Numerical modeling of plasmas with edge transport barrier D. Kalupin - - PowerPoint PPT Presentation

Numerical modeling of plasmas with edge transport barrier

• D. Kalupin, M.Z. Tokar, B. Unterberg, Y. Andrew,
• G. Corrigan, A. Korotkov, X. Loozen, V. Parail,
• S. Wiesen, R.Zagorski

TEC

Outlines:

Introduction Transport model and possibilities for the barrier formation Evolution of major plasma parameters during ETB formation Interplay between the dominant mechanism for heat losses and barrier onset Comparison with inter-machine scaling for the H-mode threshold ETB formation trough the pulsed gas puffing Conclusions

Introduction

Formation of the ETB is the most outstanding feature of the H-mode performance Parameters at the barrier region can determine both the local and, due to profile stiffness, the global plasma behavior For the modeling of plasma parameters, it is important to have the ETB description in a transport code Recently, 1-D transport code RITM was amended by introducing the model for the edge transport which allows for the modeling

• f the ETB formation

RITM code

RITM solves one-dimensional transport equations for the densities and temperatures of electrons, main and impurity ions and the current diffusion equation. particle sources are due to ionization of neutrals recycling from limiters, from neutral beam injection and impurities eroded or puffed into the plasma heat sources are due to Ohmic and auxiliary heating and energy exchange between different plasma components particle fluxes include diffusive and convective components heat fluxes are composed of conductive and convective contributions all charged states of impurities as He, C, O, Ne, Si, Ar can be considered simultaneously D.Kalupin et al, (2005) NF 45 468

Transport model

CORE TRANSPORT EDGE TRANSPORT

e eff eff D Te eff tr

T en i i i f n ϕ ν ω ν ω ω ω ν ω ω ~ 1 ~

*

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + + − + − + = ~ ~

,

= + − dr dn V n i

r i

ω

i i D e Ti

T T n n T e ~ 3 5 ~ 3 2 ~ 3 2

*

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − τω ω ω ϕ ω ω

( )

c B j n T T ik c B j V n m i

r i e y r i i

~ ~ , ~ ~

,

− = + = − ω ~ ~

,

= + − dr dn V n i

r i

ω ~ ~ ~

||

= ∂ ∂ + + ∂ ∂ = ⋅ ∇ r j j ik l j j

r y y

r r

( )

e j m B B r nT n T E en V m i

ei e r e e e e || || || || ,

~ ~ ~ ~ ~ ν ω + ∂ ∂ − ∇ − − = −

|| || || 2 2 ||

~ 4 ~ , ~ ~ 4 ~ j c k i B j c k i E

y r y

π ϕ πω = ∇ − =

quartic dispersion equation dispersion equation of Mathieu type Re , > ω γ if k ITG

ITG

Re , < ω γ if k TE

TE edge edge k

, γ

Bifurcation into improved confinement state

( )

if the total heating power exceeds Pth the confinement improves

T n S T n T n P P

heat

∇ ≡ ∇ ∇ =

⊥

χ , , ,

*

1 σ n l =

thi i i cx

V k k k / ) (

*

+ = σ l T T l n n / , / ≈ ∇ ≈ ∇

global power balance:

the critical power varies with ne and Bt in the same way as it is predicted by multi- machine scaling for H-mode threshold

D.Kalupin et al, (2006) POP 13 032504

Transport coefficients

Improved mixing length approximation ( )

2 2 2 2

Reω γ γ γ + =

⊥

k D

0.0 0.2 0.4 0.6 0.8 1.0 40 80 120

normalised minor radius growth rate, kHz

0.0 0.5 1.0 1.5 2.0

kρI

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 χ, m

2s

• 1

normalised minor radius

ITG

Total transport coefficients

( )

2 2 , , , , , ,

) ( , 1 max 1 ) / ( 1 1 s s C R

edge TE ITG ExB edge TE ITG edge TE ITG

− ⋅ + ⋅ = εγ ω

ExB and magnetic shear stabilization:

( )

r T n en c B V B V E

i i i r

∂ ∂ + − = 1

ϕ ϑ ϑ ϕ

Radial electric field: Electron transport Ion transport Heat transport

core edge edge TE TE ITG tr ITG e

D R D R D R f D D + + + =

⊥

( )

[ ] (

)

dr q d R D R R r f D V

TE TE ITG tr ITG e

/ ln 3 / 4 + =

⊥ e Z

D D

⊥ ⊥ = NEO Z e Z

V V V

, ⊥ ⊥ ⊥

+ =

( )

core edge edge TE TE ITG tr ITG e

D R D R D R f D + + + =

⊥

2 / 3 χ

( )

core edge edge TE TE ITG ITG NEO i i

D R D R D R D + + + + =

⊥ ⊥

2 / 3

,

χ χ

Preparatory modeling for H-mode experiment in TEXTOR

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4

normalised minor radius ne, 10

13cm

• 3

0.0 0.5 1.0 1.5 2.0

Ti, keV

1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Wtot, MW P, kPa

2 4 6

χion, m

2s

• 1

0.80 0.85 0.90 0.95 1.00 2 4 6 8

χ⊥

D⊥ m

2s

• 1

normalised minor radius

P<Pth, transport coefficients have the maximum at the LCMS, temperature profile reproduce the Ohmic shape P>Pth, transport coefficients at the edge reduce to the neoclassical level, pedestals are formed on density and temperature profiles

Influence of the boundary conditions on the ETB formation

convective heat loss conductive heat loss

n TD ∇ −

⊥

3

T n∇ −

⊥

χ

at the LCMS

T n

T T n n δ δ − = ∇ − = ∇ ,

1

3 1

− ⊥ ⊥

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

T n tot conv

D Q Q δ δ χ

Sudden improvement of confinement occurs if the fraction of the convective heat losses reduces below 50 % (D.Kalupin et al, (2006) PPCF 48 accepted for publication)

