Verlag des Forschungszentrums Jülich
JUEL-4173
Harting, Derek; Reiter, Detlev
3D Monte-Carlo-Simulation der ergodisierten Randschicht von TEXTOR-DED
139 S., 2005
In controlled nuclear fusion research, the science of edge plasma physics is
of key importance in many ways: ideally, the edge plasma should transport
the helium ash outward (towards the pump) and prevent that the surface
released impurities penetrate the core plasma, while the hydrogen ions and
the energy are confined in the core plasma. To provide active control over
the edge plasma region, a novel Dynamic Ergodic Divertor (DED) [6] was
installed at the tokamak TEXTOR of Forschungszentrum Jülich. According
to its conceptual design, the DED should spread the power load to the
divertor plates over a larger area, and hence reduce erosion and sputtering of
the first wall materials. At the same time, the particle removal of the toroidal
pump limiter ALT-II should be maintained, or it might even be improved due
to forced flows. All these tasks are currently under experimental observation.
Furthermore, there are indications from earlier experiments and theory that
the DED might modify the radial transport in the ergodized magnetic field
of the edge plasma layer in such a way that the edge plasma can even shield
the core plasma from the remaining eroded impurities.
In doing so, the option of actively cooling the edge plasma by a radiation
layer, in which recombination processes of deliberately introduced impurities
(mostly nobel gases) emit a lot of photons and with them energy, may
become more efficient.
To achieve an ergodisation of the magnetic field structure in the edge
plasma, a set of perturbation coils has been installed at the high field side
of the vacuum vessel. These perturbation coils are arranged in such a way,
that they run parallel with the magnetic field lines of the resonant q = 3
surface. The electrical circuit of the DED-coils can be changed, so that the
perturbation field is resonant with the 12/4-mode, the 6/2-mode or the
3/1-mode. For this purpose, the perturbation coils can be supplied with a
four phase current with up to 15 kA. The perturbation current may be DC
(constant perturbation field) or AC to achieve a rotation of the perturbation
field. The frequency of the perturbation current may either be set to 50 Hz
or tuned in the frequency band between 1 kHz and 10 kHz.
To achieve understanding about the behavior of edge plasmas with an ergodized
layer, it is mandatory to accompany the experiment with numerical
simulations of the ergodic edge plasma. Only this allows to quantify known
edge plasma physics effects with sufficient detail in order to identify possibly
new synergistic effects. For conventional toroidal symmetric magnetic field
configurations of the edge plasma, there exists quite a number of 2D numerical
edge plasma codes. Prior to the installation of the DED, the edge plasma
of TEXTOR was simulated with some of them (e.g., with the B2-EIRENE
code). But in case of the activated DED perturbation field, the toroidal
symmetry is broken. Moreover, any common symmetry between the plasma
flow to the targets and the backflow of neutral gas from the targets is lost,
independent of the co-ordinate system chosen. One is forced to carry out
the much more computing time intensive fully 3D plasma edge simulations.
The same problem occurs in simulating stellarator edge plasmas.
In the last few years, some edge plasma codes for these stellarator plasmas
have been developed, but the extensions towards more complete physics
and numerical optimization of these codes is still a task of active research.
The most advanced models presently are the EMC3-EIRENE-Code
[2, 3, 4, 5], the E3D-Code [17, 16] and the BoRiS-Code [18]. Only the first
two codes can handle ergodic magnetic field configurations because of their
Monte Carlo fluid simulation techniques. The model used and presented in
this report is the EMC3-EIRENE code. The EMC3 code was developed for
the stellarators W7-AS and W7-X by Dr. Yühe Feng from the Max-Planck-
Institute for plasma physics in Greifswald (Germany). The EIRENE code
[14] was developed at the institute for plasma physics of Forschungszentrum
Jülich (Germany). The version of EIRENE used in this case was optimized
for 3D calculations by a strong parallelization, so that it efficiently performs
on supercomputers with parallel platforms. In 2002, Dr. Masahiro Kobayashi
(now: NIFS, Toki, Japan) carried out some slight modifications in the
EMC3 code to implement the recycling of particles and energy for the particular
DED divertor plate configurations. As a result of this, the EMC3 code
is now able to simulate the ergodic edge plasma layer of TEXTOR-DED.
In chapter 2 of this present report, the theoretical basics of the EMC3 model
will be developed. For this purpose, initially the full plasma fluid equations
by Braginskii will be re-derived in general terms. These are the basis
of the EMC3 model. Following, the particular set of (reduced) EMC3 model
equations will be derived from these Braginskii fluid equations, and the
approximations made in doing so will be discussed. Finally, the numerical
method (the Monte Carlo synthesis of 3D plasma flows), which solves the
EMC3 equations will be described.
In chapter 3, the modelling of the particular TEXTOR-DED configuration
with the EMC3 code will be described. At first the magnetic field
configuration of TEXTOR-DED is discussed. This will be done by means
of Poincaré plots, connection length plots and so called “Laminar plots“.
Furthermore, it will be detailed how the magnetic field is discretised for the
numerical grid generation and which numerical constraints have to be considered.
Finally, the coupling to achieve consistency between the EMC3 (plas-
ma flow) and EIRENE (neutral particle recycling) will be discussed and a
typical simulation sequence will be described.
Chapter 4 represents the central section. By means of model parameter
studies, the influence of various free model parameters on the simulation
results will be examined. At first, the influence of the boundary condition
on the outermost boundary will be studied. There is neither experimental
evidence nor theoretical information on how this boundary condition should
be set. Therefore, it is shown here how this influence can be minimized.
Furthermore, the streaming behavior of the plasma parallel to the magnetic
field lines as well as the influence of the perturbation field of the DED
on the simulation results will be examined. In addition, the total recycling
flux at the DED plates as well as the anomalous transport coefficients, which
also have to be regarded as free model parameters, will be varied over some
simulations.
Finally, the influence of the perturbation field on the effective radial heat
transport will be studied by averaging the 3D profile information over the
poloidal coordinate in chapter 5. This allows to assess the applicability of
idealized theoretical predictions of cross field transport in ergodized fields
under the more realistic configuration of the DED edge plasma with full
account of geometrical details and recycling.
Summarizing: it has been shown that conventional 2D edge plasma transport
models, which are used routinely since more than 20 years for axially
symmetric limiter or divertor edge plasmas, have been extended successfully
now to a complex 3D magnetic field topology. This is largely due to
progress in computing power. Consequently, it has now become possible to
employ this detailed numerical bookkeeping tool in future applications on
TEXTOR-DED scenarios. By comparison with experimental results, it is
now possible to distinguish by numerical calculations, between possible new
phenomenons in ergodic edge plasmas on the one hand, and merely complex
geometrical effects on the other hand. The future task of edge plasma
science with the DED will be to constrain the numerical model as much
as possible by experimental data, and then to identify and document those
mismatches between calculation and experiment which survive despite the
still large number of free model parameters.
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