Differential Equations of Mathematical Physics

Axion Electrodynamics and Dark Matter Fingerprints in the Terrestrial Magnetic and Electric Fields

“…We are interested to solve the master equations of the axion electrodynamics, which guide the evolution of the magnetic and electric field in the spherical resonator "Earth-Ionosphere". In the framework of the FaradayMaxwell electrodynamics this problem is solved and discussed in detail, in particular, in terms of Hertz and Debye potentials [35]. These results are classical and they were used in numerous applications, in particular, in radio-and tele-communication, navigation, magnetic storm predictions, etc.…”

“…When the electric current four-vector is equal to zero, the equations (27)- (30) and (33), (34) can be reduced to the coupled pair of equations for two new potentials U and V , which play in axion electrodynamics the same role as the Debye potentials [35] play in the electrodynamics of Faraday -Maxwell. Let us use the substitutions…”

“…i.e., we neglect the axion influence at all, this function is [39,35] ℜ n (r, 0) = A n r R n + B n r R…”

“…When the axion-photon coupling is taken into account, these results require serious modifications, since in this case the electromagnetic wave propagate in chiral (quasi)medium. For instance, in classical terrestrial electrodynamics the so-called E-waves and H-waves are introduced [35], for which the radial components of the magnetic and electric fields, respectively, are equal to zero. From the mathematical point of view, such decomposition of the total electromagnetic field essentially facilitates the analysis of the problem.…”

“…where J n+ 1 2 (qr) is the Bessel function of the first kind with the half-integer index [39,35]. The constants of integration are chosen so that lim q→0 ℜ n (r, q) = ℜ n (r, 0) (see (57)).…”