Wavelet analysis and the determination of coronal plasma properties

The usefulness of wavelet analysis is demonstrated by considering analytica l expressions for phase mixed Alfven waves in different physical circumstan ces. The wavelet analysis is briefly introduced, using the complex-valued M orlet wavelet, consisting of a plane wave modulated by a Gaussian, as the b asic wavelet. The time and scale resolution of the wavelet transform are th en discussed in more detail, by working out the transform of simple harmoni c functions analytically. As an illustration of the power of wavelet analys is, phase mixed Alfven waves are investigated. A comparison is made between a truly finite harmonic wave and an Alfven wave, dissipated by phase mixin g and, using the wavelet transform, it is demonstrated that it is possible to distinguish between these two 'finite' signals. It is also possible to e xtract the value of the dissipation coefficient from the wavelet transform. When considering phase mixing of Alfven waves in a gravitationally stratif ied atmosphere, the lengthening of the wavelengths is clearly evident in th e transform, which provides an independent estimate of the value of the pre ssure scale height. In a radially diverging atmosphere, the shortening of t he wavelengths is also apparent in the wavelet transform, showing how the A lfven speed varies along the loop and thus providing information on the cor onal density and magnetic field. When applying wavelet analysis to observed wavelike oscillations, it should be possible to infer properties of the co ronal plasma by making a detailed study of the wavelet transform.