ITER reflectometry diagnostics operation limitations caused by

strong back and small angle scattering

E.Gusakov1, S. Heuraux2, A. Popov1

1 Ioffe Institute, St.Petersburg, Russia2 IJL, Nancy-Universite CNRS UMR 7198, F54506 Vandoeuvre CEDEX, France

Introduction

The ITER fast frequency sweep reflectometer[*] would be able to diagnose very flat density profiles, which correspond to long probing wave paths (several meters). Under these unfavorable conditions the reflectometers can suffer from destructive influence of plasma turbulence which may lead on one hand to multiple small angle scattering or strong phase modulation and on the other hand to a strong Bragg backscattering (BBS) or to an anomalous reflection.

The multiple small angle scattering leads to the probing beam decorrelation making the standard fluctuation reflectometry approaches not applicable. The BBS results in the reflection of the probing wave far from the cut-off position thus complicating or making impossible the density profile reconstruction.

[*] G. Vayakis, C.I. Walker, F. Clairet et al 2006 Nucl. Fusion 46 S836-S845

Outline

Density and temperature profiles in ITER and probing wave

refractive index behavior

Phase RMS and strong multiple small angle scattering criteria

Limitations of standard fluctuation reflectometry and the new

approach.

Bragg backscattering and the criteria of strong anomalous

reflection

Conclusions

Scenarios of ITER discharge

(a) Flat density profile (solid) (b) Absolutely flat density profile

(dashed) [*]

Temperature profile [**]

relativistic corrections to the plasmapermittivity are needed

[*] A R Polevoi, M Shimiada et al 2005 Nucl. Fusion 45 1451 [**] G.J. Kramer, R. Nazikian, E.J. Valeo, et al 2006 Nucl. Fusion 46 S846 

Relativistic effects[*]

max

2

min 0 2

2.5mode: 20 1

51

2.1 , 1 pe

oTO k

c

[*] H Bindslev 1992 Plasma Phys. Control. Fusion 34 1093

2 21 1

02 2

2 42

2 22 0

2

( ) ( ) ( )1 ; 1 ( );

2

( ) exp 1 , 1; 0; 13 1 1

( );

pe pe

s

ce e

e

x x xx

dx s

K s q x

x m cq x

T

0 0

0 0

0 0

C

Dispersion curves for O- and X- mode in 1D slab

,o ek kc c

400 500 600 700 8000,0

0,2

0,4

0,6

0,8

1,0

X-mode, absolutely flat profile

165 GHz

40GHz

35 GHz

155 GHz

k ec/

x, cm

400 500 600 700 8000,0

0,2

0,4

0,6

0,8

1,0

35 GHz

40GHz

175 GHz

155 GHz

k ec/

x, cm

X-mode, flat profile

600 700 8000,00

0,25

0,50

0,75

1,00

flat density profile

90GHz

85GHz

k oc/

x,cm

WKB phase of scattered wave

00

22

20

2

2 ( ) , ,

( ) ,( ) 4

c

c

x

xe

cc

k x dx o e

h mdxn x n

n k x ec

regular phase

phase perturbation

0WKB

1,o

e

h

h

2 strong phase modulation due to multyple BFS

Phase RMS

222

22 2

0

cx

cc

nh x n xl dx S x

nc n x

625 650 675 700 725 750 775 800 8250,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

absolutely flat density profile -red curve

flat density profile - blue curve

sqrtn

2n

(x)

x,cm

Next page

Form–factor S for the exponential spectrum of turbulence

122

22 2

2

2 2

, ,

,( )

c c

c c

c c

kL cS x x x l L

xx x l

S x x x lc k x

The expression of the phase RMS for the linear profile of the wave vector squared and the homogeneous turbulence:

22 22

2 2 2ln 2ln 2

cc

cc

cc x x

n a xh nLl

lc n n

2 exp cn l

Phase RMS for ITER (O-mode)

650 700 750 800 8500

25

50

75

100

125

O modeblack circles - integral formulared circles - logarithm

x_cut-off, cm

Phase RMS for ITER (X-mode)

400 450 500 550 600 6500

10

20

30

40

black circles-integral formulared circles-logarithm

X modeflat density profile

x_cut-off,cm

650 700 750 800 8500

50

100

150

200

250

x_cut-off,cm

X modeflat density profileblack circles - integral formulared circles - logarithm

650 700 750 800 8500

100

200

300

400

X mode, absolutely flat density profileblack circles - integral formulared circles - logarithm

x_cut-off,cm400 450 500 550 600 6500

25

50

75

100

black circles-integral formulared circles-logarithm

X modeabsolutely flat density profile

x_cut-off, cm

Radial correlation reflectometry at Radial correlation reflectometry at large phase RMSlarge phase RMS

2 2

1 2

2

2 1

/( , ) exp , ,

2 c

efc

c

xCCF x x t t

l

22

2 2

222

2

2

2 2

8ln 1 , 0.577

1

2

2 ,

cc c

c c c

cefcx c c

n

nx

l

a xx l

c t

c l

n l

n

22

2 2ln 1cc c

c c

n a xl x

c n l

At the linear analysis

is not valid

22

2 2 1c c

c

nl x

c n

At CCF takes the form:

E.Z. Gusakov, A.Yu. Popov Plasma Phys. Control. Fusion 44 (2002) 2327–2337

Radial correlation Radial correlation reflectometry at large phase reflectometry at large phase

RMS (cont.)RMS (cont.)

