport Barrier (ITB) has been found at T-10 earlier by means of heat pulse propagation (HPP) andcold pulse propagation (CPP) analysis in target sawteeth-free plasma created by off-axis ECRH. Regimes with higher
current (up to 0.22 MA) and density (central electron line-averaged density n–e up to 2.7×1019/m3), and various input
power of the non-central ECRH are described in the present paper. Outward HPP was created by switching on the onaxis ECRH. Inward CPP was created by turning-off the off-axis ECRH. In both cases, R/LTe=R∇Te /Te rises significantly(up to 23) above Ohmic value on heat (cold) wave front, meanwhile dynamic electron heat diffusivity χeHP values arelow (0.06–0.25 m2/s). CPP analysis shows important new feature. χeCP values increase by ~3 times (from minimum
level ~0.1 m2/s inside r/a < 0.4 either by variation of the resonance position at the same off-axis power or by increaseof power level. In all cases stronger redistribution (increase of wideness) of Te (r)/Te (0) profile (normalized to OH
level) leads to the increase of χeCP. Probably, χeCP ≈ 0.1 m2/s corresponds to some “optimal” profile of safety factor q
with low shear zone and q(0) slightly above 1; χeCP values rise under higher values q(0).
Results of HPP/CPP study at LHD low density discharges show that HPP/CPP propagate in non-diffusive manner.
In contrast, purely diffusive HPP (χeHP ≈ 1.5 m2/s at 0.2 < r/a < 0.4) is observed in some LHD shots with moderatedensity and NBI power.
Keywords:
heat pulse propagation, cold pulse propagation, electron cyclotron resonance heating, internal transport barrier,dynamic electron heat diffusivity

1. Introduction

wave front R/LTe value rises up to 17. Slow inward CPP iswell described by χeCP ≈ 0.1 m2/s at r/a < 0.3 in a ~20 ms
time interval limited by the appearance of the first sawteeth
oscillation. The combination of large gradients with lowtransport indicates the presence of Internal Transport Barrier(ITB) formed in low magnetic shear region with q (safety
factor) slightly above 1. Nowadays, the dependences of χePB
on R/LTe=R∇Te /Te and ∇Te /Te are usually discussed (“criticalgradient” models). In the context of a “critical gradient”
model, Ohmic value of R/LTe lies above the “critical” one
because enhanced HPP (induced by sawteeth or on-axis
ECRH) is observed at all tokamaks at Ohmic background. In
present paper, we analyse CPP and HPP characteristics inwider parametric range (0.18–0.22 MA shots with n–e up to
2.7×1019/m3) at various level of ECRH power and resonanceposition.

In the previous T-10 experiments [1], target sawteeth-freeplasma was created either by high-field-side (HFS) off-axis
electron cyclotron resonance heating (ECRH) with 140 GHz
frequency or by low-field-side (LFS) off-axis ECRH (130GHz) at r/a ≈ +/- (0.45). Regimes with 0.18MA/2.3–2.5T,
limiter radius aL= 0.29m, major radius R=1.5m, central lineaveraged electron density n–e varied from 1.4 to 2.1×1019/m3(normalized to camera radius 0.38m) were studied. Outward
heat pulse propagation (HPP) with dynamic electron heatdiffusivity χeHP ≈ 0.2–0.3 m2/s at 0.2 < r/a < 0.37 was createdby on-axis ECRH (130 or 140 GHz) imposed on the target
created by off-axis ECRH. At HPP front, R/LTe=R∇Te /Te rises
up to 23 (Ohmic value of R/LTe=10). These data confirm ourold similar result [2]. Inward cold pulse propagation (CPP)
was created by turning off the off-axis ECRH. At the cold

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: neudatchin@nfi.kiae.ru
1134Neudatchin S. et al., Study of Electron Heat Pulse Propagation induced by ECRH/on-off on T-10 and LHD

Contradictory picture given by the results of HPP/CPP
analysis in low density LHD plasma is described anddiscussed. The evidences of ITB existence (laser data) are
observed in these shots after application of nearly central
ECRH (e.g. see [3-5]). At higher density, HPP is fully
diffusive.

