Proceedings of ITC/ISHW2007

Abrupt flushing of the high-density core in internal diffusion barrier
plasmas and its suppression by plasma shape control in LHD
J. Miyazawa, R. Sakamoto, S. Ohdachi, M. Kobayashi, S. Masuzaki, T. Morisaki, S. Sakakibara,
M. Goto, S. Morita, I. Yamada, K. Narihara, H. Funaba, K. Tanaka, C. Michael, Y. Suzuki,
K.Y. Watanabe, N. Ohyabu, H. Yamada, A. Komori, O. Motojima, and LHD experimental group
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan(Received day month year / Accepted day month year should be centered 10-point type)
A super-dense core of the order of 1020 m-3 is formed inside the internal diffusion barrier (IDB) during the reheat
phase of the central pressure after pellet injection in LHD. Large Shafranov shift of the plasma center is observed in
IDB plasmas and it reaches roughly 50 % of the plasma minor radius. In some cases, abrupt flushing of the central
density takes place and this event is called as “core density collapse (CDC)”. CDC must be suppressed since it
inhibits further increase of the central pressure. CDC is always accompanied by large Shafranov shift of the plasma
center exceeding a critical position. Theoretically, it is predicted that vertical elongation of the plasma shape (κ > 1)
is effective to mitigate the Shafranov shift and the κ is controllable with the quadrupole magnetic field, BQ.
According to this prediction, BQ scan experiment has been performed in LHD. Shafranov shift is indeed mitigatedby increasing κ. As a result, CDC is suppressed and high central β values reaching ~ 7 % have been achieved invertically elongated plasmas.
Keywords: heliotron, pellet injection, SDC, Shafranov shift, beta limit, equilibrium, elongation.

1. Introduction
In toroidal plasmas, the vertical component of dipole
magnetic field induced by the Pfirsh-Shlüter (PS) current,
BzPS, causes the shift of magnetic axis from R0 to R0 + Δ.
This is called the Shafranov shift. Since the PS current is
proportional to the pressure gradient, Δ is determined by
the central plasma beta, β0 [1]. Large Shafranov shift,reaching a half of the plasma minor radius, a, for example,
causes destruction of magnetic surfaces that leads to loss ofconfinement. From this point of view, it is expected that
there will be an equilibrium beta limit at Δ ~ 0.5 a [2].
Mitigation of Shafranov shift is therefore an important
issue to achieve high β0.
A discovery of internal diffusion barrier (IDB)
plasmas in LHD [3] makes it possible to realize the highcentral plasma pressure reaching 1.3 atm [4,5]. IDB
plasmas are produced by hydrogen ice pellet injection andcharacterized by a strongly peaked density profile withrelatively low density in the edge region, which is called“mantle”. The low mantle density enables deeper
penetration of heating beams reaching the plasma center.
As long as the central heating power is kept constant, thecentral pressure increases with the density, following thepreferable density dependence in the global confinement
scalings, such as ISS95 and ISS04 [6]. IDB plasmas areauthor’s e-mail: miyazawa@LHD.nifs.ac.jp

also characterized by large Shafranov shift due to the highβ0. Recently, an unexpected phenomenon has been foundin IDB plasmas. This takes place when the Shafranov
shift of the plasma center exceeds a critical position.
Then, the density in the core region is flushed out to themantle region within < 1 ms [7], while the temperature
profile scarcely changes. We call this event as “coredensity collapse (CDC)” [4,5]. CDC must be suppressedsince it inhibits further increase of the central pressure
and the fusion triple product. Since CDC is always
accompanied by large Shafranov shift, its mitigation
might affect CDC.
At least three methods are effective for Shafranov
shift mitigation, i.e. 1) plasma position control with avertical magnetic field that compensates BzPS, 2) increaseof the rotational transform, ι = ι / (2π) (note that the PS
current and BzPS is inversely proportional to ι and as aresult, Δ ∝ BzPS / ι ∝ 1 / ι2 ), and 3) vertical elongation of
the plasma shape. The first method is straightforward andwill be effective only if it is applied with feedback control.
Use of a strong vertical field from the beginning of adischarge is not preferable, because the initial magnetic
configuration should be strongly inward shifted and MHD
instabilities are expected to be unstable in suchconfigurations [8]. Unfortunately, feedback control of theProceedings of ITC/ISHW2007
vertical field is not equipped on LHD, to date, although it
is under discussion as a future program (available magnetic
field strength is expected to be low). As for the second
method, this indeed works as reported in [9]. In LHD, ι iscontrollable by changing the magnetic configuration, andespecially, ι increases with the aspect ratio of the torus.
However, the magnetic field strength available in highaspect ratio configurations is limited to ~ 1 T, for instance.
Therefore, the third method of vertical elongation is the
only possible solution applicable at the maximum magnetic
field strength of ~ 3 T.
In this study, experimental results of the elongation
scan and its impact on CDC are reported.

