Spherical harmonic representation of the electromagnetic field produced by a moving pulse of current density

On Magnetization Reversal of Co–Cr Films with Perpendicular Anisotropy

“…It extends the results obtained earlier in [1] for the inhomogeneous wave equation to the case of dispersive media. Explicit solutions of the initialvalue problem are constructed in the spacetime domain by application of the Smirnov method of incomplete separation of variables [2].…”

“…We write ψ n = ψ on + ψ an , where the second term determines the wave dispersion while the first term gives the solution of the wave equation. The latter was investigated in [13] (see also [1]), wherefore we discuss ψ an only. It is clear from figures 1 and 2 that we have to discuss the case r < r 0 for the time interval τ > r + r 0 (see figure 1(b)).…”

Electromagnetic Waves Generated by Line Current Pulses

“…Practically important analytical solutions describing waves generated by a linear combination of exponentially decaying current pulses propagating in lossy media are constructed in (Utkin, 2008). Although the present discussion is constrained to the line sources, its extension to the more complicated source configurations is straightforward: for instance, the multipole expansion and introduction of the Debye potential result, in the spherical coordinate system, to the Euler-Poisson-Darboux equation of known Riemann function with respect to the transient spherical-harmonic expansion coefficients of the desired wavefunction (Borisov et al, 1996). Less complex solutions were obtained by Borisov and Simonenko for sources located on moving and expanding circles (Borisov & Simonenko, 1994, 1997, 2000.…”