observed in shot 34573. Analysis of CPP after final powerswitching-off at t=0.955s in shot 34573 shows the reductionof χeCP in 2–3 times inside r/a=0.3 in comparison with
t=0.86s. R/LTe rises at cold wave front up to 14 (1.4 OH value
at r/a=0.26) instead of the increase up to ~7 (below OH value)
during the same 15ms time interval analysed after t=0.86s.
The variation of CPP characteristics with ECRH power wasstudied in various plasmas. Fig. 1(b) displays the timetracesof T e (0) and PECRH (t) for another pair of shots (0.18 MA/
2.34T, n–e ≈ 2.1×1019/m3) with different PECRH (~0.45 MW inshot 35762 and ~0.25MW in 35764). Te (0) responds to power
cut-off in obviously different manner. CPP with χeCP ≈ 0.1
m2/s (shot 35764) and ~0.3 m2/s (shot 35762) inside r/a <0.3 is found in 15 ms time interval (with R/LTe ar r/a=0.27
rises up to 11 in both cases). Estimations show that q(0) (qvalue in the centre) for shot 35762 is higher, and the analysis
with ASTRA transport code [7] is in progress. The decay ofTe (0) stops before first sawteeth crash in shot 35762 (seeinterruption of diffusive CPP observed as disappearance of
decay at time shown by second vertical line in Fig. 2). In
many shots with χeCP ≈ 0.3 m2/s, after the period of Te decay,
the rise of Te in the central region (inside r/a < 0.15) isobserved before the first sawteeth crash. The rise of Te could
be explained by abrupt reduction of χe in the central region(estimated level of χe variation δχe ≈ –0.12 m2/s at r/a=0.15).
Probably, q reaches the value of 1 at the time of χe reduction.
The redistribution of Te profile at ECRH shown in Fig.

2. Analysis of HPP/CPP in T-10
The variation of CPP characteristics with the shift ofresonance position will be our initial concern. The inward
CPP in cases described below is induced by the reduction of
the off-axis ECRH in two steps. Fig. 1(a) displays thetimetraces of Te (0) and ECRH power PECRH (t) in 0.18 MA
shots 34573 and 34575 (n–e ≈ 2.1×1019/m3, safety factor atlimiter qL=4, all parameters are the same besides Bt). The
resonance lies at r/a ≈ –0.45 for shot 34573 (toroidal
magnetic field Bt =2.34 T) and at r/a ≈ –0.38 for shot 34575(Bt =2.38T). Te (0) response to first reduction of power at
t=0.86s is obviously lower in shot 34575, thus the position ofresonance lies closer to the plasma centre. CPP is analysedwith numerical solution of the simplified transport equationfor δTe , as usually, with boundary condition taken fromexperiment at r/a=0.3 (see details e.g. in [1,6]). Slow inward
CPP with χeCP ≈ 0.1 m2/s inside r/a < 0.3 is found in shot
34575 for 23 ms time interval. Faster CPP with χeCP ≈ 0.3
m2/s is obtained for 15 ms time interval in shot 34573. Later,
sawteeth oscillations appeared in shot 34575 but were not

Fig. 2
Fig. 1(a) Variation of Te (0) response with resonance position.
(b) Same with ECRH power.

2135Interruption of diffusive CPP by abrupt decrease oftransport in central zone (observed as disappearance of
decay at time shown by second vertical line).

Neudatchin S. et al., Study of Electron Heat Pulse Propagation induced by ECRH/on-off on T-10 and LHD

Fig. 3Comparison of Te wideness factor for (a) 0.18MA shots
34573 and 34575 (see Fig. 1(a)). (b) 0.22MA shots 37241(χeCP ≈ 0.1 m2/s) and 37171 (χeCP ≈ 0.25 m2/s) withdifferent power.
Fig. 4

CPP at 0.22MA/2.33T, n–e ≈ 2.7×1019/m3, bold and dottedlines represent calculations with χeCP = 0.1 m2/s and 0.2
m2/s.

