1. 07.10.2009 IPP - Garching Reflectometry Diagnostics and Rational Surface Localization with Fast Swept Systems José Vicente jvicente@ipfn.ist.utl.pt

2. Motivation Perform physics studies with help from reflectometry systems, namely the density profile systems, from AUG and JET.

3. Outline Waves in plasmas Reflectometry: principles of operation Density profile systems AUG and JET systems Rational Surface Localization Other applications/systems

4. Remember waves in plasmas... Consider high-frequency electron oscillations (ions remain at rest)! The plasma neutrality is broken and an electric field arises pushing electrons back to equilibrium while leading to a density perturbation… electron displacement electric field force Momentum eq. Poisson eq. Fluid continuity eq.

5. Remember waves in plasmas... Taking the time derivative yields the linear wave equation: Cold Plasma! Simple temporal oscillation with angular frequency:

6. Remember waves in plasmas... The well known solutions in vacuum, far from the source, are the plane waves, for E and B:

7. Remember waves in plasmas... The formal study of an uniform magnetized plasma finds that a solution to the Maxwell equations in the form of a e-plane wave is only possible if the wave vector and the frequency satisfy a dispersion relationship, which in the cold plasma approximation (all electrons have the same speed) is given by:... where it is used the vectorial refractive index, N = k c/  with N 2 = N  2 + N  2

8. wikipedia ! 2 electromagnetic modes for electron waves, and k  B 0, but other modes are possible for instance for electrostatic conditions and/or ion species…

9. The solution gives two characteristic modes of propagation, the ordinary and extraordinary modes with different dispersion relations. And we get that N 2 = 0 condition (phase velocity becomes infinity) is satisfied for some cutoffs – the wave is reflected! Remember waves in plasmas...

10. Reflectometry Microwave Diagnostics

11. Reflectometry Probing frequency Take for instance the O-mode… Cutoff density (Cutoff density)

12. Reflectometry  Phase  Time of flight After propagation into the plasma and back, the reflected wave presents a phase shift. This phase shift gives in fact an equivalent time delay, or group delay: So, we “throw” waves at the plasma, wait for their reflection and measure:

13. Density Profiles Both phase measurement and time-of-flight measurement techniques may be applied to plasma profiles. For O-mode operation, in which the cutoff frequency is solely a function of electron density, the group delay data (in the case of time-of-flight techniques) or a derivative of the phase delay data (in the case of phase measurement techniques) may be Abel-inverted to reconstruct the electron density profile of the target plasma. The most common approach is a phase measurement technique called swept frequency modulation (FM) reflectometry, while two different time-of-flight techniques have been applied to this problem: amplitude modulation (AM) reflectometry and ultrashort pulse reflectometry (USPR). from Textor-94

14. Density Profiles - FM Main components Microwave Source (Sweep frequency) Transmission Line + Front-ends Detection System (e.g. Quadrature- phase scheme below)

15. Density Profiles - FM Heterodyne detection allows the basic measurement to be of the fringe frequency resulting from the beating between the reference and plasma signals! This (with a sliding FFT e.g.) gives the group delay needed for profile reconstruction.

16. Density Profiles - FM From the group delay measurements inside the range of interest (frequency range) the cutoff layer positions are determined by an Abel inversion Probing frequency Density Profile

17. Density Profiles – JET and AUG Both systems measure up to ~ 12x10 19 m -3 Just commissioned, profile reconstruction algorithms still being optimized. 10 μs sweep time Edge to magnetic axis and beyond ~ 15 years old (Q band detectors damaged, HFS mixer lost sensit/!) 20 μs sweep time

18. Density Profiles - AUG Plasma current NBI and ICRH power Core and edge line integrated density Plasma stored energy D-alpha

19. Density Profiles - AUG Different diagnostics, Shifted profiles!

20. Density Profiles - AUG Poor S/N in Q-band

21. Density Profiles - AUG

22. Whole pedestal is probed!

23. Density Profiles - AUG ELM resolved profiles Pedestal studies Transport…

24. Density Profiles - JET W-band - back wall, resonances and not pure X-mode are issues... - shift in profiles compared with HRTS also present… - equilibrium reconstruction?

25. Rational surface localization L. Vermare, et al PPCF 2005 When MHD modes develop in the vicinity of rational surface, they can be used to give one or two points of the current profile. Magnetic islands modify density profiles by involving a local flatness due to the reconnection of flux surfaces. But an analysis based on jumps on the time of flight during fast sweeps is possible and more straightforward then through the “flatness” of the profiles!

26. Rational surface localization F. Clairet, et al 2005 In addition to the jumps associated with magnetic islands, incoherent turbulence may produce random jumps, detected at random radial positions. Radial positions retrieved by profile reconstruction. Magnetic islands dynamics also possible to be studied (crossing of X and O points) Rational surfaces calculated by equilibrium code. Magnetic islands have to be present! (t=9, t=11)

27. Summary Reviewed waves in plasmas (O-mode, X-mode) Reflectometry principles and measurements (phase or time of flight) Density profile systems (FM-CW at AUG and JET) A different application – Localization of rational surfaces Some characteristics: + local measurement, + high time resolution, - cannot look over local maxima, +- sensitivity to turbulence

28. Thanks! Questions? jvicente@ipfn.ist.ut.pt