ITER reflectometry diagnostics operation limitations caused by

1. ITER reflectometry diagnostics operation limitations caused by strong back and small angle scattering E.Gusakov1, S. Heuraux2, A. Popov1 1Ioffe Institute, St.Petersburg, Russia 2 IJL, Nancy-Universite CNRS UMR 7198, F54506 Vandoeuvre CEDEX, France

2. 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. Fusion46 S836-S845

3. 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

4. (a) Flat density profile (solid) (b) Absolutely flat density profile(dashed) [*] Temperature profile[**] relativistic corrections to the plasma permittivity are needed Scenarios of ITER discharge [*] A R Polevoi, M Shimiada et al 2005 Nucl. Fusion45 1451 [**]G.J. Kramer, R. Nazikian, E.J. Valeo, et al 2006 Nucl. Fusion46 S846

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

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

7. WKB phase of scattered wave regular phase phase perturbation

8. Phase RMS Next page

9. Form–factor S for the exponential spectrum of turbulence The expression of the phase RMS for the linear profile of the wave vector squared and the homogeneous turbulence:

10. Phase RMS for ITER (O-mode)

11. Phase RMS for ITER (X-mode)

12. Radial correlation reflectometry at large phase RMS the linear analysis is not valid At At CCF takes the form: E.Z. Gusakov, A.Yu. Popov Plasma Phys. Control. Fusion 44 (2002) 2327–2337

13. Radial correlation reflectometry at large phase RMS (cont.)

14. Radial correlation reflectometry at large phase RMS (1D analysis) • 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 G Leclert, S Heuraux, E Z Gusakov et al. Plasma Phys. Control. Fusion 48 (2006) 1389

15. Radial correlation reflectometry at large phase RMS (2D analysis) Reflectometer correlation length versus density perturbation level δn/n. Reflectometer correlation length versus turbulence correlation length for givendensity perturbation level δn/n. E.Z.Gusakov, A.Yu.Popov Plasma Phys. Control. Fusion46, 9, 2004, 1393-1408

16. Possibility of local turbulence parameters estimation using RCR CCF at strong phase modulation • Turbulence level • Turbulence correlation time

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

18. The transmission and reflection coefficients through the BR layer la X X_BR

19. Strong reflection due to BBS(analytical & modeling) Dependence of transmission on the fluctuation amplitude . Analytical formula (dashed green line), modeling (solid red line)

20. Effect of strong BBS Amplitude decreasing ~Sii Plasma density (red), electric field of the wave (blue) Amplitude increasing due to “Airy” behaviornear Bragg resonance point

21. Criterion for strong BBS reflection For O-mode reflectometry at the linear density profile the criterion reads as

22. Strong BBS threshold in ITER , O-mode probing from the low magnetic field side for modestly flat density profile for frequencies 85 GHz and 90 GHz

23. Strong BBS threshold in ITER X-mode probing from high and low magnetic field side for modestly flat density profile for frequencies 40, 45 GHz and 180,190 GHz

24. Strong BBS threshold in ITER X-mode probing from high and low magnetic field side for absolutely flat density for frequencies40, 45 GHz and 170,175 GHz

25. ! 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.

26. 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.