A Brief tutorial to Thomson Scattering With a focus on LIDAR By Mark Kempenaars

1. A Brief tutorial to Thomson Scattering With a focus on LIDAR By Mark Kempenaars For the EFTS/EODI training, 12th June 2009 at Culham Science centre

2. Outline of Talk • Introduction • Thomson scattering theory – the highlights • Conventional TS • LIDAR TS • Towards ITER

3. Introduction • Thomson scattering was first described in 1903 by J.J. Thomson, many years before lasers existed. Thomson discovered electrons in 1897. • First application to a laboratory plasma in 1963 by Fünfer (First ruby laser in 1960) • First measurements in hot plasmas by Peacock et al., in 1969 at the Russian T3 Tokamak

4. dW Scattering Electron ks R k E0 j q k0 rj Origin Thomson scattering theory Thomson scattering is nothing more than the interaction of EM radiation with an electron any light will do. We can use Maxwell’s equations (1873) to describe the forces on and movements of the electrons. The highlights… Let’s consider this experimental setup: Incident EM wave with amplitude E0, propagation vector k0, and angular frequency w0, so electric field at the electron is given by:

5. Theory cont’d - 1 This electric field will then apply a force on the electron (with mass m and charge e at position rj) and following Maxwell’s equations, we get the acceleration of the electron: This equation clearly shows us that the electron will be oscillating up and down, together with the electric field of the light wave. Since this electron is now a moving charged particle it will create an EM field of its own, with the same wavelength as the incoming light!

6. Theory cont’d - 2 When a moving electron like this is observed from a large distance (R>>l) its radiation can be described as dipole radiation: This equation shows us that the radiation from ions is negligible compared to that of electrons, since r0 ~ 1/m: Where k is the differential vector (ks-k0). and r0 is the classical electron radius:

7. Theory cont’d - 3 In this lay-out dW is the solid collection angle, it basically describes the fraction of scattered radiation we collect. If we then divide the total scattered power by this solid collection angle we get the differential scattering cross section: Which tells us that the re-radiation is maximum perpendicular to E0; dsT/dW=r02. And that the scattering cross section is very small This makes it clear that every photon is important! And we want as big a window as possible.

8. Theory cont’d - 4 Obviously the scattered power depends on the number of electrons caught by the laser, but also on the interaction between them. This interaction start to happen above the Debye length. So this depends on the density and temperature of the electrons For Te = 10 keV, ne = 5×1019 m-3: lD ~ 100 mm (typical for JET) The so-called Salpeter-parameter tells us whether the scattering we are observing is coherent or not: If a<< 1 : then the scattering is from individual electron: Incoherent TS If a≥ 1 : then scattering by electrons surrounding ions; (Ion) Coherent Thomson Scattering If a~ 5-20 : Scattering by electron density fluctuations, or Bragg-scattering Coherent Thomson scattering

9. Theory cont’d - 5 The total scattered power is given by: With P0 : Incident (laser) power ne : Electron density in the plasma DL : Length of scattering volume S(k,w) : Scattering form factor describes frequency shifts from electron motion as well as correlation between electrons. The scattered light is clearly proportional to the density. The form function is given by: where f(n) is the velocity distribution In this equation the delta function tells you about the Doppler shift:

10. Theory cont’d - 6 If the velocity distribution f(v) is Maxwellian (i.e. low density, no interaction between particles) then: with ‘a’ the thermal velocity: One then finally finds an equation that contains wavelengths: With l0 the incident wavelength and ls the scattered wavelength Where we then find the spectral width of the scattered light, which has a Gaussian shape: If we were to take a Ruby laser (694.3nm) and 90º scattering then this would give:

11. Theory cont’d - 6 Once the electrons get really hot (i.e. really fast) we have to start including relativistic effects, which effectively change the scattering cross section of the electrons, by a factor 1/g 2 where g is the Lorentz factor , which shows that for a 1% deviation we need an electron temperature of 2.56 keV. Also there is a “search light” effect or relativistic aberration, which means that the electrons radiate preferentially in their forward direction. E.g. moving at 10% of c, then power in forward direction increases by 36%, it decreases by 26% in backwards direction. This leads to a blue shift of the spectrum…

12. TS spectra So, what does this look like? l/llaser

13. TS Spectrometer What does a spectrometer look like? If we cut our scattered light “broadband” light into sections: Incoming collected light 4 3 2 1 4 3 2 1

14. So, what do we need? • A powerful pulsed laser • Typically one would get 1 photon in every 1×1014 back, e.g. if we use a 3GW laser pulse we get 30 mW back on a high density plasma (1020m-3) and 100% transmission. • Fire this laser into the plasma • A window on the machine that can stand the high laser power and does not get dirty • plus the optics to deliver it there. • Collect as much light as possible • A large window is needed that can see the laser line • This window can’t get dirty, or if it does we must be able to clean it. • The other optics need to be aligned and stable (also during disruptions etc.)

15. Laser Plasma Collection optics 90º TS - Single point In the early days of TS on Fusion devices all TS systems were “single point” diagnostics, i.e. the optics were only looking at one point. This seems archaic but it was still one of the better and more reliable diagnostics. This was also the case on JET, where a ruby laser was fired vertically into the plasma. A large set of windows and mirrors was used to relay the light to a spectrometer.

