Investigator: Dr. Yue Wu
It has long been known that the refractive index of air is proportional to the gas density, with the constant of proportionality known as the Gladstone-Dale “constant”. This “constant” is in turn related to the microscopic polarizability of atoms and molecules through the relationship , where is the scalar polarizability and is the permittivity of free space, assuming the medium is dilute. In many commonly encountered environments, such as low speed flows and hydrocarbon combustion, the Gladstone-Dale “constant” is approximately constant,,. However, in non-equilibrium hypersonic flows, species are found in appreciable quantities in their excited states due to high excitation energy in hypersonic flight condition. As the result, species alter their polarizability, the Gladstone Dale “constant”, and the Rayleigh cross-section.
In this project, we carried out a lab-scale test bed to quantitatively study the Gladstone Dale “constant” and scalar polarizability under thermal nonequilibrium gas conditions. The non-equilibrium conditions of flight are reproduced by a pulsed nanosecond discharge in quiescent gas (90 Torr N2) as shown in the figure below. The discharge afterglow offered an ideal non-equilibrium condition to help us investigate the properties (i.e. refractive index, gas rotational and vibrational temperature).
The first property, the refractive index value is measured by using Mach-Zehnder interferometer by observing the optical path difference (OPD) as shown in the figure below. The OPD is related to the index of refraction by , where is the refractive index and is the optical path length. The refractive index is both dependent on the gas density and polarizability by the Lorentz-Lorenz relation,, where is the gas number density and is the scalar polarizability as a function of wavelength, rotational and vibrational temperatures. In order to quantify , we need to know , , and .
In this project, spontaneous Raman scattering spectroscopy is then used to measure the vibrational temperature and rotational temperature which are further applied to infer gas density and calculate the Gladstone-Dale term and scalar polarizability. As shown in the plot below, spontaneous Raman scattering is collected from an 8-mm-length, 75-µm-diameter volume of the focused probe beam through the center of
plasma region halfway (∼2.5 mm) between the top and bottom electrodes. The plot below shows a typical raw image of spatially-resolved spontaneous Raman spectra in N2 during the discharge afterglow at a time delay of 10 µs. High vibrational levels (up to ν=7) are observed off-axis. The low Raman signal on-axis indicates a low density and likely the high rotational temperature.
By using Mach-Zehnder interferometry and spontaneous Raman scattering spectroscopy, the refractive index n, rotational temperature, and vibrational non-equilibrium state have been quantitatively measured. The scalar polarizability as the function of the rotational temperature and vibrational temperature has been shown in the plot below, respectively. Specifically, at the time delay of 10 s, the scalar polarizability has a rapid increase with the rotational temperature range of 300 to 800 K which is due to the significant vibrational population at higher energy levels. With the molecular redistribution and the V-T energy exchanging, the vibrational non-equilibrium keeps attenuating at later time delays indicated by the scalar polarizability decreasing at the same rotational temperature.
A semi-classic model with relevant oscillator strengths has been used to calculate the polarizability based on the experimental conditions. The slope of polarizability increase depend on rotational and vibrational temperature has been predicted by the model which has fairly good agreement with the experimental result. More details about the model can be found in our paper.
This work was supported by the Air Force Research Laboratory through the Ohio Aerospace Institute and overseen by Dr. Eswar Josyula.
 Farbar E D and Boyd I D 2010 Physics of Fluids 22 106101
 Kadochnikov I N and Arsentiev I V 2018 Journal of Physics D: Applied Physics 51 374001
 Mackey L E and Boyd I D 2019 AIAA Journal 0 1~13
 A. Tropina, Y. Wu, C. Limbach and R. Miles, 2018 AIAA Aviation Forum, 3904
 Miles R B, Lempert W R and Forkey J N 2001 Measurement Science and Technology 12 R33~R51
 Y. Wu, C. Limbach, A. Tropina and R. Miles, 2019 AIAA SciTech Forum, 2066.
 A. Tropina, Y. Wu, C. Limbach and R. Miles 2019 Journal of Physics D: Applied Physics