Completing the complex Poynting theorem: Conservation of reactive energy in reactive time

2014/12/11 by Gerald Kaiser, Kaiser, Gerald
Mathematics · Physics and Astronomy · #30-XX #35-XX #78-XX #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #math-ph #math.MP #msc:30-XX #msc:35-XX #msc:78-XX #physics.optics

paper · pdf · doi:10.48550/arxiv.1412.3850

21 pages, no figures

arxiv created 2016/01/25 · arxiv updated 2016/01/26

Abstract

The complex Poynting theorem is extended canonically to a time-scale domain (t, s) by replacing the phasors of time-harmonic fields by the analytic signals X(r, t+is) of fields X(r,t) with general time dependence. The imaginary time s>0 is shown to play the role of a time resolution scale, and the extended Poynting theorem splits into two conservation laws: its real part gives the conservation in t of the scale-averaged active energy at fixed s, and its imaginary part gives the conservation in s of the scale-averaged reactive energy at fixed t. At coarse scales (large s, slow time), where the system reduces to the circuit level, this may have applications to the theory of electric power transmission and conditioning. At fine scales (small s, fast time) it describes reactive energy dynamics in radiating systems.

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