Proceedings of ITC/ISHW2007

Density Control by Second Harmonic X Mode ECRH in LHD
Shin KUBO1) ,Takashi SHIMOZUMA1) , Kenji TANAKA1) , Teruo SAITO1) ,Yoshinori TATEMATSU1) , Yasuo YOSHIMURA1) , Hiroe IGAMI1) , Takashi NOTAKE1) ,Shigeru INAGAKI3) , Naoki TAMURA1) and LHD Experimental Group1)
1)

National Institute for Fusion Science, Toki 509-5292, Japan
Research Center for Development of FIR Region, Fukui Univ.,
3)
Research Institute of Applied Mechanics, Kyushu Univ., Kasuga 816, Japan2)(Received 26 October 2007)
Density clamping or pump out phenomena are observed both in tokamaks and helical systems during highpower heating, in particular electron cyclotron resonance heating. If the change of the particle ﬂux and resultant
electric ﬁeld can be localized by the local heating of ECRH, it can be a powerful nob for the control of the particle
as well as the heat transport. High power density local second harmonic X (X2) mode ECRH is applied to NBI
target plasma at ripple top and bottom resonance conditions so as to keep the identical power deposition proﬁlefor both cases to distinguish the ECRH induced ﬂux and enhanced diﬀusion due to the electron temperature rise.
Experimental results indicates that the ECRH induced ﬂux can explain the diﬀerence of the density clamping
between ripple and bottom heating.
Keywords: ECRH, density pump out, density control, direct loss, radial electric ﬁeld1Introduction

Density clamping or pump out is the common phenomena
in tokamaks and helical systems during high power density
heating, in particular electron cyclotron resonance heating.
These phenomena are discussed in terms of the enhancedelectron diﬀusion induced by the perpendicular acceleration in velocity space and the resultant electric ﬁeld [1] [2][3]. It is also pointed out that the change in the electrontemperature proﬁle can enhance radial ﬂux due to a nonzero oﬀ-diagonal term in the transport matrix which canbe appreciable by the excitation of turbulent instabilities
like trapped electron modes[4]. If the change of the particle ﬂux and the resultant electric ﬁeld can be localized by
the local heating of ECRH, it can be a powerful nob forthe control of the particle as well as the heat transport. Inorder to distinguish the eﬀect of enhanced electron ﬂux directly driven by the ECRH or enhanced diﬀusion due to thechange in the electron temperature or oﬀ-diagonal transport matrix, series of experiments are performed. Highpower density local second harmonic X (X2) mode ECRH
is applied to NBI target plasma at ripple top or bottom resonance for the diﬀerent ripple conditions. The diﬀerencein the transient behavior of density proﬁle is observed between top and bottom heating, or high and low ripple conﬁgurations. X2 mode is selected because the perpendicular
acceleration is more enhanced in X2 than in fundamental O mdoe (O1) mode. The role and the mechanism ofECRH induced particle ﬂux in the particle and heat transport is discussed based on these phenomena. Such degradation of particle conﬁnement is also observed in a tanauthor’s e-mail: kubo@LHD.nifs.ac.jp

Fig. 1 Vertically elongated cross section of Mod-B, ﬂux surfaces, second harmonic resonance layers and ECRH
beams for ripple a) top and b) bottom heating geometries.
for Rax = 3.60m.

gential negative ion neutral beam (N-NB) heated plasma in
LHD for low density discharges, where the electron heating is dominant but heating in parallel to the magnetic ﬁeld.
Such observations also support the enhancement of the oﬀdiagonal transport term. In order to distinguish both effects, series of experiments are performd. High power density second harmonic local ECRH is applied on the ripple
top or bottom resonance position where the width of theloss cone is wider for bottom than that for top, but expected
power deposition proﬁle is identical to each other in LHD.

2

Experimental results

2.1

Ripple top and bottom heating condition

In order to enhance the diﬀerence in the electron ﬂux by
ECRH, the heating positions and magnetic ﬁeld strength

