Measurement of Gas Properties by Incoherent and Coherent Rayleigh Scattering Richard B. Miles Princeton University Dept.

1. Measurement of Gas Properties by Incoherent and Coherent Rayleigh ScatteringRichard B. MilesPrinceton UniversityDept. of Mechanical & Aerospace Engineering The Ohio State University Frontiers in Spectroscopy Feb 16-18, 2005

2. Two approaches to the measurement of local neutral gas temperature in a weakly ionized plasma • Filtered Rayleigh Scattering (Joe Forkey, Walt Lempert, Pingfan Wu, Rene Tolboom) • Uses an optically thick atomic cell for filtering the Rayleigh signal to reject background scattering • Requires a tunable, narrow linewidth laser and an atomic or molecular vapor filter • Yields a single point, line, or cross sectional plane measurement • A single pulse (10 nsec) measurement possible if pressure is known • Coherent Rayleigh Brillouin Scattering (Xinggau Pan, Mikhail Shneyder, Jay Grinstead, Peter Barker) • Four wave nonlinear effect similar to CARS • Gives very strong background rejection and high signal strength • Requires one broad band laser and one narrow line tunable laser • Yields a single point measurement, but a line measurement possible

3. Field Surrounding a Dipole k=ω/c=2π/λ ~107 m-1. For r>> λ

4. The Dipole Field For Rayleigh scattering, the dipole is driven by an incident field that creates the polarization. since we have

5. The Induced Dipole The induced polarization is proportional to the incident field. In the case of an atomic gas, the polarizability is a scalar. and For molecular gases, the polarizability is a tensor

6. Scattering Cross Section Total Scattering Power integrate over a sphere surrounding the dipole The differential scattering cross section is The total scattering cross section is so

7. Polarizability The polarizability can be written in terms of the index of refraction Note that this comes from with the 3/(n2+2) Lorentz-Lorenz factor added to account for the local field correction This gives (Air is ~1.00027) If as in a gas and

8. Power Collectedfrom a single dipole The optical system can only collect light from a small fraction of the sphere into which the light is scattered. The differential detected power per steradian is The power collected from one dipole is that differential power integrated over the collector solid angle

9. Coherent vs Incoherent Scattering • For coherent dipoles, the peak intensity is n2 times the single dipole intensity, but that only occurs where all the phases add. For many dipoles, this corresponds to a very small angle. At other angles, the intensity is low. • For incoherent scattering, the interference washes out, so the intensity increases as n, i.e. linearly with the number of dipoles and the scattering is not well collimated

10. Incoherent Scattering n= # of molecules in the observed volume For Rayleigh scattering, the density fluctuations in the air cause the interference to be washed out in all but the forward direction, where all the path lengths are the same because there is no scattering delay, so the phase of the scattered light matches the phase of the propagating light. In this direction Rayleigh scattering is suppressed and the effect reduces to the index of refraction

11. Rayleigh Signal • N = the number of dipoles per unit volume • V=the illuminated volume of the sample • ΔΩ=the collection solid angle • η=the detector and optical system efficiency • II=the incident laser intensity Laser detector

12. Filtered Rayleigh Scattering Narrow linewidth laser • Rayleigh scattering is very weak • High power laser is needed • Exclusion of background scattering Camera Test Molecular or atomic vapor Cell Section

13. Iodine • Simple to build - cell is close to room temperature • Overlaps both doubled YAG and argon ion lasers • Note that with injection locking, both Ar++ and Nd:YAG are tunable over many iodine lines • Maximum attenuation is 105 because of weak continuum absorption

14. Absorption Spectrum of Iodinein Doubled YAG region

15. Optically Thick Iodine Absorption Spectrum (measured and modeled: 3 Torr) Forkey

16. 500,000 Frame per Second Imaging of Supersonic Air withCO2 Nanoparticles and an Iodine Filter Particles in the Rayleigh range (2πr<<λ) have a large cross section so they can be used for flow visualization