16. 90º TS - Multi point More modern systems have a range of points. Where each spatial point is imaged onto an optical fibre. Each fibre then represents a spatial point in the plasma, a high spatial resolution can be achieved by using a lot of fibres. Keep in mind however that a smaller volume will scatter fewer photons. Laser Plasma And this setup means one needs a spectrometer for each spatial position, so can get very expensive Collection optics

17. 90º TS on JET – HRTS • A new system was installed on JET in 2004. High Resolution Thomson Scattering. • High power (5J, 15ns) Nd:YAG laser. • Fire at 20Hz, horizontally • Scattered light is then collected from a window at the top of the machine. In order to collect as many photons as possible we need a big window, largest on JET 20cm diameter. 63 spatial points on the LFS, at approximately 1.5cm resolution

18. 90º TS on JET – HRTS cont’d 1

19. MAST 90º TS A set of lasers can be fired in sequence or in a burst, giving a high temporal resolution ~1ms

20. Plasma Laser (short pulse) Mirror labyrinth LIDAR – 180º TS Now we go to q = 180º, or back scattering Light detection and ranging, we fire a laser pulse and count the elapsed time before we get a signal back, like in radar. Of course we have to count very quickly, since light travels at ~3×106 m/s (or 1m every 3ns) Major advantages: ‘Point and shoot’ method, which requires minimum access Very short laser pulse ~250ps Only one spectrometer needed, but it has to be fast!

21. LIDAR – 2 • The main advantages of LIDAR: • The alignment is relatively easy • Only one spectrometer • Because of the previous two, much easier to calibrate and maintain • The main disadvantage of LIDAR: • Time is of the essence! • If anything is slow it will contribute to the spatial resolution. HOWEVER! Time is on our side:

22. Laser Pulse Plasma, Length L Scattered Light Scattered Light LIDAR – 3 Note that the profile length in time is dt=2L/c. Effectively 15cm/ns! Instead of normal 30cm/ns Detector and laser response defines spatial resolution 7cm (ITER requirement) is equivalent to ~460ps combined laser and detector response time (so det/laser response ~300ps FWHM)

23. LIDAR on JET - 1 JET is the only fusion machine in the world that has LIDAR. LIDAR only really works on big machines due to its limitations in spatial resolution. Two LIDAR systems on JET, the Core LIDAR and the Edge LIDAR. The edge LIDAR has recently been upgraded with new detectors and digitiser, so it has better resolution.

24. LIDAR on JET - 2 The total distance the laser beam has to travel is about 50m, important to keep the beam “nice”. Light is collected through a set of 6 windows

25. LIDAR on JET - 3 Collected light is relayed via a set of mirrors and lenses to the spectrometer. The Core LIDAR spectrometer has 6 detectors in a 3D layout. Each detector generates its own trace, these are then combined to form a temperature and density profile

27. Core LIDAR (C.01 group 1b – advanced plasma control) Target requirements Te 0.5 – 40 keV (10%) ne 3x1019-3x1020m-3(5%) r/a < 0.9 ~7см (a/30) 10 ms (100 Hz) NEXT: ITER LIDAR • Short line indicates the required measurement resolution of a/30. • This is equivalent to approximately 7cm in real space. • Note: the full profile from -0.9r/a to 0.9r/a is required ~2m

28. ITER LIDAR - 1

29. Beam dump ~2m Lasers enter machine boundary Mirrors Large mirrors collect suitable amount of light Exposed to plasma Mirrors Access to anywhere inside this area is similar to accessing a satellite-very infrequent ITER LIDAR - 6 • Low impact diagnostic access required • In vacuum mirror protection (passive/active) • Detectors (sensitivity, response time, wavelength) • Materials (neutrons/radiation)--fit purpose • Long term, low maintenance reliability • Laser development

30. ITER LIDAR - 2 Need to have radiation below 100uS/Hr 14 days after a shutdown in area behind plug

31. ITER LIDAR - 3 From Attila code • Influence of optical labyrinth • Minimising activation of components just outside the tokamak will be key to easier maintenance in the future

32. ITER LIDAR - 4 Several options, but none good enough yet. GaAsP GaAs NIR S-20 PhotocathodeResponse time, ns Wavelength coverage S-20 0.2 ns(below) UV, visible up to 500 nm GaAsP 0.3 ns (as above) visible up to 750 nm GaAs 0.35ns (estimated) visible up to 850 nm InGaAs ? NIR

33. ITER LIDAR - 5 • Needs reasonable energy and short pulse simultaneously • Options to chose from: • Nd:YAG (1064nm) • Ruby (694nm) • Ti:Sapphire (~800nm) • Nd:YLF (1056nm) • Wide temperature range • Time repetition expected from laser(s) – 100Hz • Also need to consider • Space envelope/ Maintainability/ Power consumption/ Data quality

34. ITER LIDAR - 6 • Laser specifications • wavelength~ ~1.06microns (1ω +2ω +cal ) • laser energy ~5J/pulse • laser pulse ~250-300ps (20GW) • Proposing 7 lasers at ~15Hz • More achievable technology • Compact footprint • Measurement capability maintained even if 1,2,3... lasers malfunction • Burst mode available to exploit plasma physics e.g. very fast MHD events

35. At the end… • This tutorial is intended as a first introduction in to Thomson scattering and not as an exhaustive review • Only some typical examples were given (mostly JET), every fusion machine has TS • I’ve only focused on incoherent TS • The aim was mainly on demonstrating how it works and how powerful a technique it can be Epilogue Thank you for your attention

36. Any extras… ?

37. Space time domain