Proceedings of ITC/ISHW2007

MHD instabilities with sharply peaked pressure profile after
ice-pellets injection in the Large Helical Device
Satoshi OHDACHI1) , Kazuo TOI1) , Satoru SAKAKIBARA1) , Kiyomasa WATANABE1) ,Yoshiro NARUSHIMA1) , Fumitake WATANABE2) , Ryuichi SAKAMOTO1) ,Junichi MIYAZAWA1) , Ichihiro YAMADA1) , Kazumichi NARIHARA1) , Kenji TANAKA1) ,Tokihiko TOKUZAWA1) , Kazuo KAWAHATA1) and the LHD Experimental Group1)1)2)National Institute of Fusion Science, Oroshi-cho Toki-shi 509-5292, Japan
Department of Energy Engineering and Science, Nagoya Univ., Nagoya 464-8603, JapanThe eﬀect of peaked pressure profiles on the MHD behavior of the Heliotron type plasma is investigated.
The pressure profile is more peaked with the ice-pellet injections than with normal gas-puﬃng. The degree of thepeaking depends on the vacuum magnetic axis position. In inward-shifted plasma, where the interchange modes
are unstable in the core region, larger levels of the MHD fluctuations are observed. Sawtooth-like relaxation
events, which terminate the peaking, are also observed when the pressure gradient exceeds a threshold value.
Existence of these MHD instabilities may explain the fact that we do not obtain internal density barrier discharge
with inward shifted configurations.
Keywords: LHD, MHD instabilities, pellet, relaxation

In the Large Helical Device (LHD), the highest volumeaveraged beta are obtained in so-called inward-shifted configuration (the radius of the vacuum magnetic axis, Raxis ∼3.6 m) because this configuration is favorable for particle
confinement and heating eﬃciency. However, they are unfavorable as MHD stability is concerned. Therefore, it has
been believed that MHD stabilities are not important fornormal operation in LHD; the pressure driven instabilities
are saturated at a certain level and they do not deteriorate
the confinement of the plasma seriously. Then, the next
fundamental question is that in which experimental condition do MHD activities aﬀect the confinement. We haveobserved several MHD related phenomena having impact
on the confinement of the plasmas. They do restrict theoperational regime of the LHD considerably. One is theconfiguration with low magnetic shear. When the magnetic shear is reduced at ι = 1 surface, an m/n = 1/1 structure evolves and results in a minor collapse phenomena [3].
Another examples is that when the neutral beam injectionis switched from the co-direction to counter direction, themagnetic shear at the ι = 1/2 rational surface is reduced and
m=2 MHD oscillations with large amplitude are observed[4].
The other experimental condition where the MHD
instabilities aﬀect the operational regime is the peakedpressure profile whose gradient is much larger than theMercier–stable condition. When ice-pellets are injected
into the plasma sequentially, the pressure profile is getting
peaked after the last pellet. Several MHD related event
author’s e-mail: ohdachi@nifs.ac.jp

have been observed in this experimental regime where theMercier condition is profoundly violated [5]. The acievable pressure gradient in this type of discharges depends
on the vacuum magnetic axis position (See, Fig. 1). When
the Raxis is larger than 3.75m, a fairly high central beta
value β0 is realized. This kind of plasma is called as ’theinternal diﬀusion barrier (IDB) plasma’ or ’the super dense
core (SDC) plasma’ [1, 2]. In this paper we investigate theeﬀect of the pressure driven modes with a pressure gradientexceeds the stability limit, which depends on the locationof the vacuum magnetic axis.
54β0 [%]

1 Introduction

IDB/SDC region

β0 max32
1

just after pellets
03.6

3.65

3.7

3.75

3.8 3.85
Raxis [m]

3.9

3.95

Fig. 1 Increase of the β0 as a function of the vacuum magneticaxis Raxis .

2 Experiments
Typical time evolution of high-density plasma with pellet
injection is shown in Fig. 2. After the last injection, apeaked density profile and a flat electron temperature profile are made (Fig. 3(a)). While the density is slowly de-400neL(TS)(b)
2Te [keV]

ISX [ a.u. ]2000(c)
4.0

3.8
1.0

1.5
Time [s]2.0Fig. 2 Time evolution of the plasma parameters with pellet injection. The stored energy w p and the line integrated electron density (a), soft X-ray radiation intensity(b) and themagnetic axis position estimated by the soft X-ray radiation profile (c) are shown. Vacuum magnetic axis in thisdischarge is 3.85m.

