24P037-P
Development of coupled IMPGYRO-SOLPS codes
for analyzing tokamak plasmas with tungsten impurities
タングステン不純物を含むトカマクプラズマを解析するための結合コードIMPGYRO-SOLPSの開発
Mitsunori Tomaa, Xavier Bonninb, Kazuo Hoshinoc,
Akiyoshi Hatayamaa, Ralf Schneiderd and David Costerea
藤間光徳 , Xavier Bonninb, 星野一生c, 畑山明聖a, Ralf Schneiderd, David Costerea

Keio University, 223-8522 Yokohama, Japan
Université Paris XIII, F-93430 Villetaneuse, Francec
Japan Atomic Energy Agency, Aomori 039-3212, JapandMax-Planck-Institut für Plasmaphysik, D-17491 Greifswald, GermanyeMax-Planck-Institut für Plasmaphysik, D-85748 Garching, Germanyb

For the purpose of a consistent treatment of tungsten impurity together with background plasma, couplingof the IMPGYRO and SOLPS codes has been undertaken. The fluid part of SOLPS transfers thebackground plasma data to the IMPGYRO kinetic code, while IMPGYRO transfers the effect of tungsten
impurities to SOLPS. An initial test calculation has been performed under a simple model for the impurity
generation. The initial impurity generation results in a relatively large radiation loss and plasma cooling.
The resultant suppression of further impurity generation leads to the quasi-steady state in the coupledcalculation.

1. Introduction
A numerical simulation code IMPGYRO is
being developed for kinetic treatment of high-Z
impurities, such as tungsten. The main features ofIMPGYRO are as follows: 1) The code solves
exactly the equation of motion for each impurity
particle for a given magnetic field configuration
and background plasma without any guiding
center approximation, 2) Coulomb collisions withbackground deuterons are included by the binary
collision method, 3) Multi-step ionization andrecombination processes are simulated, and 4)
IMPGYRO has been coupled to the EDDY
(Erosion and Deposition based on the DYnamicmethod) code [1] to evaluate sputtering andreflection processes of tungsten.
The calculations assume a trace impurity limit
and the code calculates the impurity density for a
fixed background plasma. In order to make more
self-consistent calculations, it is necessary tocouple IMPGYRO to a background plasma code.
For this purpose, the coupling activity ofIMPGYRO to the edge plasma code package
SOLPS [2] was started and IMPGYRO has been
extended to calculate the particle, momentum andenergy sources/sinks due to the interaction
between the background plasma and tungsten
impurities as a first step [3]. These parameters aretransferred from IMPGYRO to SOLPS in thecoupling
procedure.
Basedonthese

improvements, initial results of the coupling of
SOLPS and IMPGYRO are presented anddiscussed in this study.
2. Coupling Scheme
SOLPS calculates the following physicalquantities: 1) background ion and electron densities
ni and ne , 2) flow velocities parallel to themagnetic lines of force u , 3) electron temperature
Te , and 4) ion temperature Ti . These quantities aretransferred to IMPGYRO. Using these quantities,
IMPGYRO calculates the following source and sinkterms in a trace-particle approximation frompropagating the tungsten test particles: 1) theparticle source S P , 2) the parallel momentum
source S M  and 3) the energy source S E for thebackground plasma calculation.
As the species followed by IMPGYRO also carrycharge, some of the plasma ionic charge is "hidden"
from the B2.5 (the plasma fluid part of the SOLPSpackage) calculation. This means the electron
density within B2.5 can no longer be considered as
the sum of its ion densities times their charge. Itwas necessary to recast the formulae where theequality between the electron and total B2.5 ionicdensities was implicitly used. In addition to thesources described above, additional informationfrom IMPGYRO must be passed to B2.5, namely
the W ion densities, fluxes and average energies.
With these data, it is possible to recover a fully

4
fixed caseElectron temperature [eV]NT [1016]

330

coupled case

210t = 16ms
100048t [ms]1216t=02000.1

0.20.3Distance from the separatrix [m]Fig. 1 Time evolution of the total numberof tungsten particles in the system

Fig. 2 Electron temperature profiles
along the outer divertor plateself-consistent plasma description and system ofequations. It is the results obtained with thisself-consistent treatment that we will present in thenext section.

Then, the incident energy of the tungsten ionsbecomes smaller. The re-emission yield tends tobecome smaller with decreased incident energy.
This makes the re-emission yield smaller, whichleads to the difference of N T between the twocases.

3. Test calculation and results
The initial test calculation of the SOLPSIMPGYRO coupling code has been made with theASDEX Upgrade geometry. Prior to the coupling
calculation, the initial background plasma has beenobtained by SOLPS under the following conditions:1) Only deuterium is taken into account asbackground ion species in this SOLPS calculation,2) the deuterium ion density at the core-interface
boundary is set to be 2.0 × 1019 m −3 , and 3) input
power of Qe = Qi = 1.0MW has been assumed.
After reaching the steady-state solution of theSOLPS stand-alone run without tungsten impurities,
the coupling run has been started.
A tungsten point source is assumed at the outer
mid-plane. As was discussed in [4], the ICRH
antennae located at the outer mid-plane have been
identified as a possible source of tungsten impurity
generation. For simplicity, the test tungsten neutrals
are constantly fed with a generation rate
1.0 ×1019 m/s with the initial velocity v = 0 .
Figure 1 shows the time evolution of the total
number N T of tungsten particles in the system.
The result of the coupled calculation is comparedwith that of the fixed background calculation. Asshown in Fig. 1, both cases reach quasi-steady state
but the total number N T for the fixed casebecomes 1.2 times larger than the one for thecoupled case.
In order to understand the suppression of N T ,the electron temperature profiles just in front of theouter divertor plates are shown in Fig. 2. Electrontemperature decreases mainly due to the radiationof tungsten impurities in the coupled case. The
sheath-potential drop and the sheath acceleration of
the tungsten ions towards the wall also decrease.

4. Summary
Coupling the Monte-Carlo impurity code
IMPGYRO and the edge plasma code package
SOLPS has been undertaken to achieve a moreconsistent treatment of tungsten as an impurity
together with a background plasma. A test
calculation has been performed under simple
assumptions for the impurity generation to checkthe coupled code. The background electron
temperature decreases in the coupled calculation incomparison with the fixed background case due tothe electron radiation loss by tungsten impurities.
The resultant suppression of further impurity
generation leads to the quasi-steady state in thecoupled calculation. These initial test calculations
give us confidence that a self-consistent IMPGYROand SOLPS coupling has now been achieved.
Further code validation will be pursued applying
more realistic conditions and making comparisonswith experiments.
Acknowledgments
This study is partially supported by a Grant-inAid for Scientific Research of the Japan Society for
the Promotion of Science.
References[1] K. Ohya: Physica Scr. T124 (2006) 70.
[2] R. Schneider et al.: Contrib. Plasma Phys. 46 (2006)
3.
[3] M. Toma et al.: Contrib. Plasma Phys. 50 (2010)
392.
[4] R. Dux et al.: J. Nucl. Mater. 363-365 (2007) 112.