δ

1(a) could be presented by the profile with the wideness of{Te EC (r)/Te EC (0)/}/{Te OH (r)/Te OH (0)} shown in Fig. 3 (a),which is higher in shot 34573. It seems that χeCP values vary
due to difference in q profiles, which should have higher q(0)values at t=0.86s in shot 34573 in comparison with shot
34575 and in shot 34573 at t=0.955s (Zeff profiles are not wellknown for these pulses).
The dependence of CPP characteristics on ECRH power
is observed also in 0.22MA/2.33T shots (qL=3.3) with n–e ≈2.7×1019/m3. The wideness of Te shown in Fig. 3 (b) is visibly
higher in shot 37171 (0.8 MW) compared with shot 37421(~0.22 MW of ECRH power). Figure 4 shows the timetracesof Te in shot 37421. Calculations with χeCP = 0.1 m2/s insider/a < 0.3 are shown by bold solid lines in Fig. 4 (dotted boldlines are calculated with χeCP = 0.2 m2/s) and χeCP ≈ 0.15 m2/
s at 0.3 < r/a < 0.4. 2.5 times higher values of χeHP (inside r/
a=0.3) are found in similar shot 37171 with ~0.8 MW of
ECRH power.
In the case of HPP induced by central ECRH-on,
according to our observation χeHP does not depend on density(at n–e = 1.4–2.7×1019/m3) or on the level of on-axis power.

3. Analysis of HPP/CPP in LHD
First, we analyse ECE (electron cyclotron emission) data
in low-density LHD shots 28614 and 28615 with neutral beam
injection (NBI). In this case ITBs were formed in the central
part of plasma column after application of nearly central
ECRH [3-5] into NBI-heated (28615) and ECRH+NBI heated(28614) plasmas. Te timetraces of these shots are shownelsewhere (e.g. [3-5]). The profiles of ⏐δTe⏐(absolute valueof the variation of Te) created by ECRH/on-off in shot 28615(after 4.5ms) are shown in Fig. 5(a) by bold and thin solidlines (⏐δTe⏐ by ECRH-on in shot 28614 is shown by dashedcurve). In general, CPP/HPP looks non-diffusive for theseshots since ⏐δTe⏐ does not decay monotonically. The exampleof HPP analysis in shot 28614 is given in Fig. 5(b). Analysis
shows χeHP ≈ 1.2 m2/s between r/a=0.39 and 0.434, χeHP ≈1.3 m2/s between r/a=0.434 and 0.475, and rise of χeHP up to~3 m2/s between r/a=0.475 and 0.566. The calculations
performed with χeHP =1.3 m2/s are shown by dotted lines inFig. 5(b). Anyway, diffusive HPP is not able to describe therise of δTe value at r/a=0.599. Moreover, the delay is absent

Fig. 5(a) Profiles of ⏐δTe⏐ created by ECRH/on-off in LHD shot
28615 (after 4.5ms) - bold and thin solid lines, same by
ECRH-on in shot 28614 is shown by dashed curve. (b)Example of HPP, dotted line -calculations.

even at r/a=0.566. In the case of CPP in shot 28614, χeHP ≈0.5 m2/s is found between r/a=0.434 and 0.475. Nevertheless,low values of χeCP could not be treated as reliable.
The HPP induced by ECRH-on in shot 45475 (2.3MW
3136

