S3-2“Physics of SOL/divertor plasmas in magnetic fusion”
磁気閉じ込め核融合に於けるプラズマ-壁境界層現象の物理
A. Hatayama1, Y. Homma1,2, S. Yamoto1, H. Inoue1, K. Takahara1, T.Shibata1,2
畑山明聖1、本間裕貴1,2、矢本昌平1、井上春如1、高原啓輔1、柴田崇統1,2
Graduate School of Science and Technology, Keio University
1
慶應義塾大学大学院理工学研究科
Research Fellowships for Young Scientists, Japan Society for the Promotion of Science2
日本学術振興会特別研究員
Present understanding and open problems of SOL(Scrape Off Layer)/divertor plasmas arereviewed and discussed. A main focus is placed on collisional transport of impurity ions,especially high-Z impurities like tungsten, in SOL/Divertor plasmas. In addition, static anddynamic characteristics of “detachment plasma” will be discussed in the presentation.
1. Introduction
Being based on steady and continuous progress in coreplasma performance for magnetic fusion devices,
International Thermonuclear Experimental Reactor(ITER) project is now underway and its construction has
been started. For ITER and future fusion demonstration
reactors, the following research and development items
become more significant than before: 1) tocontrol/suppress heat and particle flux from the hightemperature and high density fusion core plasma to thewall, and 2) to control/suppress impurity flux from thewall to the core plasma. Therefore, understanding of heatand particle transport phenomena in SOL(Scrape-OffLayer) and divertor plasmas, which are located between
fusion core plasma and the solid wall (see Fig.1), isindispensable.
A typical example of self-controlling characteristics
in fusion plasmas is “recycling” process in SOL/divertor
region (see Fig.1). Plasma heat load can be reduced by
the interaction between plasma and neutrals. Moreover,so-called full plasma detachment state from the wall is
automatically formed under relatively low input power
condition. Plasma ion and electron become a neutral
particle before reaching the wall due to ion-electron
recombination process in the plasma volume.
Another example of self-regulating characteristics offusion plasma is impurity generation and theirpenetration into fusion core plasma. Of course, impurity
concentration in the core plasma has to be kept as low as
possible for the normal operation to prevent core plasma
from radiation cooling by impurities. In case of transient
over power, however, increase in fusion power
generation possibly enhance heat and particle loads tothe wall, which in turn possibly enhance the productionof impurities and its transport towards the core.
Therefore, understanding of the impurity transport in
SOL/divertor region is very important.

Fig.1 Basic processes in a SOL/divertor plasma.
Coulomb collisions, NC theory provides the linear
relation between the macroscopic particle, momentum
and heat fluxes and the thermodynamic forces (gradientsof density, velocity, temperature). In a simple tokamakconfiguration with a large aspect ratio (A=R/r>>1) andconcentric circular magnetic flux surfaces (Fig.2),
NC-theory gives a simple expression for the impurity
particle flux averaged over a magnetic surface;dnimp< Γ ⋅ er >  Γ IWP + ΓTSE − DNC.
(1)
dr
The last term in Eq. (1) denotes the self-diffusion flux
proportional to the impurity density gradient dnimp / dr ,while Γ IWP and ΓTSE are driven by the thermodynamic forces of the background fuel ions.

2. Impurity collisional transport in closed torusmagnetic configurations : Neo-classical Theory
Before proceeding to the impurity transport in
SOL/divertor region, a very simple review is given ofimpurity collisional transport theory in the closed
magnetic configuration, i.e., core plasma. It is wellknown as “Neo-Classical (NC)” theory[1]. Starting from
Boltzmann eq. with Fokker-Planck collision operator forFig.2

A simple tokamak magnetic configuration

(a) open geometry(b) closed geometry
with a top limiter(c) closed geometry
with a bottom limiter(d) closed geometry
with a inner limiter

