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Plasma Diagnostics Lecture.Key LA3NET School | Salamanca, Spain | October 1st, 2014 Advanced diagnostics Plasma density profile measurements and synchronisation of lasers to accelerators J. Osterhoff and L. Schaper Deutsches Elektronen-Synchrotron DESY Outline > Importance of the plasma density profile > Measurement techniques > Interferometry > Absorption spectroscopy > Rayleigh scattering > Raman scattering > Laser induced fluorescence > Synchronisation of lasers to accelerators > Summary Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 002 Access to novel in-plasma beam-generation techniques requires control over plasma profile in LWFA/PWFA > Density down-ramp injection J. Grebenyuk et al., NIM A 740, 246 (2014) IB & 1kA > Laser-induced ionization injection (Trojan Horse injection) B. Hidding et al., Physical Review Letters 108, 035001 (2012) IB & 5kA > Beam-induced ionization injection A. Martinez de la Ossa et al., NIM A 740, 231 (2014) IB & 7.5kA > Wakefield-induced ionization injection A. Martinez de la Ossa et al., Physical Review Letters 111, 245003 (2013) IB & 10 kA Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 003 Access to novel in-plasma beam-generation techniques requires control over plasma profile in LWFA/PWFA > Density down-ramp injection J. Grebenyuk et al., NIM A 740, 246 (2014) n0 = 1.2 x 1018 cm-3 IB & 1kA > Laser-induced ionization injection (Trojan Horse injection) B. Hidding et al., Physical Review Letters 108, 035001 (2012) Driver: Eb = 1 GeV, Ib = 10 kA, Qb = 574 pC σz = 7 μm, σx,y = 4 μm, εx,y = 1 μm IB & 5kA injection > Beam-induced ionization injection A. Martinez de la Ossa et al., NIM A 740, 231 (2014) acceleration IB & 7.5kA > Wakefield-induced ionization injection A. Martinez de la Ossa et al., Physical Review Letters 111, 245003 (2013) IB & 10 kA Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 003 Laser diffraction mitigation in LWFA by transverse plasma density tailoring (plasma channel) 2 ZR Laser Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 004 Laser diffraction mitigation in LWFA by transverse plasma density tailoring (plasma channel) 2 ZR Laser Plasma waveguide Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 004 Laser diffraction mitigation in LWFA by transverse plasma density tailoring (plasma channel) 2 ZR Capillary discharge plasma waveguides •Plasma fully ionized for t > 50 ns Laser •After t ~ 80 ns plasma is in quasi-equilibrium: Ohmic heating is balanced by conduction of Plasma waveguide heat to wall •Ablation rate small: cap. lasts for >106 shots 17 19 -3 •np ≈ 10 - 10 cm Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 004 Laser diffraction mitigation in LWFA by transverse plasma density tailoring (plasma channel) 2 ZR Capillary discharge plasma waveguides •Plasma fully ionized for t > 50 ns Laser •After t ~ 80 ns plasma is in quasi-equilibrium: Ohmic heating is balanced by conduction of Plasma waveguide heat to wall •Ablation rate small: cap. lasts for >106 shots 17 19 -3 •np ≈ 10 - 10 cm In this example: ZR = 2 mm, guiding over 16 mm, guiding efficiency > 90 % Karsch, Osterhoff et al., New J. Phys. 9, 415 (2007) Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 004 Electron-laser dephasing mitigation in LWFA by longitudinal plasma density tailoring (plasma taper) Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 005 Electron-laser dephasing mitigation in LWFA by longitudinal plasma density tailoring (plasma taper) Constant density plasma Laser pulse, plasma wave travel with vwave = vg < c Electrons travel with ve ≈ c > vwave ⇒ they outrun the accelerating field structure Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 005 0.20 0.15 E 0.10 0.05 Electron-laser dephasing mitigation in LWFA by 0.00 longitudinal plasma density tailoring (plasma0.0 0.2 taper)0.4 0.6 0.8 1.0 1.2 ⇥ z Eˆ z 800 Ideal taper Linear taper 600 No taper γ Γ 400 Energy gain Energy 200 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ⇥ Normalized propagationz distance γ z Constant density plasma RisingEˆ density plasmaγ z Laser pulse, plasma wave travel with vwave = vg < c Plasma wave phase velocity vwave may be set to ve ⇒ electrons can be phase locked Electrons travel with ve ≈ c > vwave 13 1 18 3 Np =1 a0 =0.5 ⇤i =5.64 10 − n0 = 10 − ⇒ they outrun the accelerating field structure → Rittershofer15 1 et al., Phys. Plasmas 17∗, 0631044 (2010) ⇤ =2Jens.36 Osterho10ff | plasma.desy.de⇥ = | LA3NET 800 School, rSalamanca= 10 | Oct 1, 2014s | =2 Page .00355 N l ∗ − l l − l Interferometry >The instrument: M1 compensation plate M2 >Two wavefronts are overlapped and BS interference pattern resulting form phase