Transcript Folie 1

Member of the Helmholtz Association
Losses of particles and energy
by strong magnetic field
perturbations
A.Gupta & M.Tokar
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
Contents
Motivation
Magnetic islands
Heat flux limit
Edge localized modes (ELMs)
Conclusion
July 17th, 2008
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 2
Motivation
Diverse MHD instabilities destroy closed magnetic surfaces in tokamaks and
result in radial inclination of the field lines
Plasma parameters, density and temperature,
are inhomogeneous in radial direction and
their gradients have components along
perturbed field lines
Therefore transport along such field lines is
generated and contributes to radial fluxes
n
|| , q||
T
 , q
|| , q||
r
Along field lines with large inclinations, the heat and particles can be
transported directly to the plasma boundary
Along field lines with small inclinations parallel particles and heat flows
can be moved by some process to other perturbed field lines and after series
of such events they can also reach the plasma boundary
July 17th, 2008
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 3
Heat transport across non-overlapped
magnetic island due to tearing modes
A. Gupta and M.Z.Tokar, Phys. Of Plasmas 15, 034503 (2008)
“Optimal path” method has been applied to
magnetic island geometry
It asserts that heat is transported predominantly
along paths providing the minimum temperature
change
Perpendicular
path part
Parallel
path part
qr   
T
y
T
B 
qr  ||  r  sin 2 
g
y
B
2
Paths including one or two parallel sections have been considered. The
initial and final positions of these sections are varied in the whole space
from the symmetry surface to the resonant surface to select optimal paths.
July 17th, 2008
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No 4
Total temperature
T 
change is analytically
calculated
 T   T

//
T
w / 2 ch
Effective heat conduction
is determined from
qr   eff
Parallel vs
perpendicular
  4 // br2 /  
Figure shows the ς dependence of <eff>/  and for different σch. The parallel
transport contribute to the perpendicular one, if ς>4, and the enhancement
saturates at a certain level, depending on σch . In this case the temperature change
in the island approaches zero.
We compare the transport enhancement obtained by considering paths with one
and two parallel sections, and see no significant difference. Further increase of
parallel sections will increase computational time for no additional accuracy.
July 17th, 2008
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No 5
Elucidation of the heat flux limit from
magnetic island heating experiment
M.Tokar and A.Gupta, PRL 99, 225001 (2007)
Classen et al, PRL, 98, 035001 (2007)
Tearing mode islands (m/n=2/1) in
TEXTOR destabilized by Dynamic
Ergodic Divertor and heated by
Electron Cyclotron Resonance Heating
Island is heated uniformly at the resonant surface. Heat transfers along and
perpendicular to field lines from resonant surface to island separatrix. An
analytical model has been developed to determine  and ||, and thus the heat
flux limit in collisionless plasmas:
FS  q|| /nTVth 
July 17th, 2008
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No 6
Heat transfer for heating inside islands
Heat deposited on resonant
surface is transported first ||
and then  field lines, along
the path with minimum ΔT
Parallel
T
B 
qr  ||  r  sin 2 
g
path part
y
B
2
  m  n
Perpendicular
path part
 FS 
qr   
T
y
 //T
3.16
~ 0.03
SH
 // /  //  1 TL||
FS in agreement with interpretation of laser experiments!
July 17th, 2008
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No 7
ELMs
ELMs are an MHD activity at the edge
of tokamak plasmas, that cause high
impulsive heat and particles fluxes on
target plates which may lead to
unacceptable loads under reactor
conditions
K.Kamiya et al, Plasma Physics Control Fusion
(2007) S43-S62
H. Zohm, Plasma Physics Control Fusion
(1996) 150
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No 8
Model for ELMs loss mechanism
M.Tokar, A.Gupta, D.Kaupin and R.Singh, PPCF 49 (2007) 395
Type I ELMs are generated by ballooning-peeling ideal MHD modes
developing when the pressure gradient exceeds the critical level.
These modes produce a radial perturbation of the magnetic field, and steep
gradients of plasma parameters in the ETB (edge transport barrier) results
in radial particle and heat transport along such field lines
This model could explain the
collisionality dependence of losses
during ELMs observed on diverse
tokamak devices
A.Loarte et al, Plasma Physics Control Fusion
(2003) 1549
July 17th, 2008
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No 9
Magnetic field line inclination
Time evolution of field line inclination angle:
1

4 2  b
Spatially averaged Inclination angle:
Linear growth rate of ballooning modes:
Particle balance in edge region
for time evolution of density :
July 17th, 2008
d
  (  1/  ELM )
dt
1

Rq
2 2

0
2
 Br 
0 a  B  d d dr
b
a
B 2  cr nb  nth
4 mi nb nb
(cs )2 nb
 ELM dnb
 i 
2 dt
cs nb / ns   ELM / 2
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 10
Particle and energy losses per ELM crash
Particle loss:
Particle flux density through
separatrix
N ELM  Ssep s ELM
s  cs ELM ns nb
Energy loss:
Welm  SsepQs elm
Heat flux density through separatrix
Qs  Q//s k  Qconv
Heat conduction is dominated by the
contribution from light electrons
 ||SH 
T
Q|| k 
3.16 T r
1 
 FST r
Convective heat loss, with ions escaping
from ETB during ELM
July 17th, 2008
Qconv
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 11
Ion convective heat loss
A. Gupta and M.Z.Tokar, 35th EPS Conference, Greece, 2008, P-104
Ions, starting to move when magnetic field lines are inclined by MHDperturbations, are considered
The ion motion, energy and kinematic equations for particles in the region
inside the separatrix are integrated numerically, to determine the initial
parameter space (s, U, ε) of particles that escape from the ETB during ELM
time (τelm).
dV e
2

E
(
x
)

V
Ion motion equation
dt mi
 1 ( x)
Ion energy equation
Kinematic equation


d  miV 2
2   '

    eE( x)V 
dt  2
 1 ( x)

  m V

 2   


2
i
dx
 V (t , x)
dt
Forces from ambipolar electric field and coulomb collisions with background
thermal particles are taken into account.
July 17th, 2008
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No 12
Parallel electric field is estimated from balance of the electric field force by
the pressure gradient along field lines
0  enE // ( x)  
d (nT )
dr
The number of particles escaping during ELMs with specific initial parameters
(s, U, ε) is determined under assumption of local maxwellian distribution, and
linear profiles of n, T at the edge with sharp gradients at ETB. By integrating
over this parameter space, we calculate the net convective energy loss
 U2

2 1 n( s)
  miU 02


 S sep  ds dU  d
exp




0
 2

3
mi  VT ( s)

 VT ( s) T ( s)  2
a
0
Wconv
July 17th, 2008
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No 13
Sharp gradients of n, T at ETB, proximity of ETB to
separatrix, and higher average energy at ETB top
explain clustering of ΔWelm near ETB. Increasing ν*
implies, ions encounter more frequent collisions with
background thermal particles, an effect pronounced for
ions deeper in the plasma.
Conductive heat flux is curtailed due to ξFS for low ν*,
and small λb for high ν*.
July 17th, 2008
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 14
Conclusion
A model for transport of heat through magnetic islands has been
developed, for the cases with core heating and that with heating
inside the island.
The parallel heat flux limit has been elucidated, by analysis with this
model for islands in TEXTOR.
A model for particle and energy loss, considering both convective
and conductive losses, during ELMs, has been developed
The model reproduces the collisionality dependence of energy loss,
and dominance of ion convection in the loss mechanism, as
observed in experiments
Next steps in further development of the model are time evolution of
n, T in intra-ELM period and precise determination of αelm .
July 17th, 2008
Abhinav Gupta | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ
No 15