Proceedings of ITC/ISHW2007

Flux Surface Mapping in LHD
Tomohiro MORISAKI, Mamoru SHOJI, Suguru MASUZAKI, Satoru SAKAKIBARA,Hiroshi YAMADA, Akio KOMORI, Osamu MOTOJIMA
and the LHD experimental group
National Institute for Fusion Science, Toki, Gifu 509-5292 Japan
Magnetic flux surface measurements have been carried out in the Large Helical Device (LHD) in the standard
magnetic field configuration with toroidal magnetic field strength up to 2.75 T. Electron beam launched with asmall electron gun moving across the flux surfaces was detected with a fluorescent screen or a probe array. Nested
surfaces could clearly be visualized with both methods. Even the open ergodic region was also detected. In theexperiment an unfavorable m/n = 1/1 magnetic island was found to exist near the last closed flux surface (LCFS),
where m and n are poloidal and toroidal mode numbers, respectively. It was found that the source of the error field,in the low magnetic field strength of 0.0875 T, is terrestrial magnetism. On the other hand, in the standard magnetic
field strength of 2.75 T, the main source of the error field is though to be ferromagnetic materials near the LHD. It
was also found that such magnetic islands can be eliminated or reduced applying the correction field with some
perturbation coils.
Keywords: flux surface mapping, magnetic island, ergodic layer

1. Introduction
Unlike tokamaks, helical devices, e.g. heliotron,stellarator, torsatron, do not need a plasma current toform the magnetic flux surfaces for the plasma
confinement. These devices can thoroughly achieve theconfinement configuration only by their external coils.
This means that the magnetic flux surfaces exist invacuum without any plasma current, thus one can easily
identify or measure them, visualizing each surface with aproper instrument installed in the vacuum vessel. Several
experiments to map the flux surfaces have been
performed in major helical devices with various
techniques [1-8]. The Large Helical Device (LHD) is asuperconducting heliotron [9], which is by far a favorable
device for the flux surface mapping experiment because
the standard high magnetic field (~ 3 T) can be
maintained in steady state during the mapping
experiment.
In this paper, results of the flux surface mapping
experiment on LHD are presented. The measurements
have been performed in two different methods since thevery early phase of the LHD experiment in 1998. In
section 2, experimental apparatus and geometry are
shown. After describing the experimental results in
section 3, discussion is given in section 4. Finallysummary is given in section 5.

2. Experimental Apparatus
The principle of the experiment is simple and clear.
The electron beam launched on a flux surface from aauthor’s e-mail: morisaki@nifs.ac.jp

small electron gun (e-gun) traces a magnetic field line.
Projecting the positions on the poloidal plane, where theelectron beam passes through, the flux surface isvisualized. To identify the piercing points on the poloidal
plane, two methods were employed in the experiment.

2.1 Electron Gun
In order to launch the electron beam, a small
electron gun (e-gun) was utilized. For two different
methods, i.e. fluorescent screen and probe array, two(a) Fluorescent screen(b) Probe array

Fig. 1 Position of the e-gun scanning in the poloidal
plane in the case of (a) fluorescent screen and(b) probe array methods. The e-gun can beinserted up to ρ = ~ 0.1 with the fluorescentscreen method.

Proceedings of ITC/ISHW2007
distinct ports to install the e-gun were utilized, as shownin Fig. 1. Moving radailly in the poloidal plane, the e-gun
can reach as far as ρ = ~ 0.1 for the fluorescent screen
method and ~ 0.3 for the probe array method, where ρ isa normalized minor radius. One can trace different flux
surfaces by changing the radial position of the e-gun. For
the precise alignment of the electron beam with amagnetic field line, the direction of the e-gun can also bechanged, rotating on the supporting rod, since themagnetic shear is very high in the heliotron configuration.
The e-gun itself consists of a lanthanum hexaboride(LaB6) cathode and a tantalum plate with a 3 mmdiameter hole to extract electrons. The cathode is heated
up to 1400 K and negatively biased at ~ 150 V to theground (vacuum vessel). Although no mechanism tocollimate or focus electron beams is equipped with,practical beam width (FWHM) is about 10 mm at Bt =2.75 T, where Bt is the toroidal magnetic field strength.
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simple and straight forward, it is restricted to theconfiguration between screen and CCD to be seen eachother through the viewing window.
If one cannot obtain such a configuration mentioned
above, there is another way to detect the electron beam.
We introduced an 89 channel vertical probe array tomeasure the electron current on a flux surface. Byscanning it in the horizontal direction, two-dimensional
information which consists of 89 horizontal chords on thepoloidal plane can be obtained. With this method, noviewing port is necessary, thus we do not have to mind
about the geometrical problem. The diameter of eachprobe chip is 7.8 mm and the distance between adjacentchips is 9 mm. Since the orbit drift of the electron beamwith 150 eV is negligibly small compared to the beamwidth, the spatial resolution of the system is consequently
about 10 mm.

