Proceedings of ITC/ISHW2007

The neoclassical plasma viscosity analyses relevant tohigh-ion-temperature plasmas in the Large Helical Device (LHD)
M.Yokoyama, O.Yamagishi, K.Ida, M.Yoshinuma, Y.Takeiri, S.Morita, H.Funaba,
K.Nagaoka, O. Kaneko, and the LHD Experimental Group
National Institute for Fusion Science, 322-6 Oroshi, Toki 509-5292, Japan
High ion-temperature (Ti) hydrogen plasmas, about 5 keV at the density range of 1.2-1.6x1019m-3, have been successfully
realized in the LHD. The toroidal-view charge exchange recombination spectroscopy (CXRS) has observed the fast
toroidal rotation velocity (Vt) with a several 10 km/s at the core region in these high-Ti hydrogen plasmas. Previously,high-Ti (more than 10 keV) plasmas have also been obtained in high-Z (like Ar, Ne) plasmas in LHD, in which several 10km/s of toroidal rotation at the core region was also observed. Although, the impact of fats toroidal rotation on
confinement improvement of ions is still unclear, consideration how the toroidal viscosity can be lowered at the coreregion in the LHD to maintain the faster toroidal rotation would be an important research issue. For this purpose,
neoclassical transport code, DKES, has been begun to be applied to high-Ti LHD discharges. The present status of thisapplication and a possible future direction is reported.
Keywords: LHD, high-Ti plasmas, toroidal rotation, neoclassical viscosity and flow, DKES

1. Introduction
The high-energy (~150-180 keV) neutral beam
injection (NBI) with mainly electron heating has realized
high ion temperature (Ti) as much as 13.5 keV inlow-density (in the range of several 1018m-3) high-Z (Ar)plasmas as a proof-of-principle experiment [1] byeffectively increasing the ion heating power (per an ion).
Recent installation and the power increase (~6 MW) oflower-energy (~40 keV) NBI increases the ion heating,which has resulted in the recent achievement of morethan 5 keV in hydrogen plasmas (with a line averagedensity of about 1.21019m-3) in LHD as shown in Fig. 1[2]. This perpendicular injected beam is also utilized for
the Ti-profile measurement with the charge exchange
recombination spectroscopy (CXRS) with the toroidal
line of sight. This toroidal line of sight enhances themeasurement capability for the central region (even forthe case of a hollow profile of carbon content used formeasurement) compared to that with a poloidal line ofsight [2].

2. Toroidal rotation in high-Ti plasmas in LHD
The CXRS measurement has revealed that thetoroidal rotation velocity (Vt) increases at the core region
accompanied by the increase of Ti there as shown in Fig.
2(a) [the same shot and timing as that of Fig.1]. Since
this plasma is heated by the 2-Co and 1-Counter (Ctr)corresponding author’s e-mail: yokoyama@LHD.nifs.ac.jp

Fig.1 Ti profile in a high-Ti discharge
measured by CXRS with a toroidal line ofsight.
NBI (in a configuration with the magnetic field reversed)
with a perpendicular injection, the toroidal rotation directin the Co-direction (positive value in Fig. 2(a)). We havealso performed experiments in a configuration with themagnetic field un-reversed. In such a case, 3 parallel
beam lines provide 1-Co and 2-Ctr. About 5 keV-Ti wasProceedings of ITC/ISHW2007(a)rotation. Thus, it is meaningful to consider how thetoroidal viscosity can be lowered at the core region in theLHD, to maintain the fast toroidal rotation with lessdamping.

2. Application of DKES code for high-Ti
discharges in LHD

Fig.2 Toroidal rotation velocity profile in a high-Ti
discharge measured by CXRS with a toroidal lineof sight.
also obtained in such an experiment, where Vt directs in
the Ctr-direction as shown in Fig. 2(b). These Vt are in therange of several tens of km/s at the core region. It shouldbe also noted here that such a fast toroidal rotation at thecore region was also observed in high-Z high-Ti
discharges, which was measured by the Doppler shift of
the X-ray line as in Ref. [4,5].
The impact of fast toroidal rotation on realizing
high-Ti plasmas is uncertain. However, it is theexperimental observation that these high-Ti discharges(regardless the ion species) in the LHD have beenrealized accompanied by such a fast toroidal rotation at
the core region. Of course, large (mainly toroidal)
momentum input exists from 3 parallel beam lines forthese plasmas, which is the source of a fast toroidal