2. Plasma shape control by the quadrupole field
In toroidal plasmas, the PS current is induced tocancel the charge separation due to the variation in themagnetic field strength, ΔB, on flux surfaces, which isproportional to 1/R. Therefore, vertical elongation, which
reduces the characteristic length of the torus in the major
radius direction, ΔR, is also effective to reduce the ΔB ∝ΔR and thus the PS current. The magnetic surfaces inheliotron plasmas with l = 2 as in LHD can beapproximated by rotating ellipse, i.e. a horizontallyelongated ellipse and a vertically elongated ellipse appear
alternately as the toroidal angle changes. The plasma
elongation, κ, is defined as a toroidally averaged ratio of
the minor radius in the vertical direction to that in themajor radius direction of the last closed flux surface(LCFS). In LHD, we measure two kinds of line-density,nLFIR and nLMMW, passing through the “major axes” ofvertically and horizontally elongated ellipses, by a
far-infrared (FIR) interferometer and a millimeter wave
(MMW) interferometer, respectively. Here, we define aneffective elongation κeff ≡ nLFIR / nLMMW. Note that theseline densities include the information outside the LCFS
(called ergodic region), and therefore κeff is merely anapproximation of κ.
Both in helical plasmas and tokamaks, κ is controlled
by the quadrupole magnetic field, BQ. In the standard
configurations of LHD, the quadrupole component
generated by two helical coils is 100 % cancelled by thequadrupole field generated by poloidal coils andtherefore κ = 1. Hereinafter, the BQ that results in κ = 1 iscalled “BQ = 100 %”. When BQ is decreased to < 100 %,the κ becomes larger than 1, i.e. the plasma is verticallyelongated. The relation between BQ and experimentallymeasured κeff in low beta plasmas at Rax = 3.75 and 3.85 mis shown in Fig. 1. The elongation of the LCFS estimatedfrom the vacuum magnetic data for Rax = 3.60 m is also
shown in Fig. 1 (the point at BQ = 150 % is measured).
Even though κeff includes the information of the ergodic
region, it well approximates the elongation of LCFS.

Fig. 1

Relation between the quadrupole magnetic field,
BQ, and the effective plasma elongation, κeff, in
low beta plasmas of Rax = 3.75 m (filled squares)
and 3.85 m (circles). The LCFS elongation
estimated from the vacuum magnetic data for Rax= 3.60 m, except the point at BQ = 150 % that ismeasured κeff, is also shown (white crosses).

3. Core density collapse event
A super-dense core of the order of 1020 m-3 is formed
inside the IDB during the reheat phase of the centralpressure after pellet injection in LHD [3, 4]. Waveforms ina typical IDB discharge are shown in Fig. 2. Large
Shafranov shift of the plasma center measured on ahorizontally elongated slice, R0h, is observed during thereheat phase (t = 0.95 – 1.12 s) and it reaches roughly
50 % of the plasma minor radius. In some cases, abrupt
flushing of the central density is observed (t ~ 1.13 s inFig. 2). This is what we call CDC. The CDC event
finishes within < 1 ms, according to the fast soft X-ray
measurement (not shown) [7]. At CDC, the Shafranov
shift R0 + Δ exceeds ~ 4.1 m on a horizontally elongatedslice (this value is insensitive to the magnetic configuration,
at least for R0 = 3.75 – 3.90 m).
Radial profiles of the plasma pressure (beta) before
and after CDC are shown in Fig. 2, which are taken fromthe same discharge shown in Fig. 1. The plasma center
shifts outward (from left to right in Fig. 1), as the central
beta increases from ~ 4.5 % (t = 1.0 s) to ~ 5.5 % (t = 1.1s). At the same time, the inboard side plasma edge also
shifts outward (see also R90in in Fig. 1 (c), which denotethe inboard side radial position of β = 0.1 β0). Just after
CDC (t = 1.134 s), both the plasma center and the inboard
side edge moves inward, and the pressure profile changes
from strongly peaked to approximately parabolic. It
should be noted that the temperature profile is hardly
affected by CDC. This is the reason why we call thisProceedings of ITC/ISHW2007

Fig. 3 Temporal change of the plasma beta profile(measured on a horizontally elongated slice), inthe discharge shown in Fig. 1. Vertical lines
denote radial positions of the inboard (outboard)
Fig. 2side LCFS, R1_vach_in (R1_vach_out), and the magnetic

Typical waveforms in an IDB discharge, where (a)axis, R0_vach, in vacuum.

the diamagnetic stored energy, Wpdia, and the Hαintensity, (b) the central electron density, ne0, thecentralelectronpressure,pe0,and

theline-averaged electron density, (c) positions of theplasma center, R0h, and the inboard (outboard)side plasma edge, R90h_in (R90h_out), where β = 0.1

β0, on a horizontally elongated slice, are shown
from top to bottom. CDC takes place at t ~ 1.13 s(shaded).

