#1

F. Castejón 1), M. Ochando 1), T. Estrada 1), M.A. Pedrosa 1), D. López-Bruna 1), E. Ascasíbar 1), A. Cappa 1), A.A. Chmyga 2), N.B Dreval 2), S. Eguilior 1), L. Eliseev 3), A. Fernández-Curto 1), J. Herranz 1), C. Hidalgo 1), S.M. Khrebtov 2), A.D. Komarov

2), A.S. Kozachok 2), L. Krupnik 2), A. López-Fraguas 1), A.V.Melnikov 3), K.J. McCarthy 1), F. Medina 1), I. Pastor 1)

1) Laboratorio Nacional de Fusión. Asociación EURATOM-CIEMAT, Madrid, Spain2) Institute of Plasma Physics, NSC KIPT, 310108 Kharkov, Ukraine

3) Institute of Nuclear Fusion, RRC Kurchatov Institute, Moscow, Russia

Influence of the magnetic topology on Influence of the magnetic topology on transport and radial electric fields in transport and radial electric fields in

the TJ-II stellaratorthe TJ-II stellarator

20th IAEA Conference. Vilamoura 2004

#2

Outline

• Introduction and description of the problem.

• Low order rationals in the core.

• Kinetic effects and transport.

• Low order rationals close to the edge.

• Conclusions.

#3

Introduction and description of the problem

Transport, Turbulence and Electric fields are affected.

The effect of low order rationals was controversial: Degrade confinement (Some works [1]).

ButTransport barriers can be triggered in tokamak and stellarators:

ITB. Tokamaks [2] and stellarators [3] ETB. Tokamaks [4] and stellarators [5]

Low order rational surfaces:*Break the magnetic topology of nested flux surfaces.*Introduce magnetic islands and ergodic zones.

[1] Brakel, NF 42 (2002) 903

[2] Lopes-Cardoso et al. PPCF 39 (1997) B303

[3] Fujisawa. PPCF 45 (2003) R1

[4] Wolf. PPCF 45 (2003) R1

[5] Hidalgo et al. PPCF 42 (2000) A153

#4

Introduction and description of the problem

Two different explanations for Transport Barriers:

In TJ-II, low order rational surfaces can trigger electron heat Transport Barriers (eITB) in the core

and positive sheared electric fields appear in the edge.

Generation of electric fields:1) ExB sheared flows reduce

turbulent transport [6]. 2) Neoclassical Transport

Barriers [7]

Rarefaction of resonant surfaces in proximity of low order rationals [9,10].

Reduction of anomalous transport.

[6] Terry. Rev. Modern Phys. 72 (2000) 109

[7] Minami et al. NF 44 (2004) 342

[9] Wobig et al. 11th IAEA, 1986

[10] Romanelli et al. PhF B 5 (1993) 4081

#5

• R=1.5 m• a=0.1-0.22 m• B<1.2 T

The Flexible Heliac TJ-II

0

100

200

300

0 100 200 300

Ihx

( kA

)

Icc ( kA )

0.91.2

1.4

1.6

1.8

2.0

2.2

• High rotational transform flexibility• Low magnetic shear•Allow the control of low order rationals within the -profile

• High rotational transform flexibility• Low magnetic shear•Allow the control of low order rationals within the -profile

Magnetic configuration flexibility:

#6

0

10

20

30

40

50

60

-1 -0.5 0 0.5 1

I tota

l (nA

)

c)

Te profile is steeper, plasma potential is more positive, (strong electric field appears, and central density falls).

Core heat confinement is improved.

Te profile, plasma potential and beam intensity (proportional to density) with (red) and without (black) eITB

-5

0

5

10

15

20

25

1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32

e-ITBbefore

Er (

kV

/m)

R (m)0.3 -0.3

0

0.4

0.8

1.2

1.6

-1 -0.5 0 0.5 1

Te (

keV

)

a)

0.4

0.8

1.2

1.6

-1 -0.5 0 0.5 1(k

V)

b)

Plasma core: eITB signatures

#7

eITB signatures (2)

0,1

1

10

100

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

e (m2/s) Shot #6998

e (m

2/s) Shot #6978

e(m2 /s

)

0

0.5

1

1.5

2

2.5

-0.8 -0.6 -0.4 -0.2 0 0.2

w (

W/c

m3 )

Heat conductivity with eITB is reduced in a factor two in plasma core.

eITB appears when rational is overlapping the power deposition region.

#8

Positioning Rationals: Ohmic current (1)

Central electron temperature suddenly increases when 3/2 surface is close to plasma core.