difference is detected. Source >When can two waves interfere? x >path difference arms < coherence length ≈ λcental²/Δλ Detector >fs laser: λ = 800nm, Δλ = 80nm -> few µm! I x Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 006 Interferometry >Path difference: M1 compensation plate M2 BS Source typical: vacuum as reference and thus Nref=1 z1 z2 >Crucial for interferometers: Stability Detector >systems with sophisticated vibration damping, Δ� ≈ 10-5 more typical: Δ� ≈ 10-1 detection circuit and initial phase control resolve B. V. Weber and S. F. Fulghum, “A high-sensitivity two- color interferometer for pulsed power plasmas,” Rev. Sci. Instrum.,Vol. 68, pp 1227-1232, Feb. 1997 Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 007 Interferometry In Gases: Index of refraction varies 1"E+1" linearly with density (until N=Nvac) Thus when Nref =1 1"E+0" fringe'shi*' Example: Hydrogen 1"E$1" N-1 (at atmospheric): 1.3991x10-4 interaction length: 1mm 1"E$2" light source: NdYAG 532nm 1"E+17" 1"E+18" 1"E+19" 1"E+20" hydrogen'density'/'1/cm³' Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 008 Refractive index in plasma Assumptions: cold, non-magnetised, collision free Dispersion relation in plasma: Refractive index: Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 009 Summary on interferometry Total phase shift: Δ� Gladstone-Dale constant -15 2 Usually: c1 << c2 ≈ 5x10 m >Densities which can be measured depend on interaction length and wavelength used >Even in weakly ionised plasmas neutral background can be neglected >No calibration required >Pulsed lasers allow for high time resolution >Usually limited to 1018 cm-3 at plasma dimensions <mm λ Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 0010 72, 1, 156, 1981 ff Osterho Jens 00 00 Page | LA3NET School, Salamanca | Oct 1, 2014 | | 2014 1, Oct | Salamanca School, LA3NET | plasma.desy.de | 11 phase shift and Interferometry, J. Opt. Soc. Am., Vol. Analysis for Computer – Based Topography Fringe – Pa>ern – Transform Method of M. Takeda, H. Ina and S. Kobayashi, Fourier unwrap unwrap n = critical density k = wave vector η = index of refraction n = electron density Δ = phase shift c ϕ e n n interferogram “data” discontinuous phasephase distributiondiscontinuous distribution phase distribution distribution phase retrieved phase retrieved iFFT iFFT reference (no plasma) (no reference with plasma with reference interferogram FFT FFT Interferometry What did we measure? FFT of interferogram interferogram of FFT interferogram Measured Measured interferogram How do we determine the phase shift? shift? phase the determine we do How How do we determine the phase shift? Why did we measure the phase shift? 72, 1, 156, 1981 ff Osterho Jens 00 00 Page | LA3NET School, Salamanca | Oct 1, 2014 | | 2014 1, Oct | Salamanca School, LA3NET | plasma.desy.de | 11 phase shift and Interferometry, J. Opt. Soc. Am., Vol. Analysis for Computer – Based Topography Fringe – Pa>ern – Transform Method of M. Takeda, H. Ina and S. Kobayashi, Fourier unwrap unwrap unwrap unwrap n = critical density k = wave vector η = index of refraction n = electron density Δ = phase shift c ϕ e n n n n interferogram “data” discontinuous phasephase distributiondiscontinuous distribution phase distribution distribution phase distribution phase distribution phase discontinuous phase distribution distribution phase discontinuous retrieved phase retrieved iFFT iFFT iFFT iFFT reference (no plasma) (no reference with plasma with reference interferogram FFT FFT FFT FFT Interferometry What did we measure? FFT of interferogram interferogram of FFT FFT of interferogram interferogram of FFT interferogram Measured Measured interferogram Measured interferograminterferogram Measured How do we determine the phase shift? shift? phase the determine we do How How do we determine the phase shift? How do we determine the phase shift? shift? phase the determine we do HowHow do we determine the phase shift? Why did we measure the phase shift? How does the electron density determinate from the phase shift? z Phase Distribution Lineout f0r zm Δφ(y,zo) How to retrieve space resolved density >known: problem is radially symmetric Fitted function zm >“unwrap” density profile (Abel inversion) y y y y r symmetry axis Density Profile [m-3] x Δ� Jens Osterhoff | plasma.desy.de | LA3NET School, Salamanca | Oct 1, 2014 | Page 0012 Absorption spectroscopy >Transmission of light through a medium is measured to calculate the line of sight integrated density. >Plasma emission (decreases by 1/r2 with distance) can usually be neglected I >Lambert-Beer law applies: >In case of little absorption � >Here
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