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Diagnostics of Fusion Plasmas Spectroscopy Ralph Dux European Joint PhD Programme, Lisboa, 10.2.2009 The Methods Passive Spectroscopy (line averaged) • X-ray, soft X-ray impurity species , impurity densities, ion temperature, velocity • Visible (VUV) impurity species, impurity influx, hydrogen influx, electron density Active Spectroscopy (spatially resolved) • Charge exchange recombination spectroscopy ion temperature, velocity (radial electric field), impurity density of fully ionized species • Motional Stark Effect Polarimetry direction of magnetic field Important reactions for ionisation and excitation balance Z A e electron impact ionisation photoionisation electron impact excitation A h Z photon absorption A e' e' ' three body recombination Z A h Z A e Z 1 Z 1 A e radiative recombination Z* A e' electron impact de-excitation Z* A spontaneous photon emission Z Z A h e A e' photon absorption bremsstrahlung Reaction rates: product of densities x rate coefficient (atomic physics) Contributions to the plasma radiation Energy levels of atoms, ions and molecules (dimers) Energy levels of atoms, ions and molecules (dimers) Radiative transitions between bound states Radiative transitions between bound states Interference on gratings and crystals Types of spectrometers for different wavelength ranges Density of emitting ions from spectroscopy Density of emitting ions from spectroscopy Corona ionisation balance In fusion plasmas (and in the solar corona): low electron density three body recombination rate (ne2) << radiative recombination rate (ne) Balance of: electron impact ionisation = radiative recombination nZ ne S Z ,Z 1 (Te ) ne nZ 1 Z 1, Z (Te ) nZ 1 S Z , Z 1 (Te ) nZ Z 1,Z (Te ) ionisation degree is independent of electron density • charge state of ion increases with electron temperature • low-Z impurities are fully ionized in large part of the plasma ( no line emission from light elements) • medium to high-Z impurities can be dedected • hydrogen like ions: Eion=13.6eV Z2 Corona ionisation balance Argon ions with filled electron shells are most stable (He-like, Ne-like …) He- and H-like ionsation stages of Ar still present up to the plasma center Corona ionisation balance Tungsten fractional abundance 1.0 ionisation stages of tungsten 28+ 27+ 37+ 46+ 38+ 43+ 35+ 45+ 44+ 55+ 56+ 61+ 64+ 63+ 62+ 0.1 0.01 modified CADW+408 0.001 1000 Te [keV] 10000 Th. Pütterich Ph.D. thesis 2005 Impurity density determination X-ray spectroscopy Impurity density determination X-ray spectrum of tungsten spectral radiance [10 5 W m-2 sr -1nm -1] #16778 Te,cntr = 3.9 keV 1.5 74W - measurement This line from W46+ is used for density evaluation at AUGD. n=1 n=2 0 ADAS modelled spectrum 38+ 49+ W W 1.5 0 HULLAC modelled spectrum 38+ 49+ W W 1.5 0 0.4 0.5 0.6 Th. Pütterich, PhD thesis 2005 0.7 [nm] 0.8 Impurity density determination tungsten concentrations Impurity influx measurements Visible Spectroscopy Neutral impurity atoms (or low ion stages) radiate sufficiently strong visible line emission. Can be used to determine the erosion rates at the plasma walls (impurity influx) Impurity influx measurements Visible Spectroscopy 1dim continuity equation for neutrals (small recombination rates = ionising plasma) n0 x S 01ne n0 10 ne n1 t x ionisation recombination0 temporal equilibrium: n0 0 Integrate up to l, where all neutrals are ionised: x l x dx ( 0 ) x 0 x 0 S01ne n0 dx l l x0 0 The photons emitted on transition ik per area and time: ph ik l X 1i n0 4 dx Aik ne n0,i dx Aik ne dx ne Bik X 1i n0 dx 0 0 0 0 A in l l ph ik l n i Excitation rate and ionisation rate shall have similar temperature dependence (excitation energy ionisation energy) around x0 where the excitation and ionisation mainly occurs: S T ( x)n n dx l x (0) ph ik 0 l 0 01 e e 0 X 1i Te ( x) Bik ne n0 dx S01 Te ( x0 ) f x ne n0 dx l ph ik 0 X 1i Te ( x0 ) Bik f x ne n0 dx l 0 ikph S01 Te ( x0 ) X 1i Te ( x0 ) Bik Impurity influx measurements Visible Spectroscopy x (0) ph ik L 0 L 0 S01ne n0 dx X 1i Bik ne n0 dx ikph S XB S/XB-value: • number of ionisations per emitted photon • gives impurity influx from photon flux • independent of ne S/XB of W I 400.875 nm 5d5(6S) 6s - 5d5(6S) 6p 7S – 7P° S/XB 100 10 1 A. Geier et al., Rev. Sci. Instr. (1999) A. Geier et al., Plasma Phys. Control. Fusion (2002) Steinbrink et al., 24th EPS 1997 calculations: I Beigman et al., Plasma Phys. Control. Fusion (2007) Tw= 0.3 eV Tw= 1 eV 0.1 5 10 15 20 25 30 Te / eV Impurity influx measurements Influx of tungsten from the divertor strike point tiles Strongest W-erosion in the divertor (modulation due to ELMs) Beyond impurity densities and fluxes spectroscopy can also deliver