17. Shock-Wave/Boundary-Layer Interaction in Mach 3 Wind Tunnel Box Car PC I2 Cell Lens PD1 Pulse-Burst Laser =0.532mm PD2 Optics y Flow x z Laser Sheet Orientation: x-y:streamwise x-z:planform I2 Cell MHz Camera

18. CO2 as a Seed Material • ~1% CO2 is added to the air upstream of the supersonic wind tunnel plenum chamber • As the flow expands through the nozzle, CO2 condenses into clusters as temperature drops • In the thermal boundary layer, the temperature recovers to close to the plenum temperature and CO2 clusters sublime Mach 2.5 FLOW 240 ANGLE RAMP • Upper limit of the average CO2 cluster size is estimated around 10 nm. • Models predicted that the CO2 clusters rapidly condense or sublime so they accurately mark the temperature discontinuity in the boundary layer

20. Laser tuned to highlight high velocity Laser tuned to observe lower velocity Mach 3 core flow Flow velocity ~600 m/s 0.053 cm-1 shift

21. Visualization of Mach 8 Flow over Three Dimensional Body 4:1 Elliptic Cone X-33 Space Vehicle Model

22. X-Y Y-Z X-Z FLOW Mach 8 Flow Over 4:1 Elliptic Cone Three Dimensional Unsteady Boundary Layer: • Pressure gradient between major and minor axis generates crossflow along circumferential direction • Crossflow vortices are predicted to cause early boundary layer transition Laser Sheet Orientations • Streamwise (X-Y) • Planform (X-Z) • Spanwise (Y-Z)

23. Flow Simultaneous Imaging of Two Planes 500 kHz, Rex=1.6×106 Spanwise View Planform View Flow

24. Spanwise sequential slices taken by pulse-burst laser Planform Single-shot taken at 16 µs 20 ms 8.8 mm 16 ms 12 ms 8 ms 37.7 mm 4 ms 0 ms Flow moving out of plane Flow Volumetric Imaging of Boundary Layer at Mach 8 Using Sequential Spanwise Images • Pulse-burst imaging of centerline boundary layer in planform orientation revealed slowly-evolving structures • 3-dimensional image of transitional boundary layer is reconstructed under “frozen flow” assumption

25. 3-D Reconstruction of 4:1 Centerline Region(Rex=1.57 million) FLOW

26. Boundary Layer Structure over 2:1 Elliptic Cone(Rex=1.3 million)

27. Pressure, Temperature and Velocity Images in Air by Filtered Molecular Scattering • Mach 2 vertical supersonic jet is observed • The laser is expanded to a sheet and frequency tuned • Multiple images give the local, frequency shifted Cabannes line convolved with the iodine filter line at each pixel • Deconvolution knowing the iodine filter shape gives the Cabannes line shape at each pixel • Pixel by pixel curve fitting to theory gives T, v, P

28. Rayleigh Scattering Spectrum(of Nitrogen)

29. observer k1 Laser source k2 Scattering length, Λ Cabannes Line Broadening Y = scattering length / mean free path

30. Kinetic Regime • If Y < 1, then in the Knudsen Regime – no collective effects. The Cabannes line is Gaussian in this regime • If Y > 1, then in the hydrodynamic regime – collective effects dominate • Acoustic waves are important • In this regime there are three peaks, a central peak associated with non propagating entropy fluctuations and two side Brillouin peaks associated with propagating sound waves

31. Cabannes (central Rayleigh) Line in Air Showing the Y parameter effect

32. Cabannes Line of Air at standard conditions with doubled YAG laser with detection at 90o Y = 0.7

33. Average image Single shot image Mach 2 Underexpanded Supersonic Air Jet

34. Temperature, pressure and velocity of a Mach 2 free jet with weak crossing shocks

35. Coherent Rayleigh Brillouin Scattering (CRBS) • Two pump beams create moving gratings • Ponderomotive forces drive moving, grating like density fluctuations in the synchronized velocity groups • Coupling is to the polarizability of the molecule – force occurs for monatomic as well as polyatomic molecules • The density of gratings created reflects the thermal velocity distribution • Probe laser Bragg scatters off the density gratings • Temperature is found from the spectral profile of the coherent signal beam observed ~10 meters from the sample volume

