2015/01/05 by Gerald Kaiser, Kaiser, Gerald · 1 citation
Engineering · Materials Science · Physics and Astronomy · #30-XX #35-XX #78-XX #Electromagnetic Compatibility and Noise Suppression #FOS: Physical sciences #Lightning and Electromagnetic Phenomena #Magnetic Properties and Applications #Mathematical Physics (math-ph) #Optics (physics.optics)
paper · pdf · doi:10.48550/arxiv.1501.01005
openalex publication_date 2015/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The complex Poynting theorem (CPT) is extended to a canonical time-scale domain (t,s). Time-harmonic phasors are replaced by the positive-frequency parts of general fields, which extend analytically to complex time t+is, with s>0 interpreted as a time resolution scale. The real part of the extended CPT gives conservation in t of a time-averaged field energy, and its imaginary part gives conservation in s of a time-averaged reactive energy. In both cases, the averaging windows are determined by a Cauchy kernel of width Δt∼ ± s. This completes the time-harmonic CPT, whose imaginary part is generally supposed to be vaguely `related to' reactive energy without giving a conservation law, or even an expression, for the latter. The interpretation of s as reactive time, tracking the leads and lags associated with stored capacitative and inductive energy, gives a simple explanation of the volt-ampere reactive (var) unit measuring reactive power: a var is simply one Joule per reactive second. The related 'complex radiation impedance density' is introduced to represent the field's local reluctance to radiate.