information about • temperatures • electron density • B-field from the line shape or the splitting of spectral lines Natural line width Oscillation with decay time 1 1 m 1 1 n m Amk k m Emn Em En 1 n Ank k n h Amk Ank 2 k m k n Spectral emission coefficient: mn FWHM 1 mn h FWHM Emn 2 2 FWHM 2 2 Doppler shift and Doppler broadening measurement of ion temperature and drift velocity Active Spectroscopy on Hydrogen Beam Charge Exchange Recombination Spectroscopy Active Spectroscopy on Hydrogen Beam Charge Exchange Recombination Spectroscopy Stark broadening (Hydrogen) Linear Stark Effect In Hydrogen the electric field leads to a line splitting linear with the field strength ( linear Stark effect) E nkE0 E0 k 0, 1, ...., n 1 3 Fea0 2 In the edge plasma Linear Stark broadening due to time varying microfields from electrons and ions can dominate Doppler broadening measurement of ne Line splitting of the Balmer lines of Hydrogen (Balmer= transitions between states with principal quantum number n=3,4,5,6,7 2) Stark broadening (Hydrogen) Linear Stark Effect In Hydrogen the electric field leads to a line splitting linear with the field strength ( linear Stark effect) E nkE0 E0 k 0, 1, ...., n 1 3 Fea0 2 In the edge plasma Linear Stark broadening due to time varying microfields from electrons and ions can dominate Doppler broadening measurement of ne Profile of Balmer- lines of Deuterium (n=7 2) measured in the ASDEX Upgrade divertor Active Spectroscopy on Hydrogen Beam Motional Stark effect polarimetry Observe D spectrum of D0 beam • wavelength shifted due to Doppler effect • electric field in reference frame of D-atoms due to movement in magnetic field F vbeam B leads to splitting of energy levels via the linear Stark effect: E nkE0 k 0, 1, ...., n 1 3 E0 Fea0 2 60kV D0 beam, B=2T: F 4.8 106 Vm -1 E0 3.8 104 eV Polarization -components (m=0): parallel to el. field -components (m=±1): perpendicular to el. field D0 (60keV) Lines-of-sight Active Spectroscopy on Hydrogen Beam Motional Stark effect polarimetry Observe D spectrum of D0 beam • Wavelength shifted due to Doppler effect • electric field in reference frame of D-atoms due to movement in magnetic field F vbeam B leads to splitting of energy levels via the linear Stark effect: E nkE0 k 0, 1, ...., n 1 3 E0 Fea0 2 60kV D0 beam, B=2T: F 4.8 106 Vm -1 E0 3.8 104 eV Polarization -components (m=0): parallel to el. field -components (m=±1): perpendicular to el. field D0 (60keV) Lines-of-sight Active Spectroscopy on Hydrogen Beam Motional Stark effect polarimetry Observe D spectrum of D0 beam • Wavelength shifted due to Doppler effect • electric field in reference frame of D-atoms due to movement in magn. field F vbeam B leads to splitting of energy levels via the linear Stark effect: E nkE0 k 0, 1, ...., n 1 3 E0 Fea0 2 60kV D0 beam, B=2T: F 4.8 106 Vm -1 E0 3.8 104 eV Polarization -components (m=0): parallel to el. field -components (m=±1): perpendicular to el. field Active Spectroscopy on Hydrogen Beam Motional Stark effect polarimetry • unshifted -component is selected with very narrow interference filter (just works for one beam voltage) • polarization direction of light is determined (accuracy 1/10 degree) Additional radial electric field changes polarization direction: e F vbeam B Ψ Ψ measurement of 2 beam energy components is used to separate both contributions Line splitting in the magnetic field Zeeman Effect H H0 μ B (L 2S).B Level splitting: • Zeeman case: angular momentum of orbit and spin remain coupled in ext. B-field ELSJmJ e mJ g J B 2me J J 1 S S 1 LL 1 gJ 1 2 J J 1 measurement of B? No! but can be used to get the main emission region on the LOS Line splitting in the magnetic field Zeeman Effect H H0 μ B (L 2S).B Level splitting: • Zeeman case: angular momentum of orbit and spin remain coupled in ext. B-field ELSJmJ gJ 1 e mJ g J B 2me J J 1 S S 1 LL 1 2 J J 1 measurement of B? No! but can be used to get the main emission region on the LOS B-field splitting for CII here more emission from HFS Line splitting in the magnetic field Zeeman Effect H H0 μ B (L 2S).B Level splitting: • Zeeman case: angular momentum of orbit and spin remain coupled in ext. B-field ELSJmJ gJ 1 e mJ g J B 2me J J 1 S S 1 LL 1 2 J J 1 measurement of B? No! but can be used to get the main emission region on the LOS B-field splitting for CII here more emission from LFS Line splitting in the magnetic field Zeeman Effect H H0 μ B (L 2S).B Level splitting: • Zeeman case: angular momentum of orbit and spin remain coupled in ext. B-field ELSJmJ e mJ g J B 2me J J 1 S S 1 LL 1 gJ 1 2 J J 1 measurement of B? No! but can be used to get the main emission region on the LOS B-field splitting for Balmer- of D dominated by LFS