1,k x

x 2cx

1cx

2,k x

2 1

2 1 2c cx x

Radial correlation Radial correlation reflectometry at large phase reflectometry at large phase

RMS (1D analysis)RMS (1D analysis)

G Leclert, S Heuraux, E Z Gusakov et al. Plasma Phys. Control. Fusion 48 (2006) 1389

The symbols are numerical computations for n0/nc = 5·10-3 (), 10-

2 (), 1.5 · 10-2 (), 2 · 10-2 (▼), 3 · 10-2 (▲) and 5 · 10-2 (◄). The dashed line represents the

turbulence space correlation function The solid lines are analytical predictions

. xc = 60 cm; fj = 57.69 GHz

Radial correlation Radial correlation reflectometry at large phase reflectometry at large phase

RMS (2D analysis)RMS (2D analysis)

E.Z.Gusakov, A.Yu.Popov Plasma Phys. Control. Fusion 46, 9, 2004, 1393-1408

Reflectometer correlation length versus turbulence correlation length for given density perturbation level δn/n.

Reflectometer correlation length versus density perturbation level δn/n.

Possibility of local turbulence parameters Possibility of local turbulence parameters estimation estimation

using RCR CCF at strong phase modulationusing RCR CCF at strong phase modulation

2efc cx

c

c

ln

n a xl

c

1/ 28

ln 122

cc

c

fx cec

a x

l

lt

l

• Turbulence level

• Turbulence correlation time

Effect of strong BBS

1D modeling for ITER conditions. Plasma density (violet), electric field of the wave (blue)

1 1 1, , 2i sk x k x k x

The transmission and reflection coefficients through the BR layer

"1"

R

T

X

l

X_BR

1/ 2

2 ,

/BR

BR

x

k x

l dk dx

2 2

2 24204 2 2

1 ,

exp , ; 2 ;2

ii ii

ii BRc

R S T S

l hZS Z n k x

c n

2240

4 2 2

2240

4 2 2

1, 1

1, exp[ 1

1

]1

c

c

R Znl

Zc n

nlZ

T

R Tc

Zn

Strong reflection due to BBS

(analytical & modeling)

Dependence of transmission on the fluctuation amplitude . Analytical formula (dashed green line), modeling (solid red line)

2 20 / cn n

Effect of strong BBS

Plasma density (red), electric field of the wave (blue)

Amplitude increasing due to “Airy” behavior near Bragg

resonance point

Amplitude decreasing ~Sii

Criterion for strong BBS reflection

2

2

BR BR

th c

x x x x

n nn c

n n h n l

c cn x n x x

c c

n c

n x

For O-mode reflectometry at the linear density profile the criterion reads as

O-mode probing from the low magnetic field side for modestly flat density profile for frequencies 85 GHz and 90 GHz

0

20 3

0

20 3

5

1.2 10

0.8 10edge

B T

n m

n m

,

Strong BBS threshold in ITER

650 700 750 8000,000

0,004

0,008

0,012

90GHz 85GHz

nth/n

x,cm

0

20 3

0

20 3

5

1.2 10

0.8 10edge

B T

n m

n m

X-mode probing from high and low magnetic field side for modestly flat density profile for frequencies 40, 45 GHz and 180,190 GHz

Strong BBS threshold in ITER

500 600 700 8000,00

0,02

0,04

190GHz

40GHz180GHz

nth/n

x,cm

45GHz

0

20 3

0

5

10edge

B T

n n m

X-mode probing from high and low magnetic field side for absolutely flat density for frequencies 40, 45 GHz and 170,175 GHz

Strong BBS threshold in ITER

500 600 700 8000,00

0,01

0,02

170GHz

175GHz

40GHz 45GHz

nth/n

x,cm

The analyzed strong BBS phenomena may occur in ITER at the level of turbulent density fluctuations of less than 1% routinely observed in the present

day tokamaks.

!

Conlusions

The turbulence level thresholds for strong phase modulation and strong BBS are derived for different probing modes and frequencies.

Relativistic corrections to the plasma permittivity due to the high electron temperature were included, which induces a spatial shift of the O-mode and X-mode cut-off positions.

Two scenarios one with a rather flat density profile and the other with the absolutely flat density profile are discussed in detail. For both cases with the considered reflectometers, it is shown that the scattering transition into the non-linear regime occurs at the level of turbulent density perturbation comparable or below that found in the present day tokamak experiments.

The threshold of strong phase modulation is given by , whereas the threshold of strong BBS is estimated as depending on the mode used and the frequency.

A new approach to turbulence diagnostics based on radial correlation reflectometry useful in the case of strong phase modulation is introduced. The possibility of local monitoring of turbulence behavior in this case is discussed.

0/ 0.05 0.5%n n

0/ 0.5 3%n n