Microstability analysis of e-ITBs in high density FTU plasmas

1) Associazione EURATOM-ENEA sulla fusione, C.R. Frascati, C.P. 65--00044, Frascati, Italy.

2) Associazione EURATOM-ENEA sualla fusione, IFP-CNR, Milano, Italy.

3) Association EURATOM-CEA sur la Fusion DRFC/SCCP, CEA/Cadarache, France.

G. Regnoli1, M. Romanelli1, C. Bourdelle3, M. De Benedetti1, M. Marinucci1 , V. Pericoli1, G. Granucci2, C. Sozzi2, O. Tudisco1, E. Giovannozzi1, ECH, LH and FTU Team

Outlines

• The model (Krook operator for collisions): inclusion of collisionality in Kinezero. • Benchmark and comparison with GS2.

• Experimental results on ITB discharges: analysis of reflectometer signals • First numerical results on ITB discharges stability.

• Conclusion and Future work.

The model 1

We considered the linearized Vlasov equation for the perturbed electron distribution function, with a Krook operator as a first approximation for including collisionality in Kinezero: [G. Rewoldt, W.M. Tang and E. A. Frieman, PoF,Vol. 20,p 402 (1977)]

The following Krook operator for trapped electrons has been used :[M. Kotschenreuther et al. Comp. Phys. Comm., 88 (1995), p. 128 ]

where f0,e is the equilibrium maxwellian distribution.

We consider only collisionality effects on trapped electrons since for passing electrons we assume .

Electron-Electron collisions have been neglected since

fe////V k

1v/v the

The model 2

By Fourier transforming eq. (1)

Isolating the adiabatic response of electrons from the non adiabatic one.

By considering electrostatic approximation H1=- e Φ1

The model 3

For the trapped particles the response in the dispersion relation will be modified as follows [C. Bourdelle, X. Garbet et al. Nuclear Fusion 42 (2002), 892] :

The above expression is numerically computed in the code

The fraction of trapped electrons is kept constant since befe (Banana regime)

feA

nωde= electron vertical drift frequency nω* = electron diamagnetic drift frequency

)(0 cekJ

)(0 erkJ

is the Bessel function standing for the Gyro-average over the cyclotron motion

is the Bessel function standing for the average over the bounce motion

Test and benchmark

The code has been tested and compared with the outputs of the nonlinear electromagnetic flux tube code GS2 [M. Kotschenreuther et al.

Comp. Phys. Comm., 88 (1995), p. 128 ]

In particular the FTU pulse 12747 has been considered. B=7.1 [T]Ip=750 [kA]

The main paramenters of that pulse are show in the Figure

The experiment 12747 is a pellet injected discharge therefore an high effect of collisionality is expected.

Test: limit Aν=0

The new version of the code in the limit of zero

collisionality (Aν =0) gives

the same results as the standard version of Kinezero

The curves with diamond symbols are the growth rates obtained by artificially setting in the new version of the code.

The full lines are just the runs obtained by the standard version of the code in which collisions are not included

0A

Aν =0

Collisions effects

The Aν paramenter has been changed in the code and as expected,

a stabilizing effect with increasing Aν has been found. (r/a=0.7)

feA

Aν /100

γ at r/a=0.7 pulse 12747

[s-1]

Aν /20

Aν /5

Aν /2

ITG-TEM kθρi < 2 ETG kθρi >2

The stabilizing effect of collisionality can also be seen by plotting

the maximum growth rate γ versus the normalized radius r/a at different collisionality values.

The stabilization is due to the fact that the effect of trapped electrons TE on turbulence are less important at high collisionality (see slide 5)

[s-1]

[s-1]

Aν =0

Aν /100

Aν /20

Aν /5

Aν /2

γ max pulse 12747 γ max pulse 12747

Collisions effects

Comparison with GS2

collisionality

GS2 runs for pulse 12747 at r/a=0.7, t =0.7[M. Romanelli, C. Bourdelle, W. Dorland, Phys. of Plasmas 11, No 8, (2004), 3845]

Scan at different collisionalities νei and different density gradients An show that at

high collisionality the density gradient has a stabilizing effect whereas at low collisionality is the opposite.

