The Mathematical characteristic of the Phase and Group Velocities of Pure Alfvèn Wave in the E Region of the Ionosphere for Low Latitudes

Abstract

In this study, we mainly focus our attention on mathematical analysis of the phase and group velocities of low-frequency Alfvèn waves in the E region of the ionosphere. According to observational conclusions it is known that the phase and group velocities of such waves are equal to each other when kinematic and magnetic viscosity are ignored. On the other hand, these velocities have different velocities when we take kinematic and magnetic viscosities into account. Since it is very difficult to analyze the group velocity analytically, we plan to discuss its numerical solutions in our future investigation. Thus, in the present study, we focus on the features of phase velocity of low-frequency of Alfvèn wave and analyze its nature in the E region of the ionosphere for low latitudes. we see that the trend of change of magnitudes of the phase velocities on on March 21st and June21st resembles to the behavior of cosine function Moreover, it is concluded that the magnitudes of real and imaginary parts of the corresponding solutions are larger than the ones obtained for March 21st. The ma in reason of this case may be higher electron production in the ionosphere in June.