Line profile Doppler

Figure C3.3.6. Doppler-line profiles for molecules scattered into the CO COO O J= 72) state by collisions with hot methylpyrazine molecules as depicted by the equations above each half of the figure. The energy of methylpyrazine...

For still larger column densities, the damping wings completely overcome the contribution of the Doppler core to the EW (see Fig. 3.9) and we can take for the whole line profile A co A

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This is the Menzel-Minnaert-Unsold interpolation formula (often used assuming Roo = 1). It gives a better approximation to stellar absorption-line profiles (which are definitely not flat-bottomed) than does the exponential formula the shape of the corresponding curve of growth is much the same, but its use leads to a b-parameter that is about 25 per cent higher for the same observational data. Denoting the central value of p by po, the Doppler part of the curve is given by... 

This situation corresponds to the well-known saturation effect in the emission of most gas laser transitions, where, for the same reason, fewer upper-state molecules can contribute to the gain of the laser transition at the center of the doppler-broadened fluorescence line than nearby. When tuning the laser frequency across the doppler-line profile, the laser intensity therefore shows a dip at the centerfrequen-cy, called the Bennet hole or Lamb dip after W.R. Bennet who discovered and explained this phenomen, and W.E. Lamb 2) who predicted it in his general theory of a laser. 

AxN, Axp, AxD, Axv line-profile half-widths in cm-1 for natural, pressure-broadened, Doppler-broadened, and combined Doppler-and pressure-broadened cases, respectively generally Ax = Av/c, where c is velocity of light... 

It is essential to correctly evaluate the absorption cross-section a relative to the laser line profile, the spectral resolution of the light collection optics, and the natural HO line width as influenced by Doppler, Voigt, or collisional broadening. The principles governing absorption measurements of HO over a distance through the atmosphere are discussed by Hiibler et al. (38). 

Blickensderfer et al. (119) have recently extended the Samson theory to include various vessel geometries under conditions of pure Doppler, pure Lorentz, and Voigt (a combination of Doppler, Lorentz, and natural broadening) line profiles. The quenching cross section can be obtained also by a dynamic method in which the decay of the fluorescence intensity is measured after the exciting light is cut off. If the initial fluorescence intensity is / and the intensity after a lime f is If, we obtain... 

Doppler and Pressure Broadening, 27 I 6.2 Line Profile in Resonance Emission Four Types of Resonance Lamps, 31... 

Fig. 12.8. a The pulse duration dependence of the Heai line shape for a fixed laser energy of 49 mJ. Open circles, triangles, and squares represent experimental data for pulse durations of 30, 500, and 1000 fs, respectively. The solid, dotted, and dashed lines represent Doppler profiles obtained by fitting the central part of the line to the experimental data, b The pulse duration dependence of the kinetic energies of He-like argon ions calculated from the Doppler shift... 

For an accurate data analysis, a detailed understanding of systematic effects is necessary. Although they are significantly reduced with the improved spectroscopy techniques described above, they still broaden the absorption line profile and shift the center frequency. In particular, the second order Doppler shift and the ac-Stark shift introduce a displacement of the line center. To correct for the second order Doppler shift, a theoretical line shape model has been developed which takes into account the geometry of the apparatus as well as parameters concerning the hydrogen atom flow. The model is described in more detail in Ref. [13]. 

The method of symmetric points was used to determine the center of the interference curve. Extensive calculations showed that the line profile should be symmetric about the center frequency. The line center was then corrected for the second order Doppler shift, The Bloch-Siegert and rf Stark shifts, coupling between the rf plates, the residual F=1 hyperfine component, and distortion due to off axis electric fields. A small residual asymmetry in the average quench curve was attributed to a residual variation of the rf electric field across the line and corrected for on the assumption this was the correct explanation. Table 1 shows the measured interval and the corrections for one of the 8 data sets used to determine the final result. 

The line shapes are described by Voigt functions, which reflect the Lorentzian line profiles due to natural line width and Gaussian profiles due to Doppler broadening. The instrumental broadening by the rocking curve of the crystal, de-focusing and the finite resolution of the detector is described well by a Voigt profile shape too [3[. 

The above discussion is presented merely to give an idea of the types of EUV detectors and their applications in use on present fusion plasma experiments. It is by no means an exhaustive list of possibilities. Indeed, several different detectors are in use or being planned in future experiments. Resistive anode encoders will probably see more use in fusion experiments as they become commercially available. However, the low count rates available ( 10 to 10 sec-1) will result in these detectors being used mostly for line profile studies (e.g., ion temperature measurements via Doppler broadening measurements). Intensified CCD arrays (back-illuminated or otherwise), vidicon or CID systems, lens-coupled intensifiers, and anode detectors have all seen some use on tokamak experiments or are planned for the near future, but have not been widely used as yet. However, in terms of availability, pixel format, dynamic range, insensitivity to magnetic fields, compact package, and moderate cost, the IPDA remains the most versatile multichannel EUV detector for plasma spectroscopy. 

Figure J. 23. Lorentzian, Doppler, and Voigt spectral line profiles for approximately equal half widths and intensities. (From Andrews et al.., 1987).

This can be substituted into Equation 1.17 in the same way as was the Lorentz function, to give a value for the absorption coefficient of the Doppler broadened line profile. 

The atomic line profiles when purely Stark, these profiles arc well suited for the measurement of electron density (usually one uses Stark width of hydrogen or helium lines with the gases introduced in small quantity (less than 0.5 %) in the plasma gas) when purely Doppler, these profiles give the neutral temperature when the line profile is due to contributions from both. Stark and Doppler broadening must be separated, and one needs a high resolution apparatus. The most often studied profiles are those of argon helium and nitrogen... 

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