Ip=-1.6 kA

0

0,2

0,4

0,6

0,8

1

1,2

-2

-1,5

-1

-0,5

1160 1180 1200 1220 1240

Te

(keV

) Ip (kA)

t (ms)

=-0.01

=+0.05

=-0.07=-0.24

=-0.35

=-0.45

Ip (kA)

1,4

1,45

1,5

1,55

1,6

1,65

1,7

0,2 0,4 0,6 0,8 1

VacuumIp=-1.6 kA3/2

#9

1) As Rational is moved outwards, eITB disappears.

2) eITB only appears for low order Rationals.

Positioning Rationals: Ohmic current (2)

Ip=-1.6 kA Ip=-5.2 kA

0

0,5

1

1,5

-10

-8

-6

-4

-2

0

2

1100 1150 1200 1250

Te

(keV

) Ip (kA)

t (ms)

=-0.01=+0.05

=-0.07=-0.24

=-0.35

=-0.45

Ip (kA)

1

1,1

1,2

1,3

1,4

1,5

1,6

1,7

0,2 0,4 0,6 0,8 1

VacuumIp=-1.6 kA3/2Ip=-5.2 kA4/3

#10

Positioning Rationals: Ohmic current (3)

-3

-2.5

-2

-1.5

-1

1.54 1.56 1.58 1.6 1.62

I p (kA

)

(0)

The Current needed to position the Rational at r≈0.2 - 0.3 increases (in absolute value) with iota.

1,4

1,45

1,5

1,55

1,6

1,65

1,7

1,75

0 0,2 0,4 0,6 0,8 1

100_44_64 Vacuum100_44_64 Ip=-1.6 kA100_48_65 Vacuum100_48_64 Ip=-2.2 kA100_50_65 Vacuum100_50_65 Ip=-2.4 kA3/2

#11

Suprathermal electrons with eITB

Ln(Intensity) (a. u.)

5

7

9

11

2 6 10 14

50-150 ms160-210 ms

Ts=2.60 keV

photon energy (keV)

0.4

0.40.4

0.8Te (keV) ne x 1019 (m-3)

-1 -0.5 0.50.0 1

Temperature and density profiles, SXR spectra (100_44_64. Vacuum =1.51) with (blue) and without (red) eITBs.

When steep temperature gradient is present and the density profile is more hollow (left), the population of suprathermal electrons is larger (right).

#12

The role of power density

0

0.5

1

1.5

2

0

0.4

0.8

1.2

1.6

1000 1050 1100 1150 1200 1250

<n e>

(10

19m

-3) T

e (0) (keV)

time (ms)

0

0.5

1

1.5

2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1000 1050 1100 1150 1200 1250

ECH on axis

ECH off axis

<n e>

(10

19m

-3) T

e (0) (keV)

time (ms)

For the same density and magnetic configuration (close to n/m=3/2), the eITB appears in the high absorbed power case.

Further proofs of the role played by kinetic effects:

Magnetic configuration close to 3/2. 300 kECH power modulation is enough to trigger eITB.

#13

0

0.5

1

1.5

2

1000 1050 1100 1150 1200 1250

H,

Mir

no

v s

ign

al

(a.u

.)

time (ms)

-0.5

0

0.5

1

1.5

2

I p (

kA

)

0

0.2

0.4

0.6

0.8

#11641

<n e>

(1

019 m

-3)

0

0.5

1

1.5

2

Te (

keV

) 0.0-0.06-0.12-0.24-0.30-0.40

ne

Te

Ip

MHD

H

eITB with positive magnetic shear

0

0.2

0.4

0.6

0.8

1

1.2

#11641 @ 1100 ms#11640 @ 1100 ms

n e (1

019 m

-3)

0

0.5

1

1.5

-1 -0.5 0 0.5 1

Te (

keV

)

#14

Kinetic effects and Transport

eEr eNC

Er eTURB

Er eECH

Er eRS

Er

Er (T /e) n' /n T ' / 2T T ' / 2e

The total electron flux is: neoclassical + ExB turbulent + ECH-induced + RS-induced.

Neglecting ion flux and assuming that the main contribution is due to the rational surface, the electric field in the steady state is:

Therefore, central temperature and potential profiles evolve in a similar way, opposite to density (as observed experimentally in modulation experiments)

Measured potential: 15 kV (HIBP), similar to the obtained using this expression, 12 kV.

