Shadowgraphy for Plasma Diagnostics

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ShadowgraphyScreenICCD CameraBeam ExpanderDiode LaserMirrorNd: YAG beamShadowgraphy is an optical method that reveals non-uniformities in transparent media Works on the refractive effect of light and generates corresponding intensity patternsShadowgraphy Principlen = 1.12 10132D plume lengthE (aSensitivity(I Eg xE ! ! g I d xx xE 1 x 2n w xx g xx 2S!g Sensitivity ~10-4Differences in light intensity are proportional to the second spatial derivative of refractive index fieldShadowgraphy for temperature measurementThe refraction in the plume is given by ideal gas relationn plume nmediumPplume Tmedium ! Pmedium T plumeOr by Gladstone-Dale formula, which gives T =293 x 2.73 x 10-4 /(n-1) K Requires beforehand knowledge of plasma plume refractive index and temperatureShadowgraphy for temperature measurementOther methods 1. By point to point comparison of shadowgraphic image with the simulated image 2. Using Abel transformationThe picture of the plasma plume obtained by using the high-speed camera is the projection of the real, 3-dimensional plume onto a plane. The density of species in the volume of the plume can be calculated from this information using the inverse Abel transform.Shadowgraphy for density measurementAccording to Gladstone-Dale formula n-1 =KV K=Gladstone-Dale coefficient V=plasma density e= electronic charge Me= electron mass M = molar weight of the fluid L= 2.687 x 1019 cm-3 is Loschmidts number fi is oscillator strength Pi is resonant wavelengthe2 L K! 2Tc 2 e Mf i Pi2 P2 P2 P2 iK=0.2259 cm3/g at T=288K and P=670.4nm in airAgain beforehand knowledge of plasma plume refractive index is required Or Abel transform can be usedPlasma ShadowgramIntensity distribution after Abel transformationCorresponding electron density distributionResonant and non-resonant shadowgraphyResonant shadowgraphy shows enhancement in refractive index and hence enhances the sensitivity of the system as compared to non-resonant case because the refractive index n and absorption E depend on the frequency [ of the probe beam asNi is no. density of lower level population fi is oscillator strengthKi is damping constantme and qe the mass and charge of electronShadowgraphy and fast imagingPhotography depends on intensity of emission from the plasma and depends on number density of excited atoms. Shadowgraphy dependents on change in refractive index in the plasma. Both techniques could provide information regarding the shape and size of the expanding plume and its density pattern. Shadowgraphy has following advantages over photography: Since the plasma emission intensity depends on number density of excited atoms therefore the imaging technique gives only the information about the excited species. On the other hand shadowgraphy gives overall picture of all the species. Accurate information about the plasma boundary, which can be obtained by shadowgraphy, is important from two reasons: allows to determine actual sizes and shape of plasma, determines integration limits in the Abel transformation.Shadowgraphy ApplicationsShadowgraphy is used to visualize:- Plasma plume dynamics including size, shape of the plume and velocity-Shock waves- Refractive index/density gradientsMay be helpful for visualization of oscillations in the laser produced plasmaSchlieren methodSnells law givesScreenn2 n1 = (E2/2) + E tanUICCD CameraBeam ExpanderDiode LaserMirrorKnifeedgeNd: YAG beamKnife-edge modifies spatial frequency spectrum and converts phase variations into intensity variations Sensitivity higher than shadowgraphic method ~ 10-9Schlieren method(I Sensitivit yS ! ! I ! f 2 L xn a.n xxL21 xn 1 n xx dz LL= length of plasma f = focal length a = width of source imagexn xxmin! 0.05n a L fDensity is given by Gladstone-Dale formula n-1 =KVe2 ! 2Tc 2 meK=0.2259 cm3/g at T=288K and P=670.4nm in airf i Pi2 P2 P2 Pi2