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2.3 Geometry
2.2 Fluorescent Screen and Probe Array
In order to identify the positions where the electron
beam passes through a poloidal plane, a fluorescentscreen or a scanning probe array was employed.
The screen is made of 70 - 80 % transparent meshcoated with fluorescent powder P15 (ZnO: Zn). The
electron beam glows on the screen mesh, circling along
the torus for many times. The images on the screen in thepoloidal plane are captured with a CCD detector viewing
from the tangential port. Changing the radial position of
the e-gun, the captured images of each flux surface aresuperimposed on one picture. Though this method is very

The geometrical setup of e-gun, fluorescent screen
and probe array is shown in Fig. 2. The fluorescent screenof 2 m high and 1 m wide was installed in the toroidal
position where the flux surfaces are vertically elongated.
The CCD detector views the screen from the tangential
port though the window, as shown in Fig. 2. Although thescreen fully covers the poloidal plane of the flux surfaces,
the CCD could not perfectly see the whole area of theflux surfaces because of the structure in the vacuum
vessel blocking the CCD’s view.
On the other hand, the probe array was located at theposition where the flux surfaces are horizontallyelongated and the Local Island Divertor (LID) [10] headis inserted from outboard side of the torus. Actually theprobe head is mounted on the LID head, and travels
horizontally with it more than 2 m with the translation
mechanism of LID. Thus the 0.8 m high and 2 m wide
scanning area covers more than 90 % of the flux surfaces.

3. Experimental Results
Flux surface mapping experiments have been
performed three times since the beginning of the LHD
experiment in 1998. The magnetic configurations of Rax =3.60 m, 3.75 m and 3.85 m were chosen for themeasurement, where Rax is the magnetic axis position.
The Bt was set at Bt = 0.0875 T, 0.25 T and 2.75 T. Notethat Bt = 2.75 T is used for the ordinary plasma
experiment.
The vacuum vessel was evacuated less than 3 ×
10-4 Pa in order to avoid the plasma production along theelectron beam. Under this experimental condition, themean free path of the electron is about 2500 m (100toroidal turns).
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BFig. 2 Geometrical setup of flux surface mapping.
Electron beam is launched in the clockwise
direction for the probe array and thecounterclockwise direction for the fluorescentscreen.

Proceedings of ITC/ISHW2007(a) Calculation(b) ExperimentFig. 4

Fig. 3Flux surfaces (a) calculated with field line
tracing code and (b) mapped on the fluorescentscreen.

Flux surfaces measured with 89 ch probearray. Red and blue closed circles are theO-points of m/n = 2/1 and 1/1 magnetic islands,
respectively. Separatrix of the 1/1 island is
depicted with red line and the ergodic region iscolored in green.

3.1 Fluorescent Screen Method

3.2 Probe Array Method

Experimental result of flux surface mapping on thefluorescent screen method is presented in Fig. 3 (b),together with the calculation result with the field line
tracing code, as shown in Fig. 3 (a). This experiment wascarried out in the standard but low magnetic field
configuration, i.e. Rax (average) = 3.75 m and Bt = 0.0875
T. For this result presented in Fig. 3 (b), the position of
the e-gun was changed six times and then six pictures
were superimposed. It can clearly be seen that theexperimental and numerical results agree well. The
measured magnetic axis position which was derived byfinding the center of each flux surface was found to be at
R = 3.77 m where the calculated local magnetic axis
position is R = 3.76 m. It can be said that the difference
between them is within the error bar of experimental
conditions.
It can be seen, unfortunately, that a relatively large
magnetic island of which poloidal/toroidal mode numbers
are m/n = 1/1. Such a magnetic island is often attributed
to the error field caused, for example, by theferromagnetic materials near the machine ormisalignment of the coils. However, in this experiment,
the Bt was so low as 0.085 T that it is necessary to takethe geomagnetic effect into consideration. In thecalculation shown in Fig. 3 (a), the local geomagneticeffect (using published data at Inuyama city near Toki) is
taken into account. It is found that the m/n = 1/1 island
clearly appears by introducing the terrestrial magnetismin the calculation, and the calculated width and the phaseof the magnetic island agree well to the experimental
result, as shown in Fig. 3. The cause of the magnetic
island will be discussed later again.

