Spatial and spectral cross-correlations in the background and sodium- emission noise from a sheathed C2H2-air flame

Abstract Data are reported, for the first time, on the cross-correlation between the excess low-frequency fluctuations in the background or sodium-emission at different locations in a sheathed premixed, laminar C 2 H 2 -air flame and in different spectral intervals. These data supplement our earlier measurements of emission noise spectra in a similar flame [ Spectrochim. Acta 34B , 85 (1979)]. The cross-correlation coefficient c was simply measured, at zero-time delay, with a single r.m.s. meter and a single, tunable electronic filter in the range 5–10 2 Hz. The definition of c and its relation to the cross-correlation function as well as to the cross-spectral noise power are explained in a tutorial fashion. A theoretical model is introduced to describe the axial cross-correlations (measured along the flame axis). Also an expression is derived for the statistical error inherent in the method of measuring c . The axial cross-correlation profiles measured at the frequencies of the two noise peaks (14.5 and 29 Hz) as well as at other frequencies showed a pronounced periodicity, in accordance with the theoretical model. Full cross-correlation was found over the width of the flame and, for the background noise, also over a spectral range extending from the Na-D line to 660 nm. The background noise was also fully cross-correlated with the Na-emission noise. The measurements point to a common noise source due to fluctuations in the flame thickness. These fluctuations originate from instabilities at the outer flame border that rapidly grow with height and extend to the central flame. This explanation was corroborated by filming the Na-coloured central flame with a high-speed camera at 200 pictures/s. Conclusions are drawn as to the analytical application of flames in FES, AAS and AFS. Some of them may also be relevant to other excitation sources such as an ICP. In this respect the paper might serve as a pilot-study.