Proceedings of ITC/ISHW2007

are selected so that the toroidal ripple top and bottom areheated but keeping the identical normalized radial positionon the same vertically elongated cross section. The magnetic ﬁeld strength and ECRH injection angles are adjusted
to meet the second harmonic resonance condition ( 1.5 Tfor 84 GHz) at desired position as shown in Figs. 1 and2. Figure 1 are shown the vertically elongated cross section of LHD with the Gaussian beams from bottom for themagnetic ﬁeld strength of a) 1.36 T and b) 1.58 T for theRax = 3.60 m conﬁguration. The second harmonic resonance layer is also shown in thick red lines. Strong interactions are expected at the cross section between the injectedbeam and the resonance. The power deposition proﬁles estimated from the multi-raytracing code are conﬁrmed to beidentical and sharp at normalized minor radius, ρ=0.3, forboth cases. Relative power deposition region on the expanded ρ=0.3 ﬂux surface are shown by red circles in Fig.
2 for both magnetic ﬁeld cases. Here, the strength of thetotal magnetic ﬁeld (Mod-B) is expressed in color scaleon the plane of toroidal and poloidal angle at ρ=0.3 ﬂux
surface for a) ripple top and b) bottom heating condition.
Typical time evolutions of the plasma discharge are shownin Fig. 3. Ripple top and bottom second harmonic heating
under the condition shown in Figs. 1 and 2 superposed on
the base NBI plasma. A set of discharge is selected for theinitial density is almost the same. Time response of the averaged density clearly diﬀers in the case of ripple bottom
heating case from that of bottom case. For both cases, thetemperature responds rapidly within the time of 0.05 sec.
In order to conﬁrm the ECRH clamping eﬀect due tothe ripple and bottom heating, similar experiments are performed for the smaller ripple condition. Here, the conﬁguration Rax = 3.75 m is chosen as a reference. In Figs. 4 and5 are shown the injection condition and Mod B structure inrelation to the heating region. As is seen from Fig. 2 and5, the ripple ratio is 0.15 and 0.1 for the case of Rax = 3.60
and 3.75 m, respectively. Typical discharge waveforms
are shown in Fig. 6 for ripple top and bottom cases. The

1.2
1.1
1
0.9
0.8

Ripple Top
Ripple Bottom

Ripple Top
Ripple Bottom

102
Ripple Top
Ripple Bottom

10

1.5

2

2.5

ne,av(x1019m-3)

2Ripple Top
Ripple Bottom

Ti,ArXVII (keV)

PECH(arb)
Fig. 2 Mod-B contour on toroidal poloidal plane on ρ = 0.3 ofRax = 3.60m conﬁguration for ripple a) top and b) bottom
heating geometries. Thin blue lines indicate the second
harmonic resonance position for 84 GHz, and red circle
indicates deposition region.

Te,0 (keV)

LHD Shot 58078,58108
5432
10time (s)Fig. 3 Temporal evolutions of line averaged density, central
electron and ion temperature for ripple top (dotted lines)
and bottom (thick lines) ECRH on NB heated discharge.

Fig. 4 Vertically elongated cross section of Mod-B, ﬂux surfaces, second harmonic resonance layers and ECRH
beams for ripple a) top and b) bottom heating geometries.
for Rax = 3.75m.

Fig. 5 Mod-B contour on toroidal poloidal plane on ρ = 0.3 ofRax =3.75 m conﬁguration for ripple a) top and b) bottom
heating geometries. Red line indicates the resonance position.

Proceedings of ITC/ISHW2007

Fig. 6 Temporal evolutions of line averaged density, central
electron and ion temperature for a) ripple top and b) bottom ECRH on NB heated discharge.

increases in the electron temperature and stored energy inboth cases are clear, but the clamping eﬀect is week forboth cases. The diﬀerence of clamping eﬀect for both cases
needs to be analyzed more in detail, but it is clear from thecomparison with Rax =3.60 m conﬁguration that the density
clamping is strongly related to the magnetic ripple rate at
the heating region, implying that the ECRH related physics
plays an important role in the clamping phenomena.

2.2

Detailed comparison of electron temperature and density proﬁle for Rax = 3.60 m
conﬁguration

In Fig. 3 are shown the time evolutions of the density, central electron and ion temperature in response to the ECRH
on NB heated plasma for ripple top and bottom resonanceheating conditions. In both cases, density decrease is observed by applying ECRH, but the time behavior of thedecrease in the density clearly changes as the heating position. The line averaged density decreases faster in ripple
bottom heating case than in top one. The decrease rate saturates in the time constant of 200 ms for the bottom heating case, while that for the top heating case keeps constantduring the ECRH injection of 500 ms. Electron temperature increases within 100 ms and keeps almost constantduring the injection for both cases. The proﬁle changes ofdensity reconstructed from a multi-chord FIR interferometer are shown in Fig.7. It should be noted that the density
drops at ρ > 0.4 but central part does not aﬀected by theECRH injection for top heating case, while that drops al-Fig. 7 Density proﬁle at several time slices after ECH injection[ a) and c) ]. Time evolutions of the density at several
spatial points b), and d) for ripple top [ a) and b) ] andbottom [ c)and d) ] heating cases.

