Proceedings of ITC/ISHW2007

Neoclassical Transport Properties in High-Ion-Temperature
Hydrogen Plasmas in the Large Helical Devise (LHD)
Seikichi MATSUOKA1) , Masayuki YOKOYAMA2) , Kenichi NAGAOKA2) , Yasuhiko TAKEIRI2) ,Mikiro YOSHINUMA2) , Katsumi IDA2) , Tetsuo SEKI2) , Hisayoshi FUNABA2) ,Sadayoshi MURAKAMI1) , Atsushi FUKUYAMA1) , Nobuyoshi OHYABU2) , Osamu KANEKO2) andthe LHD Experimental Group2)
1)

Department of Nuclear Engineering, Kyoto Univ., Kyoto 606-8501, Japan2)
National Institute for Fusion Science, Toki 509-5292, Japan

High ion-temperature (Ti) hydrogen plasmas were successfully demonstrated in the experimental campaign(FY2006) in the LHD. The power increase of the perpendicular neutral beam injenction has mainly contributed
to make this realize. T i exceeded 5 keV at the average plasma density (ne ) of 1.2 ×1019 m−3 and also achieved
3 keV at ne > 3 × 1019 m−3 . The neoclassical (NC) analyses have been performed for such plasmas by utilizing
GSRAKE code. We conﬁrmed that even if T i or the plasma density became higher for any shots, the NC
transport is remained to a certain value due to the existence of the ambipolar radial electric ﬁeld (Er ), which wasroughly 2 orders of magnitude smaller for cases without considering the existence of ambipolar Er .
Keywords: high-ion-temperature, neoclassical transport, radial electric ﬁeld, GSRAKE code

1Introduction

High ion-temperature (T i ) hydrogen plasmas weresuccessfully demonstrated in the experimental campaign(FY2006) in the LHD. T i exceeded 5 keV at the averageplasma density (ne ) of 1.2 ×1019 m−3 and also achieved 3keV at ne > 3 × 1019 m−3 (See Fig. 1) [1]. In such highion temperature palasmas, neoclassical transport ion thermal diﬀusivities (χi,NC ) are thought to be increased due tothe ripple transport.
However, It has been considered that if radial electric ﬁeld (Er ) exists in the plasma, neoclassical transport
are reduced to the extent of the smaller electron diﬀusion
which is determined by ambipolar condition, Γe = Γi ,where Γe and Γi are electron and ion particle ﬂux respectively. And, by utilizing the electron or ion root of theradial electric ﬁeld, reducing the neoclassical transport has
been considered of great importance to improve the plasma
conﬁnement for non-axisymmetric helical systems. Thus,
it is important to know how the neoclassical diﬀusivities
of high-T i plasmas are aﬀected by the Er quantitatively.
For this purpose, the neoclassical transport analyses areconducted to some plasmas shown in Fig. 1 by utilizing
GSRAKE code [2]. And systematic parameter-scan calculations with varying T i and ne have been performed basedon these shots to see the parameter dependence of neoclassical ion diﬀusivity. It is clariﬁed that the neoclassical thermal diﬀusivities are restrained due to ambipolar Er . For
many cases Er < 0 is predicted, however, electron-root(Er > 0) can appear for cases with low T i . This indicatesthat neoclassical transport could be kept relatively small
author’s e-mail: matsuoka.seikichi@LHD.nifs.ac.jp

Fig. 1 The ion and electron temperature dependance on thedensity at the center of the plasma in the High-IonTemperature experiments in LHDfor even in higher T i plasmas in LHD. In Sec.2, neoclassical transport analyses for LHD shot data are shown. Andfurther neoclassical transport analyses for various plasmas
in a parameter-sacn manner are described in Sec.3. Finally,
summury is given in Sec.4.

2

Neoclassical transport analyses ofLHD shot data

Neoclassical transport analyses were performed byutilizing GSRAKE code. GSRAKE code calculates particle and thermal ﬂuxes for ions and electrons, and therefore, ambipolar Er based on LHD magnetic ﬁeld conﬁg-Proceedings of ITC/ISHW2007
is clearly indicates that ion diﬀusivity does not increase asT i is increased due to the presence of predicted ambipolar
Er .

