Ellis E. Whiting

An empirical approximation to the Voigt profile

Abstract A closed-form approximation to the Voigt profile is developed from an examination of Voigt profile calculations. This approximation matches the Voigt profile within 5 per cent at worst and is generally within 3 per cent or less. In radiant energy transport calculations this approximation is shown to closely reproduce the curves of growth given by use of the Voigt profile expression.

Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra

Two recommendations are made that can eliminate persistent confusion in the study of diatomic spectroscopy by providing uniform and consistent definitions of the electronic transition moments and the rotational line intensity factors. First, it is recommended that the equation for the line strength of a single rotational line be adopted to specify the relationship between the electronic transition moment and the rotational line intensity factor. Second, it is recommended that the electronic transition moment operator for perpendicular transitions be defined by (1212)(μx ± iμy). The adoption of these conventions results in a value of (2S + 1)(2J + 1) for the sum rule of the rotational line intensity factor for Σ± ↔ Σ± transitions and a value of 2(2S + 1)(2J + 1) for the sum rule for all other spin-allowed transitions.

Line by line calculation of spectra from diatomic molecules and atoms assuming a voigt line profile

Abstract A computer program is described that predicts the spectra resulting from electronic transitions of diatomic molecules and atoms. The program produces a spectrum by accounting for the contributions from all the individual rotational and atomic lines considered in the calculations. The integrated intensity of each line is distributed in the spectrum by an approximate Voigt profile. The program can produce spectra for either optically thin gases or for cases where simultaneous emission and absorption occur. The method allows calculations ranging from the absorption of incident radiation by a column of cold gas to the high temperature self-absorbed emission spectrum from a nonisothermal gas. The computed spectrum can be output directly and, if desired, the predicted output of a grating spectrograph or a fixed wavelength radiometer can be generated, including instrumental broadening and sensitivity. Several examples illustrating the versatility of the program are presented. Information is given which will enable the reader to acquire a copy of the program and a paper containing instructions for its usage.

Reinvestigation of rotational-line intensity factors in diatomic spectra

The theory of the intensity factors of rotational lines in diatomic molecular spectra is reviewed with an emphasis on removing obscurities and resolving ambiguities that exist. For example, a unified intensity-factor sum rule is derived that is valid for all spin-allowed and spin-forbidden dipole transitions. Further, it is shown that the electronic transition moments can always be chosen to be real and that a few simple rules ensure the application of consistent phase factors.

PAET, an entry probe experiment in the Earth's atmosphere

Abstract On June 20, 1971, an instrumented probe designated PAET entered the atmosphere near Bermuda at a velocity of 6.6 km/sec carrying experiments designed for use at planets other than the Earth. Instruments to measure in situ the structure and composition of the atmosphere included accelerometers, pressure and temperature sensors, a mass spectrometer, and a radiometer (to sense characteristic emission from the probe shock layer at high speeds). The experiments were largely successful. The thermal structure of the atmosphere, including two major reversals in gradient, was shown to be well defined to an altitude of 80 km by comparison with more conventional meteorological soundings. The atmospheric mean molecular weight was defined within a percent by the structure experiment. The radiometers defined the bulk composition accurately and the trace quantity of CO 2 to one significant figure. The mass spectrometer functioned properly, but failed to give the correct composition because of problems in its sampling system. Oxygen was depleted, apparently by chemical reactions before reaching the spectrometer, and the inlet leak conductance was reduced from its preflight value by an order of magnitude. There is reason to believe that contamination by large molecules from the heat shield was responsible. This experiment should stimulate intensive laboratory work on sampling systems, so that similar problems do not arise in measurements of atmospheric composition at the planets. Results of auxiliary experiments to measure atmospheric water vapor, vehicle dynamics and heating, and communications blackout are also given.

Computer checking of rotational line intensity factors for diatomic transitions

Abstract Previously published analytical formulae for the rotational line intensity factors of diatomic molecules have been compared with results from a comprehensive computer program, which determines numerical intensity factors for both spin-allowed and spin-forbidden electric and magnetic dipole transitions in diatomic molecules. The comparison uncovered several typographical errors and a few algebraic errors in the published formulae. The changes required in the formulae to give agreement with the results from the computer program are tabulated.

Composition of the earth's atmosphere by shock-layer radiometry during the PAET entry probe experiment

Abstract A determination of the composition of the Earths atmosphere obtained from on-board radiometer measurements of the spectra emitted from the bow shock layer of a high-speed entry probe is reported herein. The N 2 , O 2 , CO 2 and noble gas concentrations in the Earths atmosphere were determined to good accuracy by this technique. The results demonstrate unequivocally the feasibility of determining the composition of an unknown planetary atmosphere by means of a multichannel radiometer viewing optical emission from the heated atmospheric gases in the region between the bow shock wave and the vehicle surface. The spectral locations in this experiment were preselected to enable the observation of CN violet, N + 2 first negative and atomic oxygen emission at 3870, 3910 and 7775 A, respectively. The atmospheric gases were heated and compressed by the bow shock wave to a peak temperature of about 6100°K and a corresponding pressure of 0.4 atm. Complete descriptions of the data analysis technique and the on-board radiometer and its calibration are given.

Nonequilibrium effects on shock-layer radiometry during earth entry.

Abstract Radiative enhancement factors for the CN violet and N+2 first negative band systems caused by non-equilibrium thermochemistry in the shock layer of a blunt-nosed vehicle during Earth entry are reported. The results are based on radiometric measurements obtained with the aid of a combustion-driven shock tube. The technique of converting the shock-tube measurements into predictions of the enhancement factors for the blunt-body case is described herein, and could be useful for similar applications of other shock-tube measurements.

Calculation of molecular band spectra assuming a gaussian line profile

Abstract A method for computing molecular band spectra is described. The integrated intensity of each rotational line considered is distributed spectrally by forcing it to fit a gaussian line profile centered at the computed wavelength for the rotational line. The spectrum is then produced by linearly combining the dispersed rotational lines. The method is applied to CN(violet) emission and found to give an excellent qualitative description of the electronic band shape down to a resolution of about 1·0 A and good quantitative agreement with (0,1) band shock tube measurements.

Decoupled predictions of radiative heating in air using a particle simulation method

A particle simulation technique with decoupled radiation is used to estimate the radiative emission along the stagnation streamline and the radiative heating at the stagnation point of a blunt-nosed vehicle entering the earths atmosphere at hypersonic speed. The direct simulation Monte Carlo (DSMC) method is used to compute the fluid mechanics of the weakly ionized flow. The radiative emission is computed using the NEQAIR computer code with the radiation decoupled from the flowfield solution. It is concluded that the new models make it possible to decrease the predicted total radiative heating at the stagnation point of the vehicle by a factor of 15. A comparison of the DSMC approach with a continuum flow model shows that the total predicted radiative heating estimates agree within a factor of 2.