36. Coherent Rayleigh-Brillouin ScatteringPhysical process z

37. The optical dipole force produces the density fluctuations. Polarizable molecules feel a force toward the region of high field

38. f(v) v v = /k Coherent Rayleigh Scattering in Weakly Ionized GasesHow is the intensity spectrum related to temperature? • The molecules with velocity close to the wave phase velocity will be reorganized by the ponderomotive force leading to a moving density grating • I() is then related to f(v=/k). • Conclusion is: The width of the intensity spectrum depends on (T/m)1/2. The spectrum is closely Gaussian, about 10% wider than the spontaneous Rayleigh spectrum.

39. Coherent Rayleigh-Brillouin Scattering in molecular gasesTheory • Theory based on the Wang-Chang-Uhlenbeck Equation • Internal energy modes considered • Perturbative method, linearized equation, model collision term • Gas density perturbation waves: generation by the optical dipole force and relaxation through particle collisions

40. Coherent Rayleigh-Brillouin Scattering in molecular gasesTheory: Wang-Chang-Uhlenbeck equation fi is the space –velocity-time distribution function for molecules in state i. At equilibrium, fi has a Gaussian distribution of velocities and a Boltzmann distribution of states. The forcing term is from the laser interaction and accelerates along the z axis:

41. Perturbation Approach At equilibrium, the distribution function is , , and where The distribution function is assumed to be perturbed and the equations are solved for the dimensionless parameter,

42. Gas parameters needed • Mass • Shear viscosity • Bulk viscosity • Thermal conductivity • Dimensionless internal specific heat capacity (1 for O2 and N2, 2 for CO2)

43. Yip & Nelkin (1964) theory for monatomic gases Pan, Shneider & Miles, PRL, 2002

44. The Experiment • Argon plasma at 50mb • Pump laser is Frequency doubled Nd:YAG • 24.8 GHz (FWHM) with 250 MHz longitudinal mode structure • Split and intersected in the gas at 1780 crossing angle • Focal diameter is 200 μm diameter • 6 mJ per pulse • Polarized out of plane • Probe laser is injection locked and tunable frequency doubled Nd:YAG • 150 MHz linewidth • ~1 mJ per pulse • Polarized in plane • Fabry Perot Etalon • 99.6% mirror reflectivity at 532 nm • Finesse of 215 • Free Spectral Range of 11.85 GHz • Wavelength Monitoring Etalon FSR = 900 +/- 0.2 MHz

45. Experimental Details • The pump beams produce a spectrum of interference patterns • The patterns only couple to the gas over the region of kinetic motion • The pump line width is broad compared to the kinetic spectrum, so it is considered constant • The 250 MHz beat frequency is removed by Fourier transforming, filtering, and then back transforming the data • The probe laser is scanned and the intensity of the scattering is monitored by a fixed etalon • The intensity of the shifted scattering is a measure of the number of molecules in the kinetic (velocity) state that produces that shift. • The probe is polarized orthogonal to the pump to eliminate background noise

46. Coherent Rayleigh-Brillouin ScatteringExperiment setup

47. Experiment setup photo in Weakly Ionized Gases

48. Coherent Rayleigh Scattering in Weakly Ionized GasesData shows the mode structure of the pump laser

49. Coherent Rayleigh Scattering in Weakly Ionized GasesA sample result in argon gas (Tthermocouple = 293 K +/- 1 K)

50. Coherent Rayleigh Scattering in Weakly Ionized GasesA sample result in argon glow discharge