Summary 2

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Summary 2

• Caldas Weyssow Wingen NeuerLoozen Gerhauser Reise
  r KikuchiHeyn Pankratov Nicolai Rondan
• Pankratov

• Mapping of magnetic field lines
• Particle and heat transport coefficients
• Numerical modelling (simulations)

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I. Mapping of magnetic field lines

• The Mapping technique for magnetic field
  lines is in a extremely healthy shape
• Predictive mappings based on current
  distributions are available with high accuracy
  for quantitativ studies
• Maps for qualitative studies Standard map
• Wobig map Separatrix map
• Tokamap
• Revtokamap
• Symmetric simple map
• Low mn map
• Dipole map
• DED map

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TEXTOR DED mapS. Abdullaev et al.
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Tokamap Balescu et al
Flux coordinate r2 r minor radius of the torus
surfacesq saftety factor 1/w
Poloidal angle
Polar representation with Shafranov shift
Incomplete chaos
Break up of KAM surface? Escape rates?
Internal Cantori?
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Revtokamapnon-twist map, reverse shear
Magnetic internal transport barrier
Robust invariant circles (ITB) separating two
invariant chaotic zones
Weyssow
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Chandre
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Transport in incomplete chaos (Caldas,Wingen)
Stable manifold
Ustable manifold
Periodic hyperbolic fixed points
Strange transport diffusive, subdiffusive,
superdiffusive
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Open systems
X-point and unstablemanifolds
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II. Particle and heat transport coefficients
Test particle transport (stochastic transport
theory) Self-consistent (approximate) transport
coefficients
Simple and old results

• Magnetic Diffusion coefficient

Quasilinear
Kadomtsev-Pogutse

• Particle Diffusion magnetic diffusion times
  thermal velocity (without collisions)

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Running diffusion coefficient for Klt1
(JokipiiParker) oder
oder
KadomtsevPogutse
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Percolation limit Kgt1
MSD
time
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Finite gyro-radius effects
decreasingguiding field
guiding center resultin different K regions
Vlad et al, 2005
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Mixing length theory (MLT)
Semi-analytical mode foredge drift
turbulenceplus effective transportin a
stochastic layer
Anomalous transport due to unstable drift
modes and stochastic magnetic fields within an
improved MLT(self-consistent)

• Loozen, Tokar

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In agreement with measurements on Tore Supra,
calculations show reduction of transport in the
region with moderate stochastization (?_ch lt
1.6) The model developed (i) is used to
estimate characteristics of fluctuations and
transport coefficients for measured plasma
parameters (ii) is included in 1-D
transport code RITM for self-consistent
calculations of profiles
Loozen and Tokar
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2D Multifluid Code TECXY of TEXTOR Discharges
in the Presence of DED

• Tokars model
• Essential parameters are DFL (field line
  diffusivity) and LK (Kolmogorov length)
• The radial transport coefficients due to
  anomalous transport have been modified to account
  for the contribution from stochastic transport

• Additional impurity diffusion from stochastisity
  is very small
• Friction with the background plasma flow leads to
  significant increase
• of radial impurity convection

Gerhauser
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III. Modellings - transport codes with
effective coefficients - turbulence codes
in stochastic field geometry - MHD
simulation for penetration of the DED-field and
Understandings of the large magentic
island and the rotation braking
excited by the DED on TEXTOR
In recent years, progress in experiment, theory
and computation has been dramatic, yet the Holy
Grail of predictive capacity by other than
brute-force,case-by case direct numerical
simulation, remains elusive.P.H. Diamond et al
2004
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• 2D-code TECXY (Stochasticity in the DED region
  was described by a model for optimal paths and
  increased locally radial transport Tokar)In
  order to maximize the field penetration, the
  plasma column has to be shifted horizontally
  towards the HFS plasma shift is
  of major importance
• Shift of plasma from ALT-II to DED has stronger
  effect on discharge than switching on stochastic
  transport
• With DED slightly in the shadow of ALT-II and at
  sufficiently high densities a favourable
  high-recycling regime develops with good
  screening of impurities

Gerhauser
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3D Turbulence model including drift waves, shear
Alfvénwaves, sound waves, ballooning modes,
couplings
sources
Reiser
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Scott
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Parameter


Relevance for ELMs should be further discussed
Reiser
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Finken et al
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Reduced MHD model (Strauss equations)
Kikuchi
agreement withexperiment
Compare with Fitzpatrick model
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Pankratov On the basis of the two-fluid MHD
equations the influence of the plasma response
on the penetration of the DED helical
perturbations is considered
toroidal model I.M. Pankratov, A.Ya. Omelchenko,
V.V. Olshansky. Problems of Atomic Science and
Technology, Series Plasma Physics(10), No. 1,
2005, p. 18-20.
Plasma vortices with opposite direction of
rotation are found per one poloidal period of
the external perturbation. The cases with two
vortexes and the formation of four vortices per
one poloidal period are considered
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Heyn Conductivity tensor for penetration of a
rotating magnetic field
Hamiltonian kinetic approach
Nicolai Modelling of Edge Plasma RotationFluid
description for analytical estimates of plasma
braking and accelerationRondan Plasma
rotation effect on LF field penetretionCollisiona
l, cold, cylindrical plasma modelThe plasma
rotation can change significantively the
excitation of electromagnetic fields, power
deposition, impedance and ponderomotive forces.
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No Summary of Summary!

• Outlook
• Fast algorithms for magnetic field line mapping
  
• Magnetic field stochasticity and ELMs (I)
  (models!)
• Qualitative maps do have their justification
  (transport barriers,etc)
• Control of stochastic fields (potential?)
• Stochastic transport coefficiencts
  (analytical/semi-analytical)
• Transport modellings in incomplete chaos -
  precise questions (type-III ELMs, rotation,
  ) - converging results of different codes