creased, the electron temperature increases and its profile ispeaked. The recovery of the electron temperature is fasterthan the decrease in density. The pressure profile is thereby
peaked. After the maximum of the stored energy, peakingof the profile still continues, which can be seen from theposition of the magnetic axis estimated from the soft Xray emission profile (Fig. 2(c)).
This peaking of the pressure is terminated at 1.5s by
the so-called core density collapse (CDC) event ( dashedline in Fig. 2 ). The plasma density at the center is decreased within 1 ms and the core plasma is redistributed toouter region, as is shown in Fig. 3(c)-(d).
In contrast to the case of the outward-shifted plasma,
sawtooth-like activities are often observed inward-shiftedplasmas. Time evolution of the discharges with Raxis =3.65m and 3.75m are shown in Fig. 4. At the timing of
the shaded stripes in Fig. 4, small relaxation events can beseen in the soft X-ray radiation (ISX). The waveforms are
similar to those in the sawtooth phenomena observed onTokamaks. The location of the inversion radius tells us that
this instabilities are related to the ι = 1/2 rational surface.
Mode numbers of the precursor oscillations (m=2), which
are rarely observed, support this.

Te [keV]Peak Position [m]0208(b) 6

0.2
0.0
0.8
1.43s
0.6
0.4

4

0.2
0.0
0.8
1.47s
0.6

208(c) 64

0.4

208(d)
60.2
0.0
0.8
1.50s
0.6
0.4

4

0.2
0.0
2.5

205.0

3.0

3.5
4.0
R [m]

4.5

ne [a.u. ]

Wp

600

40.4

ne [a.u. ]800(a) 860.8
1.30s
0.6

ne [a.u. ](a)ne [a.u. ]69286

PelletTe [keV]

wp [ kJ ]

1200
1000

Te [keV]

Proceedings of ITC/ISHW2007

Fig. 3 The electron temperature and the electron density profile
of #69286 after the pellet injection.

Though the eﬀect of these events on the confinement
is small, the increase of the central beta (estimated by themagnetic axis position) is saturated by the sawtooth-likeevents; the events aﬀect the peaking speed of the pressure
profile. This is one example where MHD instabilities doaﬀect the pressure profile.

3 Discussion
The evolution of the β0 as a function on the magnetic axis
position R0 is shown in Fig. 5. The thick curves show
the Mercier stability criterion, DI = 0, estimated at theι = 1/2 rational surface. The area right side of the lines
is stable region; when the magnetic axis is shifter outward the magnetic well depth is deeper. Three lines arecorresponding to diﬀerent pressure profiles; assumed pressure profile is p(ρ) = p0 (1 − ρ2 )(1 − ρ8 ) (dashed line),p(ρ) = p0 (1−ρ4 )(1−ρ8 ) (dotted line) and p(ρ) = p0 (1−ρ2 )2(solid line), respectively. The symbols in Fig. 5 show thetime evolution of the central beta in the recovery phase after pellet injection.
Inward shifted plasmas (Raxis < 3.75m) are always
Mercier–unstable at ι = 1/2 in the recovery phase after thepellet injection. Sawtooth-like repeated relaxation eventsare destabilized as the pressure gradient increases. Thecorresponding area is shown in the shaded ellipse in Fig.
5. There exists a threshold value of the pressure gradientfor the appearance of the instabilities. It is estimated as(dβ/dρ ∼ 1%) [5].

Proceedings of ITC/ISHW2007

1000

30500

neL

00.8

1.0

10

1.2

68909 60

Wp

1000

40

500

01.6

1.4

PelletneL

00.8

Sawtooth-like
event

0.50

1.0
Pellet

1.2

20
0
1.6

1.4

Sawtooth-like
event

0.40
ISX [a.u.]

ISX [a.u.]

20

Wp [kJ]

Wp 68950 40

1500
19 −2
neL [10 m ]Wp [kJ]

50

Pellet19 −2
neL [10 m ]Rax = 3.70m

Rax = 3.65m
1500

0.30
0.20

0.2

0.10
0.0
4.0

Saturated

3.8

1.0

Peak Position [m]Peak Position [m]

0.00
4.0

Saturated

3.8

1.2

1.0

1.2
Time [s]Time [s]1.4Fig. 4 Time evolution of the plasma parameters with sawtooth-like relaxation. Stored energy W p and line-integrated density and the soft
X-ray radiation and the magnetic axis position are shown together.

