05aA02
モンテカルロ２体衝突モデルを用いた新しい熱力モデルによる核融合プラズマ中のテスト不純物粒子輸送シミュレーション

Impurity test particle transport simulation in fusion plasmas using anew thermal force model based on the Monte Carlo Binary Collisionmodel
本間裕貴, 畑山明聖, 澤田悠, 矢本昌平 1
Yuki HOMMA, Akiyoshi HATAYAMA, Yu SAWADA, Shohei YAMOTO1
慶應義塾大学 1
Keio University1
To realize stable energy production by nuclear fusion plasmas, the impurity particles have to be wellcontrolled. It is desirable that the impurities do not enter the core, but at the same time, do remain in theedge region because they can cool down the peripheral plasma leaking from the core, to reduce the plasmawall interactions at divertor plates. To this end, correct understanding of impurity transport processes infusion plasmas is one of the most important research subjects to develop sustainable fusion devices.
The importance to model the transport processes which are particular in the edge region (SOL + divertorregions) of Tokamak plasma, has been more and more recognized. Our group is developing such impurity
transport modeling in the edge, by checking each process step by step. Here, we present our recent progresses, especially on the modeling of thermal force caused by background plasma temperature gradient
which is perpendicular to magnetic ﬁeld.
It has been considered that the impurity transport process in the edge plasma may be diﬀerent from thetraditional classical / neo-classical transport model. Because the following large diﬀerences between thecore and the edge plasma are not completely taken into account in the actual transport modelings:
1. In the edge, the magnetic ﬁeld is open. The passing particles and a part of trapped particles arelost in the edge, because they soon end up running into the divertor. In addition, relatively stronger
parallel temperature gradient exists before the divertor plates when we consider the high-recycling or
the detached plasma. The consequent parallel thermal force can be greater than the frictional dragforce due to background plasma ﬂow.
2. Steep radial gradient of background plasma density exists in the edge. It may transport impurities
along the direction of the gradient, i.e. from lower to higher density region. This eﬀect can lead to
impurity accumulation in the dense core, but is not appropriately included in the actual impurity
transport simulations. Recently, Y. Sawada has developed a new numerical kinetic model to simulate
such impurity inward diﬀusion in the classical diﬀusion limit. The detail will be reported in thepresentation.
3. Strong radial gradient of background plasma temperature exits in the edge. The thermal force causedby such perpendicular temperature gradient drives the guiding center drift of impurities, called temperature screening eﬀect (TSE)[1]. This drift by thermal force can transport impurities in a direction
opposite to the gradient, i.e. from hotter core to colder edge region across the magnetic ﬁeld. Afterrough estimation, this drift velocity may be non-negligible compared with the anomalous diﬀusion
supposed in the actual impurity simulations. The TSE has to be included in the impurity transport
simulation in the edge.

ZY: Test particleXv∇⊥TScr.

Guiding Center

Average position [m]0.00050-0.0005-0.001

XYX Theo, Braginskii
X Theo, Trubnikov-0.0015-0.0020∇T

200

300

400

Ωa t500

600700<F100

BFig. 2.: A simulation result on the temperaturescreening eﬀect (TSE) is shown. Suﬃciently large
number of test particles started moving from theFig. 1.: Thermal force F∇T
due to perpendicular∧coordinate origin. As in the Fig. 1, the magnetictemperature gradient ∇⊥ T is depicted. Theﬁeld B is in the Z-direction and the perpendicularmagnetic ﬁeld B is in the Z-direction and atemperature gradient ∇⊥ T is along the X-axis.
perpendicular plasma temperature gradient ∇⊥ T is Time evolution of test particle’s ensemble-averaged
along the X-axis. The consequent thermal force
position has been calculated. Its X-, andacting on a test particle is oriented to theY -component are shown, respectively, by ■ and ×.
(∇⊥ T × B)-direction, i.e. along (−Y )-direction.
The vertical axis means the travel distance and theSuch thermal force drives the guiding centre drift
horizontal axis represents the time normalized totoward (F∇T
∧ × B)-direction, i.e. along
the Larmor gyration time of test particle(−∇⊥ T )-direction.
Ω−1 := (q|B|/m)−1 . The simulated results agree
well with their theoretical values: Y T heo. = 0 and
X T heo. has been estimated from the drift velocity ofTSE.

We have developed a new numerical model of thermal force for the test-impurity particle transport
simulation in fusion plasmas. Our model is able to correctly simulate the thermal force caused by not
only the parallel temperature gradient but also the perpendicular gradient, which is very steep in the edge.
Coulomb collision simulation by the Monte-Carlo Binary Collision model[2], and the random sampling of
the background plasma ion velocity from a distorted Maxwellian distribution[3, 4] play the key role in themodel.
In our previous paper[4], we have performed a test simulation for the model validation with limited
patterns of plasma parameters. In this presentation, we will show the results of test simulation on the TSE
eﬀect with wider range of the plasma parameters. We have varied the magnitude of the radial temperature
gradient, the magnetic ﬁeld, and the background plasma density, as well as the impurity ion’s mass andelectric charge. In addition, the limit length of valid simulation time step has been checked to investigate
the numerical eﬃciency of the model.
Then, we would like to discuss the eﬀects of radial density/temperature gradient on the impurity transportand compare them with the anomalous diﬀusion under realistic Tokamak conditions.

参考文献[1] P. Helander, D.J. Sigmar, Collisional Transport in Magnetized Plasmas, Cambridge University
Press, New York (2002).
[2] T. Takizuka, H. Abe, J. Comput. Phys. 25 (1977) 205.
[3] Y. Homma, A. Hatayama, J. Comput. Phys. 231, 3211-3227 (2012).
[4] Y. Homma, A. Hatayama, J. Comput. Phys. 250, 206-223 (2013).