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Thomson Scattering Thomson scattering Roberto Pasqualotto 11 February 2009 European Joint Ph.D Programme on Fusion Science and Engineering 2° Advanced Course in Lisboa, February 2009, On Diagnostics and Data Acquisition [email protected] Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 1/181 OUTLINE Theory: TS from single electron TS from plasma Æ Te & ne TS measurement: experimental issues TS diagnostic: main components Examples of existing TS systems: RFX TCV Textor HRTS LIDAR JET ITER core LIDAR issues & design Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 2/181 LASER-AIDED PLASMA DIAGNOSTICS Laser-aided diagnostics are widely applied in the field of high-temperature plasma diagnostics for a large variety of measurements. Various types of laser-aided plasma diagnostics exist, all based on different physical interactions between the electromagnetic wave from the laser and the plasma. In general one can distinguish interaction based on: (a) absorption and/or reemission, (b) changes in the refractive index, (c) changes in the polarization ellipse, (d) scattering. Incoherent Thomson scattering is used for highly localized measurements of the electron temperature and density in the plasma. Coherent Thomson scattering yields information on the fast ion population in the plasma and/or depending on the geometry and wavelength chosen electron density fluctuations. Interferometry and polarimetry are often combined in a single diagnostics setup to measure the electron density and the component of the magnetic field parallel to the laser chord. Density fluctuations can be measured by means of phase contrast imaging, scattering, and various other laser-aided techniques. A. J. H. DONNÉ, C. J. BARTH, H. WEISEN - FUSION SCIENCE AND TECHNOLOGY VOL. 53 FEB. 2008, p.397 Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 3/181 LASER-AIDED PLASMA DIAGNOSTICS Active diagnostics with lasers as the probing source have a number of distinct merits: (a) the laser beam can be focused in the plasma, resulting in good spatial resolution; (b) the measurements do not perturb the plasma because of the relatively small interaction cross sections; (c) lasers have a high spectral brightness Æ good signals @ t,x,λ; (d) both with pulsed and continuous wave laser systems a good temporal resolution can be obtained; (e) the lasers (and in many applications also the detectors) can be positioned far from the plasma, where they can be more easily maintained. Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 4/181 Why Thomson Scattering? • What is it? – Laser beam scatters off of electrons in the plasma – doppler effect gives wavelength shift • Straightforward stand alone measurement Laser beam ve (direct method: no models, assumptions,..) r to c te e • Electron velocity distribution D directly observed (ne, Te) • Accurate spatial location via imaging or time of flight Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 5/181 Thomson Scattering • Scattering of electromagnetic radiation by a charged particle. • The electric and magnetic components of the incident wave accelerate the particle, which in turn emits radiation in all directions. • Phenomenon was first explained by J.J.Thomson. • It can be split into coherent and incoherent scattering (more later). • The experimental application of TS as a diagnostic tool had to wait for the development of high power light sources, e.g., the Q- switched ruby laser in the early 1960s. Since then, various plasma parameters have been measured by means of this technique. • The first demonstration of TS as a suitable diagnostic tool for hot plasmas was given by Peacock et al. in 1969 when they measured the electron temperature and density in the Russian T3 tokamak. • Further developments: Te and ne along the full plasma diameter, resolving up to ~ 100 spatial elements with time separations of ~10 µs to 10 ms. Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 6/181 Role of Thomson scattering in Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 7/181 Thomson scattering spectrum In this lesson the focus will be on: Logic of steps to derive TS spectrum (less on math) What can be measured Under which conditions John Sheffield, “Plasma scattering of electromagnetic radiation”, Academic Press 1975 S.E. Segre, “Thomson scattering from a plasma” Course on Plasma diagnostics and data acquisition systems, Varenna 1975, P Nielsen, “Thomson scattering in high temperature devices” , Varenna 1986, Some PhD Thesis: Rory Scannel (MAST), Alberto Alfier (RFX), R. Pasqualotto (RFX) Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 8/181 Thomson scattering from a single electron (classical limit of the Compton scattering) Incident electric field electron ˆ - scattering of an incident photon r i Propagation by a moving electron (β=v/c) E & i ˆ scattering - electron energy is constant Incident θ k directions photon (Ee>>ħω) scattering sˆ angle Observer The scattered radiation is frequency shifted as a double Doppler effect takes place, one in the reception, one in the emission of radiation by the electron: 1. the photon approaching the 2. the photon leaving the moving moving electron electron Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 9/181 TS as limit of Compton scattering Conservation of energy and momentum 2 2 ħωi + mic = ħωs + msc ħki + mivi = ħks + msvs 2 ½ where: mi,s = m0/(1-βi,s ) The solution to these equations is: When incident wave has frequency ω such that 2 ħωi << mec 2 ωs = ωi (1-βi •êi) / (1-βi •ês + (1-cos(θ))ħωi/mic ) ÆThomson scattering, limit effect of Compton Scattering, 2 Ignoring the term ħωi/mec we get in which the quantum effect may be neglected: ωs – ωi = ∆ω = (ks -ki) • ve = k • ve the electron moves at same velocity as before Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 10/181 TS as limit of Compton scattering (some math) Seen by the electron, initially stationary (vi =0): With simple algebra: In the TS limit Transforming back to the lab reference system: Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 11/181 TS as limit of Compton scattering (some math) Not relativistic Compton scattering 2 ħωi << mec 1 eV << 0.5 MeV 1 eV energy of a photon with λ = 1 µm Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 12/181 TS from single electron Incident wave electric field: and associated magnetic field: Force on the electron by the e.m wave: with Acceleration produced by this force negligible if v<<c and m’=m with Such an accelerated electron produces an e.m. field. At an observation distance ρ large compared to electron displacement during measurement, electrostatic part (∝1/ρ2) is negligible. Radiative part (∝1/ρ) is the scattered e.m. wave: Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 13/181 TS from single electron distance electron – point of observation unit vector in propagation direction quantities in bracket evaluated at retarded time retarded time: delay between the photon emission and the moment at which it reaches the observer Phase of scattered field = phase of incident field (evaluated at ret- time) if v = const (influence of e.m. wave on electron is ignored and no static B field): ρ Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 14/181 TS from single electron The time dependent part of the phase indicates that the scattered wave is monochromatic, with a frequency ωs: Scattered radiation is still monochromatic Displacement in frequency proportional to the component of the e velocity in the k direction This expression is valid also at relativistic velocity. If we want to observe the drift velocity of a plasma, scattering geometry must be such that k ·vd ≠ 0 When Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 15/181 TS from single electron Only a flavour of full math formulation Incident wave electric field: and associated magnetic field: Equation of motion of the electron accelerated by the e.m wave: with Acceleration produced by this force Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 16/181 TS from single electron Only a flavour of full math formulation Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 17/181 TS from single electron Low electron velocity: non-relativistic approximation Standard geometry: 90° scattering ss the classical radius of electron Intensity of scattered wave does not depend on ψ and it is zero in the direction of the polarization (ξ=0) of the incident wave (not true if β finite) Max intensity when ξ = π/2 (s ┴ Ei) Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 18/181 TS from single electron Measured quantity is scattered power per unit solid angle: Is the Poynting vector Averaging over many periods, and using Incident intensity Is the Thomson scattering cross section Scattered power ∝ 1/m2 Æ in a plasma contribution from the ions is negligible : m_e = 10-32 kg m_p = 10-27 kg Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 19/181 TS from single electron non relativistic from Sheffield relativistic Roberto Pasqualotto Eur.PhD Fusion: Thomson scattering - 11th February 2009 20/181 TS from a plasma Total E given by contribution from each electron: Average scattered power First
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