Sawtooth-like events
Unstable

569286(3.85m)
69261(3.8m)

β 0 [%]

432

CDC

68950
(3.65m)69325(3.90m)68909(3.70m))10
3.6

Stable

3.7

3.8

3.9
R0 [m]

44.1

4.2

Fig. 5 Central beta value β0 as a function of the magnetic axis position is shown. Thick lines show the stability boundary of Mercier
mode. Three lines are corresponding to diﬀerent pressure profiles; assumed pressure profile is p(ρ) = p0 (1 − ρ2 )(1 − ρ8 ), p(ρ) =p0 (1 − ρ4 )(1 − ρ8 ) and p(ρ) = p0 (1 − ρ2 )2 , respectively. Open circle (Raxis = 3.65m), closed square (Raxis = 3.70m), open triangle(Raxis = 3.8m), cross (Raxis = 3.85m) and open diamond (Raxis = 3.9m) show the time evolution of the parameters after the pellet
injection. Larger (smaller) symbols correspond to the period when the pressure profile is being increased (decreased).

Proceedings of ITC/ISHW2007[1] N. Ohyabe, et. al., Phys. Rev. Lett., 97, 055002 (2006)[2] T. Morisaki, et. al., Phys. Plasma, 14, 056113 (2007)[3] S. Sakakibara, et. al, Fusion Engineering and Design 50, 177(2006)[4] S. Isayama, S. Inagaki, et. al., Plasma Phys. Control. Fusion,4, L44 (2006)[5] S. Ohdachi, et. al, in Proc. 21th IAEA Fusion Energy Conference, Chengdu, China, 16-21 October 2006, EX/P8-15[6] J. Miyazawa, Abrupt Flushing of the High-Density Core inInternal Diﬀusion Barrier Plasmas and its Suppression byPlasma Shape Control in LHD, this conference. to be submitted to the Plasma Fusion Research

Rax = 3.65m−4Rax = 3.75mlog(PS) [a.u.]

Rax = 3.85m−6−8−100102030
Freq [kHz]4050Fig. 6 Spectra of the magnetic fluctuations with diﬀerent magnetic axis. The spectra are calculated when the stored
energy take its maximum value.

1412dβ0/dt [ %/s ]Notice that the traces of 69286 (Raxis = 3.85m) or
69325 (Raxis = 3.90m) avoid the MHD unstable region inFig. 5. In outward-shifted configurations ( Raxis > 3.75m), Mercier stable condition for the core MHD mode is always satisfied that way. Achievable beta values are thenhigher than with inward-shifted configuration. However,as is already shown in Fig. 2, when the magnetic axis isshifted too large and exceeds a certain value (e.g. 4.1m),
the CDC events are triggered and the further increase of
the β0 is terminated. Detailed mechanism of the CDC has
not been clarified so far. However, there is a evidence thatthe magnetic axis position is a key parameter for the CDC
event; when the Shafranov shift is reduced by the verticalelongation of the plasma, the achievable central beta is increased up to 7%[6]. Therefore, the fact the highest central
beta can be obtained with Raxis = 3.85m (Fig. 1) can beunderstood by the following way. Outward shifted plasma(e.g. Raxis = 3.85m) is free from core MHD instabilities
and there is much space for the Shafranov shift until theCDC limit in configurations with Raxis = 3.80, 3.85m.
In addition to the sawtooth-like instabilities, broadband MHD fluctuations are enhanced in inward-shifted
plasmas. The spectra of the magnetic fluctuation with different vacuum magnetic axis position are shown in Fig. 6.
Coherent MHD fluctuations related to the rational surfaces
located in the edge region (e.g. m/n = 1/1) make the small
peaks in the spectra. It is clear that the fluctuation levels theemselves are larger when the vacuum magnetic axis
is shifted inward (MHD unstable). The peaking speed of
the central beta after pellet is slower in the inward-shifted
plasma (See, Fig. 7). The anomalous transport due to theenhanced magnetic fluctuation can be a candidate for this.
In summary, the plasma performance with a peakedpressure profile with pellet injections is investigated. In
MHD unstable inward-shifted plasmas, larger levels of theMHD fluctuations and sawtooth-like instabilities that affect the plasma confinement are activated. Whereas theoutward-shifted plasma, larger central beta was obtainedwith smaller MHD fluctuations. Increased transport due tothe larger MHD fluctuations and/or the sawtooth-like relaxation events might explain the fact that we do not obtain
IDB/SDC plasma in inward-shifted configurations.

1086
4
20
3.6

3.65

3.7

3.75

3.8

3.85

3.9

3.95

Raxis [m]Fig. 7 The rate of the recovery speed of the central beta.