Torsional Alfven waves and the period ratio P_1/P_2 in spicules

Abstract

The effects of both density stratification and magnetic field expansion on torsional Alfven waves in solar spicules are studied. Also, their eigenfrequencies, eigenfunctions, and the period ratio P_1/P_2 are obtained with a novel mathematical method. We showed that under some circumstances this ratio can approach its observational value even though it departs from its canonical value of $2$. Moreover, Eigenfunction height variations show that the oscillations amplitude are increasing towards higher heights which is in agreement with the observations. This means that with a little increase in height, amplitude of oscillations expands due to the significant decrease in the density.