25D03
Fast ion driven neoclassical parallel flows and radial fluxes
in non-symmetric toroidal plasmas
非対称トーラスにおける高速イオンに駆動される
磁力線方向フローと径方向輸送
11

1

1

Shin Nishimura , Hideo Sugama , Akinobu Matsuyama , Hisamichi Funaba ,2

1

2

Kenji Nishioka and Yuji Nakamura
1

1

1

2

2

西村 伸 , 洲鎌英雄 ，松山顕之 ，舟場久芳 ，西岡賢二 , 中村 祐司
1 National Institute for Fusion Science, Toki 509-5292, Japan
2 Graduate School of Energy Science, Kyoto University, Uji 611-0011, Japan
1 核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
2 京都大学大学院エネルギー科学研究科 〒611-0011 京都府宇治市五ケ庄Parallel plasmas flows driven by tangentially injected neutral beams in non-symmetric toroidal plasmas areanalyzed. The Onsager symmetric neoclassical transport matrix is now extended to include (1) Ohkawa
current, (2) fast ion driven radial fluxes, and (3) parallel momentum. In contrast to symmetric systems suchas tokamaks, these beam driven momentum and radial particle flux in stellarator/heliotron devices, inwhich the neoclassical particle diffusion is non-ambipolar, can exist without any contradictions to theexperimentally observed quasi-steady-state charge neutrality.

Though many applications of a method to obtainthe neoclassical transport matrix in general
non-symmetric toroidal plasmas [1] have been
performed especially for quantitative predictions ofneoclassical parallel flows and/or currents, only theinductive parallel electric field is taken into accountthere as the external driving force for the parallel
flows. This situation is caused by a fact that theseformulations are extensions of traditional
neoclassical transport theories for tokamaks. Instellarator and heliotron devices with externalrotational transform, however, the inductive electricfield for the toroidal current is not required. Insteadof that, the momentum input by the tangentiallyinjected heating neutral beams is more important as
the driving force. One experimentally observableeffect of it may be fast ion driven impurity flow
velocities that can be measured by the charge
exchange recombination spectroscopy [2,3], andanother may be the beam driven (Ohkawa) current[4]. Although many previous theoretical andexperimental studies in 1970’s~1980’s were
motivated by a practical reason of steady-state
operations of tokamaks and consequently many
discussions were devoted to the current, there arealso the beam driven momentum in various toroidal
confinement devices [5]. Recently, an importanceof the toroidal momentum is widely recognized also
in a viewpoint of the MHD stability.
Besides well-known these importance, additional
beam driven radial particle and heat fluxes ofheated species [6] also may be important as amethod of impurity control and as a formation
mechanism of the ambipolar potential. The
existence of these additional radial fluxes can beeasily understood by an analogy of well-known
Ware pinch driven by the inductive electric field.
One motivation of the previous experimental
studies on the effects of the external momentum
input [5] was to control the radial electric fields
artificially.
For
non-symmetrictoroidalconfigurations where the electric field is governedby the neoclassical ambipolar condition, however,any quantitative theoretical methods for the beam
driven radial fluxes had never been shown. In thisviewpoint, an important aspect of this problem (fastion driven flows) clarifying a relation between
tokamak and stellarator/heliotron studies [7] is aquasi-steady-state charge neutrality. Here is an
essential reason of a strange history in which thebeam driven momentum cannot be theoretically
discussed (at least for tokamaks) even in someneoclassical ( Bi!B " 0 ) derivations of the beam
driven current. When the external particle,momentum, and energy source term Sf (x,v) in theLandau equation of fast ions are included," Bi!i!a = mf Bi # vSf (x,v)d 3v $ 0 ,aand thus a phenomenological damping term for theplasma rotation is required in tokamaks for
explaining the experimentally observed steady-statecharge neutrality [6].
# ea ! bna i"s = 0aHere, it also should be noted that the anomalousradial particle flux caused by electrostatic and/or
electromagnetic turbulences, which is intrinsicallyambipolar [8], cannot solve this confliction on thecharge neutrality. This is one of backgrounds ofrecent discussions on the momentum transport invarious tokamak experiments [9]. Not only to solve
this ambipolar paradox, the related “momentumtransport” theories should explain also thepreviously observed beam driven currents.
However, systematic theories are still underconstructions.
In contrast to it, the flows in non-symmetricstellarator and heliotron configurations, where theparallel viscosity and the non-ambipolar particle
diffusion are not directly connected to each other,can be consistently determined by the neoclassicalprocedure without any phenomenological damping
terms. In other words, the injected momentum in
non-symmetric plasmas is effectively consumed forsustaining the ambipolar potential and accompanied
Er-driven flows while that in symmetric plasmas
should be removed by the radial transport. In thepresent study, the thermalized particles’ kinetic andmoment equations for general multi-ion-species
plasmas [10] are extended to include the fast ion
friction term, which is obtained by combining theeigenfunction method in Ref.[11] and the adjoint
equation method in Ref.[12]. Then the radial
particle and heat diffusions are derived by using the[Na , La] matrices defined in Ref.[1].

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