24P036-P
One-dimensional dynamical analysis of detached divertor plasmas
非接触ダイバータプラズマの1次元動的解析	 
aMakoto Nakamura, bSatoshi Togo, cKatsuhiro Shimizu, cTomonori Takizuka,bYuichi Ogawa, and aKazuo Hoshinoa中村 誠, b東郷 訓, c清水勝宏, c滝塚知典, b小川雄一, a星野一生

abJapan Atomic Energy Agency, 2-166 Oaza-Obuchi-Aza-Omotedate, Rokkasho, Kamikita, Aomori 039-3212
Department of Advanced Energy, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwanoha 5-1-5,Kashiwa, Chiba 277-8561
cJapan Atomic Energy Agency, 801-1 Mukoyama, Naka, Ibaraki 311-0193
a
日本原子力研究開発機構 〒039-3212	  青森県上北郡六ヶ所村大字尾駮字表舘2-166b
東京大学大学院新領域創成科学研究科 〒277- 8561 千葉県柏市柏の葉5 -1- 5c
日本原子力研究開発機構 〒311-0193	  茨城県那珂市向山801-1
Plasma operation with detached divertors is considered to be a promising way to resolve this issue of
divertor heat load reduction. However, transient characteristics of the detached divertor plasma have notbeen studied yet. The edge localized mode can cause temporally changing cross-field heat and particle
inputs from the core to the scrape-off-layer. Even in such a situation the plasma should be kept detachedand re-attachment onto the divertor should be avoided. In this presentation we report extensions of ourrecent one-dimensional analysis of detached divertor plasmas. We investigate response of the detachment
fronts propagating upstream to the temporally changing heat and particle inputs.

1. Introduction
Reduction of divertor heat load is a crucial
issue for next generation fusion devices such as
ITER and DEMO. Plasma operation withdetached divertors is considered to be a promising
way to resolve this issue. For example, a partiallydetached divertor regime will be one of the ITER
operation senarios [1] and has been used for thedesign of the DEMO reactor Slim-CS [2].
However, the plasma operation with divertor
detachment involves an issue that should beresolved; detachment fronts of plasma parameters,e.g. density, temperature and particle and heat
fluxes, should be ”captured” in a divertor region.
Otherwise, cold neutrals and impurities would betransported upstream and cool a core plasma
region. It is, therefore, crucial for divertor heat
handling to elucidate characteristics of thedetachment fronts.
Stability and propagation of the detachment
fronts have been studied by some researchers sofar. For example, Krasheninnikov et al. havefound that the detachment front is thermallydestabilized when Q H < Q rec where Q H is the total
power input which can reach a recombination
region of a divertor plasma and Q rec is the powersink due to recombination [3]. A similar power
balance condition was found independently by
one-dimensional (1D) plasma fluid simulations
by Nakazawa et al [4]. They also analyzed
time-dependent behavior of the detachment fronts.