most whole region for bottom heating case. The change ofthe electron temperature proﬁle at several timing during theECRH phase and the temporal evolutions at several radial
positions are shown in Fig. 8. The temperature increase of
the central region for the case of ripple bottom due to theECRH is larger as compared with the ripple top case. In
both cases, the proﬁle change occurs in less than 100 msand kept almost constant after 100 ms from the ECRH injection. This means that the change in the density proﬁleevolutions after 100 ms of ECRH injection are attributed
to the diagonal term and direct ﬂux due to the ECRH in theelectron diﬀusion.

3Discussion

Neglecting the source and sink term other than that due to
ECRH, diﬀusion equation can be written by electron density ne (r, t)and temperature proﬁles T e (r, t) asΓe (r, t) =∂ne (r, t)∂r∂T e (r, t)+De,T (r, t)∂r+ΓECH (r, t).
De,n (r, t)(1)Here, De,n (r, t) denotes the normal electron diﬀusion coefﬁcient, while De,T (r, t) does an oﬀ-diagonal element due toelectron temperature gradient. Then, the diﬀusion equation
is expressed with this electron ﬂux Γe (r, t) as)∂ (∂ne (r, t)=−rΓe (r, t) .
∂tr∂r

(2)

Proceedings of ITC/ISHW2007
term from the temperature gradient. As is described above,
the temperature proﬁle change occurs only at the beginning 100 ms after ECRH injection for both cases. So thecorrelation between the deduced ﬂux and the temperature
gradient should also be weak. These results indicate thatthe change in the deduced particle ﬂux for the ripple top
and bottom cases are directly driven by ECRH, although
the dynamical dependence of the diﬀusion coeﬃcient on
the temperature and its gradient, oﬀ-diagonal term and theeﬀect of the radial electric ﬁeld should be considered more
carefully.

4 Conclusion

Fig. 8 Temperature proﬁle at several time slices after ECH injection [ a) and c) ]. Time evolutions of the density atseveral spatial points b), and d) for ripple top [ a) and b)] and bottom [ c)and d) ] heating cases.

Integrating over radius of Eq. (2) gives∫
1 r 0 ∂ne (r0 , t) 0
Γe (r, t) = −r
dr .
r 0∂t

(3)

Thus total electron ﬂux can be deduced from Eq. (3) by
the experimentally observed quantity ne (r0 , t). In Fig.9 areshown the change in the particle ﬂux deduced from Eq. (3)for the ripple a) top and b) bottom cases. Fast increase of
the ﬂux at ρ > 0.3 is clear in the ripple bottom heatingcase than that in the top case. The density gradient proﬁlechanges are also shown in Figs.9 c) and d) for comparison.
As is expected from Eq. (1), the correlations between a)and c) or b) and d) indicate the eﬀect of normal diﬀusion
coeﬃcient, but there seems no clear correlation between
them. Second term in Eq. (1) describes the oﬀ-diagonal

Fig. 9 Particle ﬂux deduced from Eq. (3) for ripple a) top andb) bottom cases. c) and d) show a temporal change in thedensity gradient for each case.

By applying ripple top and bottom second harmonic
ECRH, the density clamping phenomena are investigated.
From the comparison of the density clamping between different ripple cases ( Rax =3.60 and 3.75 m ), ECRH physics
that is perpendicular acceleration of the electron, is shown
to play an important role in the clamping phenomena. This
indicates that the ECRH can be one of a nobs to control
the local density. The diﬀerence in the temporal behavior of the electron density can be explained qualitatively
by the direct electron ﬂux by ECRH due to the enhanced
ripple loss. The eﬀect of the formation of radial electricﬁeld might have mitigated the degradation. Experimental
and theoretical investigations of the eﬀect of radial electricﬁeld are left for future work.

5Acknowledgement

The authors would like to express their thanks to the continuous eﬀorts of technical staﬀ of ECRH and LHD to perform the experiments. This work is mainly performed under budget code NIFS05ULRR501-3.
[1] K. Ito et al., J. Phys. Soc. Japan 58, 482 (1989).
[2] H. Sanuki et al., Phys. Fluids, B2, 2155 (1990).
[3] H. Idei et al., Fusion Engineering and Design 26, 167 (1995).
[4] C. Angioni et al., Nuclear Fusion 44, 167 (2004).