Microwave Propagation in Warm, Collisional Magnetoionic Media

Abstract

In this paper, we present the derivation of the magnetoionic dispersion equation and the corresponding index of refraction and propagation constant for characterizing wave propagation in warm plasma immersed in a uniform magnetic field. To demonstrate the effects of plasma temperature on wave propagation and attenuation, a numerical example of the developed theory has been given. It is well known that there are two forward propagating modes of cold plasma: one is weakly attenuated and the other is weakly amplified. By comparing the cold plasma complex propagation constant of the classical Appleton-Hartree theory with the propagation constant obtained for the warm plasma case, we observed that the attenuated mode is thermally enhanced while the amplification of the other mode decreases by increasing the temperature where it becomes damped beyond a certain electron thermal speed.Index Terms-Appleton-Hartree theory, electromagnetic waves, index of refraction, magnetized plasma, magnetoionic theory, microwave propagation, warm plasma. Muhammad S. Bawa'aneh (SM'10) received the B.Sc. and M.Sc. degrees in physics from Yarmouk University, Irbid, Jordan, in 1989 and 1992, respectively, and the Ph.D. degree in theoretical and computational plasma physics from the University of Essex, Colchester, U.K., in 1999. . His current research interests include electromagnetic wave interaction with plasma and microstrip patch antenna printed on ferrite substrate in free space.

Two‐Fluid Treatment of Whistling Behavior and the Warm Appleton‐Hartree Extension

“…Whilst the employed two-fluid treatment is complete, all intricacies of damping effects (Bell et al, 2002;Hsieh & Omura, 2018;Ma et al, 2017) are inherently absent, although collisional damping, which may be strong for whistler waves (Crabtree et al, 2012), could be included in the future. Hence, the two-fluid approach could be applied to include collisional damping in the whistler description or the warm Appleton-Hartree equation, as is done in Bawa'aneh et al (2013), but studying the effects of Landau or cyclotron damping on whistler waves requires a different framework.…”

“…Hence, the two‐fluid approach could be applied to include collisional damping in the whistler description or the warm Appleton‐Hartree equation, as is done in Bawa'aneh et al. (2013), but studying the effects of Landau or cyclotron damping on whistler waves requires a different framework.…”

“…This leaves the polynomial of fourth-degree in  2 as a generalization of the Appleton-Hartree dispersion relation to the warm case. Expression 24 in Bawa'aneh et al (2013), ignoring collision terms, can be reordered to retrieve Equation 40 It is easily checked that substituting v = 0, that is, setting the electron thermal speed to zero, in this polynomial retrieves Equation 40 from Keppens and Goedbloed (2019a), which they showed to be equivalent to the Appleton-Hartree relation, usually written as a function of the refractive index     / / n ck k . This usual way of expressing this relation is only for historical reasons preferred and is possible because the polynomial is of second degree in 2 k in the cold case.…”

“…Relatively recently, Bawa'aneh et al. (2013) derived a warm version of the Appleton‐Hartree equation as a dispersion relation combining the frequency and the index of refraction. To obtain the warm Appleton‐Hartree equation in a manner consistent with the S, A, F, M, O, and X labeling scheme, it suffices to consider the μ = 0 limit of the general two‐fluid dispersion relation in and .…”

“…Recently, Bawa'aneh et al. (2013) extended the Appleton‐Hartree relation, which is presented in the majority of plasma physics textbooks, to describe the high‐frequency waves of a warm ion‐electron plasma. The μ = 0 limit can be applied to the warm ion‐electron dispersion relation discussed in De Jonghe and Keppens (2020) to recover this warm extension of the usual Appleton‐Hartree equation.…”