Improved two point model for the SOL

( )

ψ γ δ π sin 4

s L i L heat

V n E T R P + =

( )

SOL L s L LCMS

d n V n R

*

exp sin 4 σ ψ δ π − = Γ

S S L L

T n T n = 2

( )

S A L T T T T T T T T T T T T T T T T T

LCMS k L S C L S C L S L C L C S C S C C

Γ + − + − + − = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − + − − + δ

2 2 / 1 2 / 1 2 2 / 3 2 / 3 2 / 5 2 / 5 2 / 5

5 3 5 ln ln 2

S n LCMS

n D S δ

⊥

= Γ

S S T n heat

T n D S P ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

⊥ ⊥

δ χ δ 3 ) ( /

T n T n

δ δ δ δ δ + =

power balance in SOL: pressure balance: particle balance in SOL: parallel heat transport:

LCMS heat C

P T Γ = 5

particular assumption:

Two point model for the SOL

Both, decreasing density and decreasing dSOL lead to the increase of convective losses For a given heating power, a larger convection fraction results in lower temperature and its gradient, this hinders the ETB formation

Comparison with multi-machine scaling

The multi-machine scaling established from divertor machine data predicts that the transition to the H-mode takes place when the total power transported through the LCMS exceeds:

94 . 78 . 64 .

042 . S B n P

e th =

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5

Psep / Pth edge density, 10

13cm

• 3

JET, Septum discharges

Computed threshold power coincides with the scaling predictions if the fraction of convective heat losses does not exceed 50% (D.Kalupin et al, (2006) POP 13 032504) This can explain the deviation of the thresold power from the scaling at low densities (JET, Y.Andrew et al, (2006) PPCF 48 479)

Predictions for TEXTOR

The first indication for the ETB formation is observed at the power just above the critical one computed with the RITM code prior to the experiment

δn = 1cm δT = 1.5cm

(more details in the presentation by B.Unterberg at this meeting)

Typical e-folding lengths for the edge density and temperature in TEXTOR L-mode:

Gas puff triggered ETB

Is it possible to reduce the threshold power?

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4

ne, 10

13cm

• 3

0.0 0.5 1.0 1.5 2.0

Ti, keV Γgas= 1*10

21part s

• 1

Γgas= 3*10

21part s

• 1

0.0 0.2 0.4 0.6 0.8 1.0 2 4 6 8

m

2s

• 1

normalised minor radius D⊥

χ

⊥

0.8 0.9 1.0 4 8

D

⊥

χ⊥

For the total heating power, substantially lower than a critical one, the stationary ETB forms after the short (~5ms) intense blip of deuterium gas. This occurs due to suppression of the turbulent transport by the shear of the radial electrical field, which emerges at the plasma edge due to the formation of the steep density gradient driven by the gas injection

( )

r T n en c B V B V E

i i i r

∂ ∂ + − = 1

ϕ ϑ ϑ ϕ

Gas puffing can trigger the ETB (TUMAN tokamak, Lebedev et al, (1996) PPCF 38 1103)

1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5

Γgas, 1

21part s

• 1

P, kPa

2 4 6

χion, m

2s

• 1

Critical gas puff intensity

Computations predict the critical intensity of the gas puffing allowing to trigger H-mode onset Injection of the same amount of particles but with intensity lower than a critical one do not trigger the ETB formation, on contrary, it leads to the amplification of the edge transport due to increased collisionality

Role of the ExB shear in the barrier formation under different scenarios

0.80 0.85 0.90 0.95 1.00

• 3.0
• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0

before ETB se ts in Er, 10

4V m

• 1

normalised minor radius

0.0 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10 12

normalised minor radius m

2s

• 1

χ⊥

with ExB terms w/o ExB terms Ptot = 4.1 MW

0.80 0.85 0.90 0.95 1.00

• 6
• 5
• 4
• 3
• 2
• 1

Er, 10

4V m

• 1

normalised minor radius

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5

normalised minor ra dius m

2s

• 1

χ⊥

with ExB terms w/o ExB terms Γ

gas =3*10 21 part s

• 1

stabilization of the turbulence by the ExB shear is not the dominant mechanism in the ETB triggered by heating, in this case the stabilisation occurs due to decreasing collisionality and inceasing density gradient

• n contrary, in case of the

gaspuff, when collisionality do not decrease or even increases, stabilization can

• ccur only due to ExB

shear

Coupling to the JETTO code

The model can be used in other transport codes to provide a self-consistent description of the ETB To set up the default settings of the model, the benchmarking against JET data should be done

Conclusions

The transport model allows a self-consistent modeling of L and H-mode plasmas. The ETB forms if the total heating power exceeds the certain critical value which increases with density and magnetic field. For the given heating power, the transition to improved confinement occurs if the e- folding length of density is increased and the temperature e-folding length is reduced. This can be explained by the change of the dominant mechanism for the heat losses at the plasma edge, where the strong convective heat losses hinder the H-mode onset The pulsed gas puffing can be an effective tool to reduce the threshold power. In this case, the suppression of the turbulent transport by the radial electric field, increased due to increased pressure gradient, is the dominant mechanism for the ETB formation. The transport model was coupled with JETTO transport code, where the formation of ETB with increasing heating power was observed. The benchmarking of the coupled version is to be done.

Discussions 1

4 5 6 7 8 5 6 7 8 9 10 Δ , cm 3.3 ε

1/2 ρpi , cm

Discussions 2

Discussions 3