Fig. 2 Er dependence of Γe and Γi at ρ = 0.2 of shots for 75232(top) and 75235 (bottom). The intersection provides ambipolar Er .

urations, using T i and T e (T e is the electron temperature)and the plasma density proﬁles. At ﬁrst, I chose the shot
75235 (at 1.35 sec) and 75232 (at 1.35 sec) from the highion-temperature experiments. While the ion temperatureof 75235 is 4.8 keV at the density of ∼1.8×1019 m−3 , thatof 75232 is ∼ 3 keV at ∼3.2×1019 m−3 . T i of 75232 is comparable to T e , T i of 75235 is higher than T e . Neoclassicaltransport calculations are carried out for these two shots.
Γi and Γe at ρ = 0.2 for 75235 and 75232 are shown inFig. 2. Here, ρ is normalized minor radius. Ambipolar Er
are shown in Fig. 3(a) for 75235 and 75232 respectively.
Fig. 3(b) shows the ion-ion collisionalities νi,p , normalized by the value at the platue-banana boundary. FromFig. 3(a) and (b), it is recognized that these plasmas arein 1/ν regime in which neoclassical diﬀusion steeply increases in proportion to ν−1 when Er = 0. In fact, as seenin Fig. 2, Γi becomes extremely large near Er = 0. Then,ion thermal diﬀusivities devided by T i1.5 (Gyro-Bohm factor), χi,NC /T i1.5 , are shown in Fig. 3(c) where χi,NC /T i1.5 at
Er = 0 is also shown for reference. The diﬀusivities are
obviously reduced to almost the same magnitude (about 23 orders of magnitude smaller than that for Er = 0), in spiteof about 2 times higher T i in 75235 than that in 75232. ItFig. 3 Radial proﬁles of (a) ambipolar Er , (b) ion collisionality
with and (c) thermal diﬀusivities with or without Er areshown for 75235 and 75232 respectively.

3 Temperature and density scan calculations
Then, in order to investigate the dependence of neoclassical transport on plasma parameters, such as T i andProceedings of ITC/ISHW2007
n, have been performede based on 75235 and 75232. T iand n of 75235 and 75232 are widely varied as shown inFig. 4. T i (0) of 75235 (∼ 4.8 keV) is multiplied by 0.3, 0.5
and 2, n(0) of 75235 (∼ 1.8 ×1019 m−3 ) is multiplied by 2,5, 10, respectively. And then, T i (0) of 75232 (∼ 3 keV)
is multiplied by 0.5, 2, 4, n of 75232 (∼ 3.2 ×1019 m−3 ) is
multiplied by 0.5, 3, 5, respectively. In these calculations,
I assumed that magnetic conﬁguration equilibrium is ﬁxed
for simplicity, although T i and n are varied.

Fig. 4 Range of n and T i scan calculations based on 75232 and75235.

The results of parameter scan calculations are summurized in Fig. 5, where χi /T i1.5 is shown for n-scan calculations and χi for T i -scan calculations is shown. χi for
T i -scan and χi /T i1.5 for n-scan are reduced to alomost thesame extent in all cases. The collisionalities are all in 1/ν
regime. In Figs. 5(a) and (b) (n-scan), it is recognized thatthe neoclassical ion thermal diﬀusivity at Er = 0 increses
as n (thus collisionality) decreased. However, it reduces
to almost the same lavel in the presence of ambipolar Er
regardless of the n-value. It is also the case for T i -scancalculations. As expected, the incease of T i (thus the decrease of collisionality) makes χi larger and lager for caseswith Er = 0 as shown in Figs. 5(c) and (d). However, it
is reduced to almost the same level in the presence of ambipolar Er . This fact indicates that the neoclassical χi will
not increase even for higher-T i (ranging of 10keV) cases inLHD, due to the presence of ambipolar Er .
It is interesting to note that, in 75235-T i scan, not only
the ion root but also the electron root is predicted to exist
at peripheral region of the plasmas when T i is decreased(case of 0.3, 0.5 in Fig. 5(d)). It is considered that since
the absolute value of electron root is larger than that of ionroot, χi can be reduced more eﬀectively. The electron root

Fig. 5 neoclassical χi /T i1.5 for n scan based on 75232 (a) and75235 (b), and neoclassical χi for T i scan based on 75232(c) and 75235 (d)Proceedings of ITC/ISHW2007can appear for the case of 0.5 times T i (0) (∼ 2.4 keV) of75235 (Fig. 5(d)), but the case of 75232 (Fig. 5(c)), although T i is almost the same. It should be noted here thatT e has been ﬁxed (T e is about 3.1 and 3.5 keV for 75232
and 75235, respectively, as shown in Fig. 1). Higher ratioof T e /T i for 75235 might help to make the electron root
appear.

4SummuryIn this paper, neoclassical transport properties (especially for ions) are reported for high-T i hydrogen plasmasachieved in LHD.
It is clearly demonstrated that ion thermal diﬀusivity
avoids to be increased even with higher-T i cases due tothe predicted ambipolar Er . It is also the case even for arange of T i ∼ 10 keV, which is claliﬁed by parameter scancalculations. This is favorable fact for further increase ofT i in LHD by avoiding the ripple transport nature.
The possibility of the electron-root scenario for highT i plasmas is also pointed out by parameter scan calculations. This is interesting topic to be investigated.
[1] K.Nagaoka et al., in this conference, and M.Yokoyama et al.,to be presented in the 49th APS-DPP Annual meeting, Nov.
2007
[2] C.D.Beidler et al., Plasma Phys. Control. Fusion. 37 463(1995).