“density collapse”.
CDC must be suppressed since it inhibits further
increase of the central pressure and the fusion triple
product. Since CDC is always accompanied by large
Shafranov shift, it is expected that CDC can be suppressed
if the Shafranov sift is mitigated. This working hypothesis
has been examined by the elongation scan experimentdescribed below.

4. CDC suppression by vertical elongation
As was explained in section 2, the plasma elongationis controlled by the quadrupole field, BQ. Verticalelongation with BQ < 100 % that results in κeff > 1 (see Fig.
1) will mitigate the PS current and thus the Shafranov shift.
In Fig. 4, compared are the radial beta profiles indischarges with BQ = 100 % (κeff ~ 1.0), which is identicalto that shown in Fig. 3 (t = 1.1 s), and BQ = 25 % (κeff ~1.2). Even though β0 of ~ 5.5 % is similar for both cases,
the Shafranov shift of the plasma center is smaller in thecase of BQ = 25 %.
Since the Shafranov shift is a function of β0, theFig. 4Comparison of the plasma beta profiles (measuredon a horizontally elongated slice), in twodischarges with BQ = 100 % (κeff ~ 1.0) and BQ =25 % (κeff ~ 1.2). Vertical lines denote radial
positions of the inboard (outboard) side LCFS,
R1_vach_in (R1_vach_out), and the magnetic axis,
R0_vach, in vacuum.

impact of vertical elongation on Shafranov shift mitigation
is clearly observed when it is plotted against β0, as in Fig. 5.
The difference between BQ = 100 % and 25 % is clearlyseen at high β0 of over 3 %, while it is small in low β0cases. Compared at β0 ~ 5.5 %, R0h reaches ~ 4.15 m and
CDC takes place in the case of BQ = 100 %, while R0h isProceedings of ITC/ISHW2007

Fig. 5

The radial position of the plasma center position

Fig. 6

The radial position of the inboard side plasma

on a horizontally elongated slice, R0h, versus theedge on a horizontally elongated slice, R90h_in,

central plasma beta, β0. The magnetic fieldstrength, B0, is 1.5 T in the cases of BQ = 100 %where β = 0.1 β0, versus the central plasma beta,

β0. The magnetic field strength, B0, is 1.5 T in theand 25 %, denoted by circles and squares, and B0

cases of BQ = 100 % and 25 %, denoted by circles= 1.0 T in the case of BQ = 53 % (“+” withand squares, and B0 = 1.0 T in the case of BQ =horizontal error bars). Filled circles denote the53 % (“+” with horizontal error bars). Filled

data just before CDC.

circles denote the data just before CDC.

below 4.1 m and no CDC is observed in the case of BQ =25 %. Also shown in Fig. 5 is the data obtained in anintermediate case of BQ = 53 %, where B0 is decreased to1.0 T to achieve higher β0 under a limited heating power
condition of ~ 10 MW. In this case, R0h is ~ 4.1 m at β0 ~5 % and reaches ~ 4.15 m at β0 > 6 %. The highest β0 of ~7 % is achieved without CDC in this configuration.
The influence of vertical elongation is also recognized
for the inboard side plasma edge position, R90in, as isshown in Fig. 6. CDC takes place when R90in reaches ~3.35 m at β0 ~ 5.5 % in the case of BQ = 100 %. In small
BQ cases, R90in remains less than 3.35 m even with high β0of > 6 %. It is expected that CDC will also take place invertically elongated plasmas as in the case of BQ = 100 %,but at higher β0. It remains, however, for future study toexplore the higher β0 regime of > 7 %.

5. Discussion
It has been shown that plasma elongation is effective
for Shafranov shift mitigation. No CDC is observed aslong as the shift of the plasma center (or, the inboard sideplasma edge) is kept apart from a critical position. In thissense, CDC seems to be related to the equilibrium limit.
On the other hand, it is widely believed that theequilibrium limit will appear as a “soft limit” at which nofast event like CDC is expected. There still is a possibility
that CDC is a phenomenon resulted from an unknown

instability. This instability, if it really exists, should have acharacteristic that it is stabilized in vertically elongatedconfigurations. Because high β0 reaching ~ 7 %, which ishigher than those observed at CDC, is achieved invertically elongated plasmas without CDC. It should bealso noted that in vertically elongated plasmas, the pressure
gradient, which might be a source of this instability, issimilar to, or even larger than, those at CDC.

Acknowledgement
The authors are grateful to the LHD operation groupfor their support. This work is supported byNIFS07ULPP517.

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