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

While for the ITER wall the mode coupling is negligibly small,
the complex structure of the additional AUG wall segment leads
to a significant coupling of the n=1 and n=2 toroidal harmonics.
Furthermore, the feedback optimization code OPTIM has
been supplemented with a robust control package. Eigenvalue
sensitivity is now taken into account by the concept of
pseudospectra. The computed feedback controllers are optimally
robust with respect to, e.g., model imperfections, and
transient amplifications of initial perturbations are kept at a
moderate level.
Preliminary investigations indicate that both robustness and
transient growth could be a severe issue when attempting to
stabilize RWMs in ITER.
Kinetic MHD and Fast Particle Physics
A comprehensive and self-consistent kinetic investigation of
global fast particle driven modes in tokamak plasmas below
the toroidal Alfvén Eigenmode (TAE) frequency requires
the inclusion of the bulk ion compressibility. This extension
enables the linear gyro-kinetic eigenvalue code LIGKA to
analyse the low-frequency properties of the Alfvén cascade
modes (AC), the beta-induced Alfvén eigenmodes (BAE)
and the energetic particle modes (EPM). Furthermore, also
the linear phase of micro-instabilities like ion-temperaturegradient
modes, trapped-particle modes or micro-tearing
modes can now be described with LIGKA. Thus, it closes
the gap between global low-n MHD descriptions and high-n
micro-scale turbulence codes (in their linear phase). As an
application, the kinetic damping mechanisms of the resistive
wall modes have been investigated. It was found that not
only the sound wave damping near the rational surfaces contributes
but also the coupling to the electrostatic drift branch
modifies the mode structure and therefore modifies the
damping rate.
Linear MHD Stability Analysis
Within the Integrated Tokamak Modelling effort (IMP#1), a
matching suite for optimized linear MHD stability analysis
has been created by improving and adapting the converter
tool RWSHOT for experimental shotfiles, the fixed boundary
equilibrium code HELENA, and the linear MHD stability
code ILSA.
It is now possible to calculate the linear MHD spectrum of
edge modes vs. their toroidal mode number starting from
free boundary equilibria generated by the equilibrium codes
CLISTE and EFIT, thereby facilitating comparison of most
major tokamak devices in the fusion community. In the light
of this new possibility, benchmarking studies of edge stability
have been carried out at DIII-D and ASDEX Upgrade,
highlighting the influence of near-X-point geometry on the
stability of the peeling-ballooning mode. While there is
good agreement on the stability of the ballooning term,
results with respect to the pure peeling and kink terms
Theoretical Plasma Physics
82
remain inconclusive due to numerics limitations in the
vicinity of the X-point. Further, potentially analytical, effort
is needed to elucidate on the relevance of the peeling mode
in strongly sheared geometries.
Non-linear MHD Studies
The locking of neoclassical tearing modes (NTMs) by error
fields was studied numerically. In the regime with low mode
frequency and large plasma viscosity, the required field
amplitude for mode locking is found to be proportional to
the plasma viscosity and the mode frequency but inversely
proportional to the square of the magnetic island width and
the Alfvén velocity, indicating that NTMs will be locked to
low amplitude error fields in a fusion reactor. The stabilization
of NTMs by RF current in the presence of a static helical
field was therefore further investigated. The applied helical
field allows controlling the location of the island’s o-point
to be in the RF wave deposition region, to enable the NTM
stabilization by RF current after mode locking. When the
island is large enough to be locked by a small amplitude helical
field in the desired phase, the island is reduced to a
smaller width by RF current compared to the case without
the helical field. This suggests a possible way to enhance the
stabilization of NTMs by RF current.
The error field (or externally applied helical field) penetration
was studied numerically based on the two fluids equations.
It was shown that there is a minimum in the required
field amplitude when the applied helical field frequency is
the same as the mode frequency being determined by both
the background equilibrium plasma rotation and the diamagnetic
drift. The mode penetration threshold significantly
increases as the field frequency deviates from the mode frequency
and can become asymmetric on both sides of the
minimum due to parallel transport. After mode penetration,
the non-linear saturated island width is found to be smaller
for larger electron diamagnetic drift frequencies.
Transport Analysis Group
In the field of core transport, work has been dedicated to
understanding the central behaviour of Si laser ablated impurities
in response to localized central electron heating in
AUG H-mode plasmas with a background of NBI heating.
The Si impurity central profile flattens in response to central
electron heating up to exhibiting a hollow profile which cannot
be explained by neoclassical theory. The gyrokinetic
code GS2 has been used to calculate the turbulent transport
of the Si impurity under these experimental conditions.
It has been found that in the presence of strong central electron
heating, modes rotating in the electron diamagnetic drift
direction are destabilized in the central region of the plasma,
generated by the non-adiabatic response of passing electrons
and featuring extremely elongated eigenfunctions along
the field lines. The related fluctuations in the electrostatic