Aν /5

real An An /5

Comparison with GS2

Kinezero runs are in good agreement with GS2 results, showing the same

dependence of low kθρi turbulence on Aν and An as in the paper

[M. Romanelli, C. Bourdelle, W. Dorland, Phys. of Plasmas 11, No 8, (2004), 3845]

feA

Aν /20

γ a

t r/

a=0.

7

γ a

t r/

a=0.

7

γ a

t r/

a=0.

7

Aν /2

real An real An An /5 An /5

Kinezero runs for pulse 12747 at r/a=0.7, t =0.7

Comparison with GS2

• Note that the order of magnitude of the Kinezero growth rate is similar to GS2 but consistently lower.

• Aν /2 is the limit frequency for the banana regime. (νei /ωbe ~1)

feA γ

at

r/a=

0.7

γ a

t r/

a=0.

7

Aν =0Aν/100

real An real An

An /5 An /5

Experimental setup and ITBs

][0

][3.1

][5.3)0(

][108

][360

][3.5

319

0

MWpowerECRH

MWpowerLH

keVT

mn

kAI

TB

e

ol

p

Plasma paramenter during the heating phase

26672 26669

Pulse 26669 develops an e-ITB

][0.1

][7.0

][5.5)0(

][108

][360

][3.5

319

0

MWpowerECRH

MWpowerLH

keVT

mn

kAI

TB

e

ol

p

26672 26669

Reflectometer data

2667226669

refl

ecti

on

ra

diu

s

[m

] During the heating phase the reflection radius of the reflectometer was about the same in the two pulses R =1.13 [m] (r/a=0.4)

The Fourier spectra of reflectometer signal show a stabilization of turbulence in the shot with ITB (26669)

r/a = 0.4; νei = 0 r/a = 0.4; νei = real νei

ωr

[s-1]

γ [

s-1]

Runs by Kinezero

•As expected it is found that for FTU plasmas collisionality may change the nature of turbulence from TEM-ITG turbulence to pure ITG.

•This is also confirmed by the fact that the power exchanged by the mode with the

trapped electrons is found to be 60% at νei = 0 and 5% at νei = real νei

•Similar results are obtained for the shot 26672

Positive ωr means electron drift direction ; Negative ωr means ions drift direction

shot 26669

The ion temperature is measured by the multicollimator.

At low current the measure is affected by strong errors since it is related the neutron rate which is low for r/a >0.3

The Bohm –Gyro Bohm model has the advantage that gives Ti=Te at the edge but is not accurate enough for reproducing the exact Ti gradient.

The actual Ti profile should be in the region between the Ti measured (red curve) curve and the Gyro bohm model curve (green curve)

Temperature profiles

Scan with η

η= Ln/LTi

FTU pulses 26669 and 26672 have high collisionality and, according to the multicollimator diagnostic (Ti measurements), η close to threshold for pure ITG modes.

This suggests that the ITB can develop when η is below the threshold.

Since Ti measurements at low plasma currents are affected by strong errors we decided to perform a

scan in η in order to find

the threshold in η for the destabilization of pure

ITG modes (η~1.8) at high collisionality

(νei = real νei ), q=1.7, s=1,

Te/Ti=1.7, Zeff=2.5, r/a=0.4

Conclusions

•Collisionality effects have been included in Kinezero using a Krook operator

•The new version of the code has been tested and benchmarked against GS2.

•First results of stability analysis of e-ITB discharges in FTU have been presented:It has been found that at high FTU collisionalities TEM are suppressed and turbulence level is very sensitive to Ti profiles

•Dependence from other important paremeters is under investigation

Future work :

Study of the stability of high desity plasmas in order to better understand the collisionality effects on turbulence

Experiemental validation by dedicated campaigns on FTU