Estimation of the specific real phase and group refractive indexes by the altitude in the earth’s ionized region using the first order appleton-hartree equations

Abstract

The specific phase and group refractive indexes concerning the specific phase and group velocities of single and packet electromagnetic waves contain all interactions between the electromagnetic waves and the propagating medium. The determination of the specific refractive indexes vs. altitude is also a challenge and complicated problem. Based on the first-order Appleton-Hartree equations and the values of free electron density by altitude this paper outlined the numerical estimated results of the specific real phase, group refractive indexes vs. the altitude from 100 km up to 1000 km in the ionized region. The specific real phase refractive index has value smaller than 1, corresponding to this value, the specific phase velocity is larger than the light speed (c) meanwhile the value of the specific real group refractive index is larger than 1, the specific group velocity will always be smaller than light speed (c). These estimated results are agreed with the theory and forecasted model predicted. These results could be applied for both the experiment and theoretical researches, especially for application in finding the numerical solution of mathematics problems of Wireless Information and Wireless Power Transmissions.