The neoclassical transport coefficients can beevaluated from the solution of the drift kinetic equation.
The Drift Kinetic Equation Solver (DKES) [6] can solve
the linearized DKE and provide mono-energy
neoclassical transport coefficients in 3D magnetic
configurations, without approximations connecting
collisionality regimes. The mono-energy transportcoefficients can be evaluated at given /v and Er/v, where is the energy-dependent collision frequency, Er is theradial electric field and v the thermal velocity. Since theevaluation of the ambipolar Er is a key element of theanalysis, the module interpolating the mono-energy
transport coefficients on parameters /v and Er/v has been
added to the DKES code [7], so that ambipolar radial
electric field can be determined by balancing the electron
and ion particle fluxes depending on Er.
DKES code, Sugama-Nishimura’s method [8]included, has been applied to analyze high-Ti discharges
in LHD such as shown in Fig. 1. Before injecting 3
parallel NBI, core Ti is about 1.5 keV at the samedischarge. Calculations for these two cases (one is a caseof Ti(0)~1.5 keV and the other is one with Ti(0)~5.2 keV)have been performed, and the evaluated ambipolar Er iscompared with those by GSRAKE code [9], as shown inFig. 3. The parameters used for DKES calculations are asfollows;(mpol,ntor,mpolb,ntorb,lalpha)=(16,12,6,2,100), where notations indicate
poloidal and toroidal mode numbers for perturbed
distributions function and magnetic field expression andLegendre polynomials, in order. For a case of lower Ti(0),DKES and GSRAKE results are fairly close each other.
The convergence of DKES calculations with themini-max variational principle employed is rather wellsatisfied. On the other hand, for a case of higher Ti(0), thedifference between two codes becomes apparent
especially toward the core region with higher Ti. It is also
noted that the range of mini-max variation shown by“error bars” becomes larger there, indicating that theconvergence becomes poorer at lower collisionality.
To examine the convergence properties, above
mentioned parameters for DKES calculations are varied
for the calculation at ~0.37 of “74282-1.15s”. Figure 4
shows the parameter dependence of evaluated ambipolar
Er for several conditions with varied parameters written
in the figure. It is noted that “the condition 1”
corresponds to the result shown in Fig. 3. It seems that

Proceedings of ITC/ISHW2007

Fig. 4 Ambipolar Er evaluated at ~0.37 for“74282-1.15s” with varied parameters used for
DKES calculations. The parameters are listed infigure according to the condition number.

Fig. 3 Ambipolar Er evaluated by DKES(blue) and GSRAKE (red) for cases withTi(0)~1.5 keV (upper) and 5.2 keV (lower).
(see the parameters used for DKES
calculations in the text).
the averaged values (circles) tend to become graduallyless negative according to the increase of mode numbers
for perturbed distribution function (condition 3 to 4) with
reduction of mini-max variation. The increase of mode
numbers for magnetic field seems to increase themin-max variation (condition 1 to 2 and 3) with fixedmode numbers for perturbed distribution function, whichindicates that the further increase of mode numbers of
perturbed distribution function is required for larger mode
numbers for magnetic field.
The difference of evaluated ambipolar Er between

DKES and GSRAKE are still large even for the largest
parameters used for DKES calculations (condition 6).
Detailed comparison between results from both codes andadditional information provided by other neoclassicaltransport code (such as DCOM [10]) will be performed
soon. It would be necessary to further increase the mode
numbers used for DKES calculations when we consider
the application to low collisional plasmas like high-Ti
discharges in LHD. It has been already confirmed that
DKES and GSRAKE predict almost similar values ofambipolar Er each other [8] in collisional plasma like
IDB/SDC (Internal Diffusion Barrier/Super Dense Core)in LHD [11].
The further investigation will be extensively
performed so that DKES can be properly and practicallyapplied for neoclassical transport analyses of high-Ti
discharges in LHD. This will allow us to apply DKES
code for analyses of further high-Ti and evenreactor-relevant situations.

4. Conclusion and discussion
The fast toroidal rotation has been commonly
observed in high-Ti (high Z and low Z (hydrogen),regardless the ion species) plasmas in LHD incircumstances of high power NBI heating.
DKES code has been attempted to apply for theviscosity and flow analyses for such plasmas. However,
unfortunately, the difficulty for treating low collisional

Proceedings of ITC/ISHW2007
regime (high-Ti region) has been encountered so far sothat relevant analyses have yet been performed. Extensive
investigation how to resolve this difficulty will beperformed so that DKES can be practically and properly
applied for neoclassical transport analyses of high-Ti
discharges in LHD.
At last, an “intuitive” consideration for plasma rotation
is drawn. It is experimentally confirmed that the toroidal
rotation is enhanced towards the core region in high-Ti
discharges. It has been predicted by ambipolar Er analysis
and also experimentally demonstrated (as measured byCXRS with poloidal line of sight [12]) that the poloidal
rotation is usually enhanced towards the plasma edge
(either in ion-root and electron-root regime) [13]. Thiscombination of radial variations of toroidal and poloidal
rotation can provide a macroscopic shear of plasma
rotation, which may be helpful to reduce radial transport.
This feature is unique in L=2 (where L is the poloidal
polarity of helical coils) heliotron–type configuration
where the helicity of magnetic field increase towards theedge and the toroidicity becomes larger than helicity at
the very core region. We will perform the analyses tomake this “hypothesis” more evident.

Acknowledgements
Authors deeply acknowledge Dr. S.P.Hirshman for hiskindness on providing recent version of the DKES code
for application to the LHD experiment. Fruitful
discussions with Prof. H.Sugama are also appreciated.
This work has been supported by the grant-in-aid from
the MEXT to one of the authors (MY) and also by thecollaboration programs of NIFS (NIFS07KLDD011).

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