They successfully simulated propagation of thefronts of the plasma density and temperature
toward upstream. In these studies, the cross-fieldparticle and heat inputs from the core to thescrape-off layer (SOL) region were assumed to bespatially uniform and temporally constant.
Recently, Havlickova et al. studied some transient
behaviors of a SOL-divertor plasma when thecross-field inputs are changed temporally [5]. It isdue to the edge localized mode (ELM) that suchtransient behaviors can occur. However, transientcharacteristics of the detached divertor plasma
have not been clarified yet. In order to keep theheat load onto divertor plates small, the plasma
should remain detached and re-attachment of theplasma should be avoided even if the cross-field
inputs are temporally changed. Therefore, it isimportant to study the transient characteristics ofthe detached divertor plasma.
In this presentation we report extensions of ourrecent 1D analysis of detached divertor plasmas[6]. In our previous work we analyzed
propagation of the detachment fronts toward
upstream and showed that the cross-field particle
and heat transport can affect the front propagation.
As a next step, we discuss transient response of
the detachment fronts to the cross-field inputs
that are temporally changing.
2. ModelBehaviors of the detached divertor plasma isdescribed by the 1D transport equations [4-6]:!n ! ( nv )(1)+=S!t!x2! ( mnv) ! ( mnv + P )(2)+=M!t!x!"12%$ 3nT + mnv '&!t #2(3),%! )"1!T+ *$ 5nT + mnv 2 ' v ( ! ||e - = Q&!x +#2!x .
Here, P (=2nT) is the plasma pressure, κ||e is theparallel electron heat conductivity, and the viscosityand heat conductivity of ions are neglected. Here, n,v and T are the plasma density, velocity andtemperature, respectively. In the transport equations
above, it is assumed that n = ne = ni, v = ve = vi and
T = Te = Ti, where the subscripts e and i represent
electrons and ions, respectively. The arc length x isalong the magnetic field lines from the stagnation
point (x = 0) to the divertor target (x = L).
The source/loss terms in the particle, momentum
and energy equations are represented by S, M and Q,respectively. The terms S and Q involve thecross-field particle and energy inputs S SOL andQ SOL, respectively. The terms S and Q also involve
several kinds of atomic processes, such asionizations, charge exchanges and recombinations.
For more detailed see [4-6].
For the spatial profile of the neutral particle flux
Γn, we use the following simple exponential-likedecay form:⊥⊥$ #s '! n = ! n,d exp && ")) ,% !n,ion (!n,ion =vn.
n " v ion(4)Here, it is assumed that the neutral particle flux
decays only due to ionization, and vn corresponds tothe Franck-Condon energy, <σv>ion is the rate
parameter of the ionizations. Effects of cross-field

Fig. 1 Propagation of the detachment fronts of theplasma temperature (a) and density (b). The directionof the front propagation is represented by an arrow ineach panel. The X-point is located at x = 80 m.

transport of the neutrals on divertor plasmas will be
discussed in [7].
3. Simulation result and further works
An example of propagation of the detachment
fronts of the plasma temperature and density
obtained by the 1D transport simulation is shown inFig. 1 [6]. Here the ITER-like plasma condition wasassumed. The connection length L is 100 m. The
power and particle inputs from the core to the SOL
are 80 MW and 1.5×1023 1/s, respectively. The
surface area ASOL is ~640 m2 and the SOL width
λSOL is 4.7 cm; therefore, the cross-field energy andparticle source terms in the SOL region, Q SOL andS SOL, are estimated to be 2.67 MW/m3 and 5.0×1021
1/m3s, respectively. As for computational methods,
the semi-implicit numerical scheme is employed toperform the simulations. The diffusion terms arediscretized by the conventional central implicit
scheme; the convection terms are discretized by the
first order explicit flux vector splitting method
developed by Steger and Warming [8].
As shown in Fig. 1, the detachment fronts
propagating beyond the X-point are well simulated,which is an unfavorable situation since the neutral
particles are transported upstream together with thefront propagation. Similar simulation results werereported in [4].
In the presentation we will discuss effects of atemporary changes in S SOL and Q SOL, to thedetached divertor plasma. Particularly, we simulate
response of the detachment fronts propagating
upstream to the pulsed-like change in S SOL andQ SOL like ELM. We evaluate to what extent of thechange in S SOL and Q SOL the detached plasma is
re-attached onto the divertor.
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⊥⊥References[1] ITER Physics Expert Group on Divertor: Nucl.
Fusion 39 (1999) 2391; L. Loarte, et al.: Nucl.
Fusion 47 (2007) S203.
[2] K. Tobita, et al.: Nucl. Fusion 49 (2009) 075029; H.
Kawashima, et al.: Nucl. Fusion 49 (2009) 065007.
[3] S.I. Krasheninnikov, et al.: J. Nucl. Mater. 266-269(1999) 251.
[4] S. Nakazawa, et al.: Plasma Phys. Control. Fusion 42(2000) 401.
[5] E. Havlickova, et al.: Plasma Phys. Control. Fusion
53 (2011) 065004.
[6] M. Nakamura, et al.: J. Nucl. Mater. 415 (2011)
S553; M. Nakamura, et al.: Plasma Fusion Res. 6(2011) 2402047.
[7] S. Togo, et al.: presented at this conference (2011).
[8] J.L. Steger and R.F. Warming: J. Comput. Phys. 40(1983) 263.