#15

Kinetic effects and Transport

ui

tFi

u Dik

u k , i,k , //

D Dcy1/ 2

DeterministicStochastic

F Dcy dN //(N //) Ys u//N // w

ˆ e

2dN //(N //) 1

sJ s ()

,iJ ' (),

u//

uJ s ()

Nuc /

0

0.1

0.2

0.3

0.4

0.5

0.6

-0.4 -0.2 0 0.2 0.4 0.6 0.8

u

u||

Power Density

Resonant Quasi-Linear Diffusion pushes particles inside loss cone.

An enhanced outwards particle flux is produced.

#16

Kinetic effects and Transport

0 100 200 300time (ms)

H

(a.

u.)

HRL

LRL

e

ECH n

t

ECH

f (u )

du

dt

d

S

Low Ripple Losses regime

(no Rational)

Further needed developments of flux calculation:

1) Modification of distribution function.

2) Loss cone reduction due to Electric field.

3) Inclusion of RS.

Loss cone

ECH is directed outwards.

Particle flux in loss cone:

ECH 1 r r' dr' ECH

High Ripple Losses regime

(enhancement of

direct losses by the Rational)

H

#17

Low order rationals in TJ-II edge plasmas

Sheared electric field appears in the inner part of rational surface n=4/m=2, as measured by HIBP.

Influence on transport?Electric potential profiles in presence of n=4, m=2 resonance in the plasma periphery (red) and without low order resonances (blue).

Electric field with low order rational in

plasma edge

#18

Low order rationals in TJ-II plasma edge

-5 104

0

5 104

1 105

1.5 105

2 105

She

arin

g ra

te (

s-1) (a) (b)

1000

2000

3000

4000

0.35 0.4 0.45 0.5 0.55 0.6

Erm

s/B

(m

s-1

)

Line Average Density (x10 19 m-3)

(c)

0.7 0.75 0.8

(d)

Plasma is kept in a marginal stability state (The shear flow tends to reduce turbulence and improve confinement).

The shear flow generation could be due to the turbulence (e. g. via Reynolds stress).

Sheared flow can be enhanced by:

- Positioning a low order Rational.

- Introducing a polarised electrode

Shearing rate vs. line density without (a) and with (b) polarised electrode and their

corresponding turbulence levels (c,d).

Electrode polarization experiments:

#19

• eITB are triggered in ECRH plasmas when low order rationals are positioned close to plasma core ( < 0.3) in TJ-II.

• eITB are not found in TJ-II when positioning low order rational surfaces in the confinement region (0.4 < < 0.7) for the present experiments, with low magnetic shear.

• Sheared electric fields appear in presence of low order rational surface in the edge. Polarized electrode experiments show that the created sheared flow can overcome the turbulence level and, hence, to reduce the anomalous transport.

• TJ-II results offer valuable information on the multiple mechanisms based on neoclassical/turbulent bifurcations and kinetic effects to explain the effect of magnetic topology on radial electric fields and confinement.

Summary and Conclusions

#20

Thank you!

#21

Low order rationals in the confinement zone

OH current is induced in a single shot.

Confinement evolves monotonically with current and, hence, with magnetic shear from Ip=-10 kA up to 5 kA. For higher plasma currents the confinement is restored again.

Jumps in line density, as well as in thermal signals show the presence and influence of low order rationals.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-10 -5 0 5 10plasma current, kA

line

avg

d. d

ensi

ty, 1

019

m-3

79467955

7045

7036

7972

7970

Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).

#22

Positioning RS: magnetic scan

1.46

1.48

1.5

1.52

1.54

1.56

1.58

1.6

1.62

0 0.2 0.4 0.6 0.8 1

0

0.5

1

1.5

2

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

#6978, 100_40_63, t=1150 ms #6985, 100_38_62, t=1150 ms #6985, 100_38_62, t=1250 ms #6998, 100_36_62, t=1150 ms

Te

(keV

)

eITB, intermediate case, and no eITB.

#23

Positioning RS: magnetic scan (2)

-0,5

0

0,5

1

1,5

2

2,5

1000 1050 1100 1150 1200 1250 1300

Shot #6985 =-0.45=-0.35=-0.24=-0.07=-0.01=+0.05I

p (kA)

Te

(keV

), I

p (

kA)

t (ms)

10-6

10-5

10-4

5 10 15 20 25 30 35 40

Shot #6998Shot #6978

Am

plit

ude

(a.

u.)

f (kHz)

Coherent mode detected by Mirnov coils in the case with eITB.

Intermediate case: eITB appears or disappears depending on bootstrap current.