Neudatchin S. et al., Study of Electron Heat Pulse Propagation induced by ECRH/on-off on T-10 and LHD(0.18–0.22MA shots with n–e up to 2.7×1019/m3) comparing
with [1]. Off-axis ECRH forms the region of the reduced
transport in low-shear zone with q above 1. Later, q and shear
reduce due to the current redistribution during CPP/HPP (seecalculations in [1]). CPP analysis shows that χeCP values
increase by ~3 times (from minimum level ~0.1 m2/s insider/a < 0.4 with R/LTe up to 1.5 times of OH level during CPP
at shots with 0.22MA/2.33T, n–e = 2.7×1019/m3) either byvariation of the resonance position at the same off-axis power
or by variation of power level. In all cases stronger
redistribution (namely, the increase of wideness) of Te (r)/Te (0)profile (normalized to OH level) leads to the increase of χeHP.
Probably, χeCP ≈ 0.1 m2/s corresponds to some “optimal” qprofile with low shear zone and q(0) slightly above 1. The
similar value of χeHP ≈ 0.1 m2/s was observed at JT-60U
inside strong ITB [6]. Reduction of the turbulence below OH
level after ~15ms of CPP was measured with reflectometer at
T-10 [14] in series of shots with χeCP ≈ 0.1 m2/s. Moreover,
the reduction of q during CPP with χeCP ≈ 0.3 m 2/s brings
interruption in diffusive CPP process by the decrease oftransport in the central region (inside r/a=0.15). In our
opinion, this improvement represents the influence of some
“optimal” q value, which lies near 1.
Results of HPP/CPP study at LHD low density
discharges (n–e ≈ 0.4×1019/m3) show that HPP/CPP propagate
in non-diffusive manner. Low values of χeHP obtained in somezones could not be treated as reliable. In contrast, purely
diffusive HPP (χeHP ≈ 1.5 m2/s at 0.2 < r/a < 0.4) is observedin some LHD shots with n–e ≈ 1.8×1019/m3 and 2.4 MW NBI
power. Similar values of χe HP were observed in T-10
(0.17MA/3T, n–e ≈ 2.8×1019/m3, 0.8 MW ECRH power [15])and JET (3MA/3T, n–e ≈ 2×1019/m3, 2 MW NBI power [16])in the same space region. HPP/CPP looks faster at higher NBI
power and density in LHD (χeHP order of 5–10 m2/s).
The region of HPP analysis with “single wave” method
presented in the present paper is strongly limited by small
amplitude of heat wave in LHD shots with moderate density.
The analysis of MECH experiments (modulated ECRH:
periodical short-term ECRH/on-off) [17], in principle, allows
studying wider region of plasma column. Each method has
positive and negative features. Careful application of both“single wave” and MECH methods simultaneously should
allow creating systematic scan of χeHP dependency on plasma
parameters at LHD.
The authors would like to thank Drs V.F. Andreev, Yu.N.
Dnestrovskij, V.S. Mukhovatov, K.A. Razumova and manyother members of T-10 and LHD teams for fruitful discussions
and fine collaboration. Part of experiments were performed
by V.F. Andreev and A.V. Sushkov. T-10 experiments were
supported by the Nuclear Science and Technology Departmentof Minatom RF and by RF Scientific School grant
1608.2003.2. LHD experiments were analysed during S.
Neudatchin’s visit in NIFS.

Fig. 6 Diffusive HPP created by ECRH-on in LHD shot 45475.

NBI injected power, n–e ≈ 1.8×1019/m3) looks totally different.
Figure 6 clearly shows the decay of amplitude and risingdelay of HPP during outward propagation of heat wave. The
results of calculations with χeHP = 1.7 m2/s are shown in Fig.
6 with bold lines (r/a=0.191 is taken as boundary condition).
These calculations fit the experimental data. The results ofcalculations with χeHP = 4 m2/s are shown in Fig. 6 by dashedlines; they obviously disagree with experiment.
With the increase of NBI power, HPP looks faster (withχeHP around 5 m2/s), and even more fast in some shots. Clear
delay is not observed in some shots even at r/a~0.6.

4. Discussion and conclusions
The existence of zones with improved transport near loworder-rational q values was reported for ECR-heated plasmas
at RTP [8] and many other tokamaks. ITBs were found inplasmas with dominating electron heating at JT-60U [9] andLHD [3-5]. Recent analysis of HPP created by off-axis
modulated ECRH in ASDEX-U and FT-U shows slow HPP
under R/LTe up to ~10 [10-11]. Low values of χeCP ≈ 0.3 m2/s
were observed inside magnetic island in LHD [12]. Any
perturbation imposed on Ohmic background (which increase
R/LTe) propagates in a fast manner in any tokamak (χeHP ≈0.6 m2/s or more for T-10), and χeHP value usually exceeds
power balance value in 2 or more times (enhanced HPP). It
means that the Ohmic value of R/LTe lies already above the“critical” value of R/LTe , and it was increased by more than 2times by off-axis ECRH in T-10. Enhanced CPP was observed
during inward propagation of cool wave induced by injectionof C8H8 pellet at LHD [13].
In the present paper, the transport characteristics ofsawteeth-free plasmas created by off-axis ECRH were studied
by means of CPP and HPP analysis in wider parameter range

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