Fig.3 Spatial distribution of test impurity ions in the model tokamak geometry (Fig.2). The results are obtained bykinetic modeling [2,3] based on Monte-Carlo Binary Collision Method (MC-BCM) for a given background density
and temperature gradient (dnb/dr=0, dTb/dr=300 eV/m). In order to simulate the open magnetic configurations, thesolid wall structure, which corresponds to so-called limiter or divertor plate, is installed for cases (b)-(d). Test ionshave been launched at the same location for all the cases (x). Other detailed input parameters are in Ref. [3, 5]

The flux Γ IWP and ΓTSE in Eq.(1) are given,
respectively, bydnn dT
Γ IWP ≈ DNC b , ΓTSE ≈ − DNC b b .
(2)
drTb drUsually the background density nb and temperature
Tb are larger in the core central region, i.e., their
gradients are the same sign ( dnb / dr < 0 , dTb / dr < 0 ).
Therefore, in Eq.(2), ”Inward Pinch (IWP)” flux
Γ IWP and “Temperature Screening Effect (TSE)” flux
ΓTSE are in the opposite direction ( Γ IWP < 0 ,ΓTSE > 0 ) as shown in Fig.2. The IWP Γ IWP drives
impurity ions inward to the core center, while the TSE
ΓTSE drives impurity ions outward and impurity ions
are shielded out from the core.
3. Impurity transport in the SOL/Divertor plasma
Our understanding of impurity transport in theSOL/Divertor plasma is still limited. In most ofstudies of collisional impurity transport in theSOL/Divertor plasmas, only the impurity transport
along the magnetic (B) field has been taken into
account so far, and collisional transport across B-fieldhas been neglected. In other words, it has been
believed that only the force balance along B-field, i.e.,
the force balance between “friction force” and the“thermal force” (friction driven by back groundtemperature gradient) is important for collisionaltransport of impurity ions in the open magnetic
configuration with the wall boundary.
Recently, however, it is pointed out that collisionaltransport across B-field driven by backgroundthermodynamic forces by Eq.(2) are not negligible on
the basis of a new kinetic modeling scheme [2, 3] of
impurity transport with Monte Carlo Binary Collisionmodel (MC-BCM[4]), which directly solves
Boltzmann equation. Because of the relatively steep
gradients of nb and Tb in the core periphery, andalso high charge state Z of impurities, it becomes evencomparable with the anomalous transport flux.
A systematic survey of impurity transport acrossB-field is now underway [3, 5, 6] for different
collisionalities, and other parameters. Figure 3 shows
typical examples. For the closed magnetic flux case in
Fig.3(a), our simulation result reproduces the result
predicted by NC theory. Most of impurity ions aretransported outwards due to TSE. The average radial
velocity of test impurity ions becomes positive andalmost agrees with that estimated by Eq. (2).
On the other hand, in the open magnetic field,
impurity transport depends on the location of the wall
structure. It is interesting to note that the locations incase (b) (top) and (d) (inner) are quite different, but
the average radial velocities are almost the same as in
the closed magnetic flux in Fig.3(a). Even in the open
magnetic flux cases [Fig.3 (b) and (d)], TSE effect by
NC theory becomes effective in these cases. On theother hand, the average radial velocity becomesalmost zero and therefore TSE flux almost disappears
in case (c). Physical mechanism which leads to theseresults are discussed in detail in Ref.[3, 5, 6].
Summary and future outlook
Present understanding and some new results ofcollisional impurity transport in the SOL/divertor
plasma have been briefly reviewed and discussed. For
more overall and complete understanding of transportphenomena, further progress in non-equilibrium
thermodynamics and transport theory has been
demanded, especially for the case where the linear
response theory such as Eq.(2) breaks down.
References[1] P. Helander, D.J.Sigmer, “Collisional Transport inMagnetized Plasmas” , Cambridge University Press, (2002),
and references therein.
[2] Y. Homma and A. Hatayama, J. Comp. Phys., 250 (2013)
206.
[3] Y. Homma, et al., in proceedings of 25th IAEA Fusion
Energy Conference, Russia, Oct.14-17 (2014), TH/P7-8.
[4] T. Takizuka and H. Abe, J. Comp. Phys. 25 (1977) 205.
[5] Y. Homma, et al , in these proceedings, 19PB-069.
[6] H. Inoue, et al. , in these proceedings, 21PA-028.