Recently the flux surface mapping with an e-gun anda fluorescent screen was performed. As shown in Fig. 4,
clear and precise results at the horizontally elongated crosssection were obtained with this method. In this experiment,
the standard magnetic configuration and magnetic fieldstrength for the usual experiment were employed, i.e. Rax =3.60 m and Bt = 2.75 T. Outside of the nested closed
surfaces depicted in black, it can be seen that complicatedergodic region colored in green spreads out. Such a finestructure has not been observed with the fluorescent screen
method.
In spite of high magnetic field of Bt = 2.75 T, the m/n= 1/1 and 2/1 magnetic islands were still observed, as
shown in Fig. 4. It is though that these 1/1 and 2/1 islands
are toroidally coupled each other. Moving the e-gun
precisely, nested closed surfaces within the islands werealso detected. Finding one smaller flux surface after
another in the island, we could finally reach the smallest
magnetic surface at the center of the island, i.e. at themagnetic axis of the island. This is what is called anO-point of the island. In Fig. 4, the O-points of 1/1 and
2/1 island are emphasized by drawing the final smallest
flux surface with larger symbols. Concerning the phase of
the island (poloidal angle of O-points), it is consistent
with that observed in the previous experiment withfluorescent screen, which is described in section 3.1.
Thus the island phase calculated with the geomagneticeffect almost agrees to that obtained in the experiment
presented in this section. However the relatively large
island width shown in Fig. 4 cannot be explained simply
by the geomagnetic effect, since Bt is far stronger thanterrestrial magnetism. Detailed discussion is presented in
the next section.

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Proceedings of ITC/ISHW2007

Fig. 5

Variation in magnetic island property under four experimental conditions, i.e. high (2.75 T) and low (0.0875T) magnetic field strengths, and those reversals. The O-points of each island are emphasized with large redsymbols.

4. Discussion
Further investigation for the magnetic islands
observed in the flux surface mapping was carried out tofind the source of the error field. In order to see the Bt
dependence on the island properties, its phase and width
were compared between Bt = 0.0875 T and 2.75 T. The
direction of Bt was also reversed in each magnetic fieldstrength. Summary of the experiments is presented in Fig.
5. The m/n = 1/1 and 2/1 islands measured with a probearray under four experimental conditions are shown.
Comparing Fig. 5 (a) and (c), it is found that the 1/1
and related 2/1 islands at low Bt are due to weak andsteady perturbation, e.g. terrestrial magnetism. This isbecause, in reversed Bt (Fig.5 (c)), the island phase is also
reversed, which suggests the direction of the error field
never changes, according to the environmental field.
With increase in Bt, the island width surely decreases,
however the decreasing rate is very small, as is seen
between Fig. 5 (a) and (b), or between (c) and (d). If thesource of the error field were purely from terrestrial
magnetism, the island width decreased drastically,
because Bt increased more than 30 times between two.
This experimental result suggests the existence of anothersource of the error field, which increases with Bt.
Comparing Fig. 5 (b) and (d), another important
information can also be seen, namely the island phasenever changes, even if Bt is reversed. This means that thedirection of the error field changes with Bt direction. Thus
we can conclude that there must be another source of theerror field in addition to the terrestrial magnetism.
One of the candidates of the error field which has
Bthe characteristics mentioned above is the unsaturated
ferromagnetic materials near the machine, e.g. magnetic
shield for the neutral beam injector and/or diagnostics,
deteriorated stainless steel by welding, etc. Fortunately it
was also confirmed that these magnetic islands can beeliminated or reduced by using small correction coils.

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5. Summary
Flux surface mapping with electron beam andfluorescent screen or probe array was successfully carriedout in LHD. It was confirmed that the nested closed
surfaces are formed in the standard LHD configuration.
The m/n = 1/1 and 2/1 islands were found to exist, but canbe eliminated or reduced with small correction coils.

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Acknowledgement
This study was partially funded by the Grant Aid for
Scientific Research from MEXT of Japanese government.

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