Transcript No Slide Title

Summary on transport
IAEA Technical Meeting, Trieste
Italy
Presented by A.G. Peeters
Contents
• Toroidal momentum transport (S. Newton,
A.G. Peeters, G. Falchetto [other session])
• Gyro-kinetic calculations (Y.A. Sarazin, V.
Grandgirard, G. Rewoldt, B. Scott)
• The Edge (M. Tokar, N. Kasuya, N. Bisai,
J.J. Ramussen, V.I. Maslov, S. H. Mueller)
• Stabilization of turbulence P.K. Kaw
S. Newton Redistribution of impurities changes
toroidal momentum tranport
    L11
  
 q    L21
  L
   31
L12
L22
L32
L13   d ln pi  dr 


L23   d (ln Ti ) dr 
L33   d ln   dr 
• Restricted to subsonic rotation to calculate neoclassical terms
• Zeff = 1 - recover Braginskii, Hinton & Wong results
Most experimentally relevant limit: conventional
aspect ratio,  q  << 1, strong impurity redistribution
L31 ~ L32 ~  iz
q2  2
 3/ 2
L33 ~ M i2  iz
q2  2
 3/ 2
NEOCLASSICAL COEFFICIENTS
Numerical evaluation using magnetic surfaces of MAST -  = 0.14
Zeff  2
L31
0.015
Zeff  1.5
0.010
0.005
previous
level
0.00024
0.1
0.2
0.3
0.4
ion Mach number
Zeff  1
0.5
- increase with
impurity content
- increase with
Mach number
as impurity
redistribution
increases
• Transport
~ 10 times
previous
predictions
Main Conclusions
• At conventional aspect ratio, with impurities pushed towards
outboard side, angular momentum flux seen to increase by a
factor of  -3/2  now typical of banana regime
• Radial bulk ion pressure and temperature gradients are the
primary driving forces, not rotation shear  strong density and
temperature gradients sustain strongly sheared Er
• Spontaneous toroidal rotation may arise in plasmas with no
external angular momentum source
Anomalous transport
Gyro kinetic simulations
Y.A. Sarazin – 2D interchange turbulence (kinetic
as well as fluid description)
• Transition in kinetic
simulations not well
understood (Same
zonal flows)
• Zonal flows do not
explain the whole
difference between
kinetic and fluid
simulation
(analogous to "Dimits graph" with the same code)
2 fluid moments are not enough
Ortho-normal basis
Lpx 
Slow convergence towards 0
Suggest any fluid description
of the problem
should account for
high order moments Mk (k>2)
Αlternative closure motivated by entropy production rates –
Works well in the linear regime (nonlinear ??)
V. Grandgirard Interplay of density profile and zonal
flow in slab ITG turbulence
• Semi Lagrangian method
(Good energy conserv.)
• Currently 4D slab ITG
• Zonal flows are strongly
connected with the
background density
gradient
• Density gradient both
linearly as well as nonlinearly stabilizing
Extremely nice picture
G. Rewoldt – Progress in the
development of the GTC code
•
•
•
•
•
ETG studies (reviewed by T.S. Hahm?)
General geometry
Parallel velocity nonlinearity
Electromagnetic effects
Neoclassical studies
B.D. Scott, Edge turbulence
The Edge
M. Tokar – Density limits in tokamaks
Alternative Mechanism for MARFE Formation:
instability of plasma recycling on inner wall
Charged particle losses to wall:
n
   D  n  D  D n 2
la
Plasma
Plasma
Flows
B
Neutrals
flows ||B
Heat flux
to the edge
Energy losses with particles:
qconv / rec   T  Ei  
 D n 2 T  Ei 
Model for edge anomalous transport
Linearized parallel Ohm’s, Faraday’s and Ampere’s law, ion momentum balance,
quasi-neutrality, ion continuity equation 
Eigen function equation for electric potential perturbation of Mathieu’s type:
 2~
~0







A

,
k
,

,

,


2
Q

,
k
,

,

,

cos



c
n

c
n
 2
2L
d
2q 2 R me
1
 q R
, c 

, n  n
dr
e
mi  d
R
2
MARFE at HFS: result of recycling
instability at high heating when
Shafranov shift dominates poloidal
asymmetry
Detachment at LFS: develops at lower
heating power because of transition to
anomalous transport driven by DRBmodes
DA
DRB
N. Kasuya – Poloidal shock formation
And particle transport in the H-mode
N. Bisai and J.J. Rasmussen (2 independent
papers) – 2D SOL turbulence
•Formation of density blob
Fig. From Bisai (2D cold ions, edge and SOL)
•Density blob forms near edge-to-SOL regions by the
detachment from density streamer.
• In the SOL structures move mostly radially and eventually
die out (small structures live shorter, not all move)
From J.J.Rasmussen (2D SOL turbulence warm ions)
V.I. Maslov Density transport
due to convection and diffusion
• Equation for density
evolution due to
convective cells (finite
lifetime) combined
with diffusive regions
• Also propagation of
the cells due to electric
field was studied
S. H. Mueller – Experiments on TORPEX
Important Parameter: The Vertical Magnetic Field Bz
Theory and measurement of confinement time:
Important mechanism
Generation of
Parallel flows 
„Short circuiting“ of
electric field
F = -eE||
Collisions inhibit
parallel motion
 Equilibrium
vB,i
B
B
vB,e
Toroidicity drifts lead
to charge separation
and electric fields
E
Implications for confinement
Competition between two basic loss channels:
S. H. Müller et al, PRL 2004
cs q
Sheath
B
parallel loss
 sin q
 Important role of Bz for basic confinement
E
ExB loss
 1/sin2q
Profiles as a Function of Bz
1 Shot = 1 Profile = 1 Movie Frame
P.K. Kaw – Stabilization of
turbulence with RF waves
• Use of the ponderomotive force of the wave field
to compensate the unfavourable curvature force
• Stabilization of turbulence (over a region of the
size of the skin depth) for ITER like parameters is
possible using 10 MW RF
• Reduction due to the change of chaotic behaviour
through the introduction of small perturbations in
the electric field