IPP Annual Report 2007 - Max-Planck-Institut für Plasmaphysik ...

Fundamental Theory
The proper form of magnetic non-linearities in gyrofluid
equations which treat electron gyroradius effects was
worked out. These equations can be used for reconnection
studies which involve non-linearly generated current sheets
on the plasma skin depth and electron gyroradius scales.
The complete derivation of the reduced MHD equations
from fully non-linear (“total-f”) gyrokinetic field theory was
worked out. Improved numerical schemes using this as a
splitting method are under investigation.
EU-Task Force on Integrated Modelling
We are participating intensively in the turbulence benchmarking
projects under the auspices of the EU Task Force
on Integrated Tokamak Modelling. B Scott is the Project 4
leader.
Scientific Staff
C. Angioni, A. Bergmann, R. Bilato, A. Bottino, M. Brüdgam,
A. Chankin, D. Coster, A. Dodhy-Würsching, S. Gori,
S. Günter, M. Hölzl, O. Kardaun, H.-J. Klingshirn, C. Konz,
K. Lackner, P. Lauber, P. Martin, P. Merkel, R. Meyer-
Spasche, G. Pautasso, G. Pereverzev, E. Poli, T. Ribeiro,
W. Schneider, E. Schwarz, B. Scott, M. Sempf, M. Siccinio,
H. Siddiqui, E. Strumberger, C. Tichmann, C. Wigger, Q. Yu,
R. Zille.
Guests
C. V. Atanasiu, Institute of Atomic Physics, Bukarest, RO;
N. Bertelli, University of Pavia, IT; O. Maj, University of Pavia,
IT; P. McCarthy, University College, Cork, IR; G. J. Miron,
Institute of Atomic Physics, Bukarest, RO; E. Quigley, University
College, Cork, IR; V. Rozhansky, Technical University,
St. Petersburg, RU; G. Sias, RFX Consorzio, IT;
G. N. Throumoulopoulos, University of Ioannina, GR;
S. Voskoboynikov, Technical University, St. Petersburg, RU;
H. Weitzner, Courant Institute, New York, USA.
Theoretical Plasma Physics
85
Stellarator Theory Division
Head: Prof. Dr. Per Helander
During 2007, Jürgen Nührenberg retired from his post as head
of the Stellarator Theory Division, and the W7-X Applied
Theory Group was incorporated into the Division.
ITG Turbulence Simulations
Ion-temperature-gradient turbulence constitutes a possibly
dominant transport mechanism in optimized stellarators, at
least in some regions, in view of the effective suppression
of neoclassical losses characterizing these devices. The gyrokinetic
code GENE has been extended to work in general
geometry and nonlinear turbulence simulations for W7-X
have been performed, assuming an adiabatic electron response.
Several interesting results have been found, including
the role of zonal flows for turbulence saturation, the
resulting flux-gradient relationship, and the coexistence of
ion-temperature-gradient modes with trapped ion modes in
the saturated state.
Global Gyrokinetic Simulations
The particle-in-cell code EUTERPE which is used for the
global simulation of linear ITG modes in stellarator geometry
has been extended to allow for the inclusion of density gradients.
Since a radial electric field can also be prescribed it
is now possible to run simulations under realistic conditions.
When the electron response is adiabatic the equation for the
electric field consists of a Helmholtz operator plus a nonlocal
term given by the flux surface average of the electrostatic
potential. This term is important to correctly capture
the behaviour of zonal flows which are important for nonlinear
simulations. While the matrix representation of the
Helmholtz operator is sparse that of the averaging operator
leads to a dense matrix. To overcome the related memory
problems a new solver has been developed which treats the
non-local term as matrix-free in the context of preconditioned
iterative solver methods. As an application for this
new solver the Rosenbluth-Hinton test was performed for
tokamak configurations with different aspect ratio and elongation.
It was found that the residual flow level increases
with increasing elongation or decreasing aspect ratio in
good agreement with semi-analytical theory. To perform
global simulations of turbulence, a non-linear version of
EUTERPE has been developed. Scalability has been demonstrated
for up to 512 processors, which is a prerequisite for
non-linear simulations.
Plasma Rotation in Stellarators
The conditions were investigated under which rotation
comparable to the ion thermal speed may occur in threedimensional
equilibria. For tokamaks, it is well known that
the plasma can rotate toroidally but not poloidally if the ion