Electromagnetic Wave Energy and Momentum Equations in Transparent, Dispersive, Space- and Time-Varying Media

Geometrical optics response tensors and the transport of the wave energy density

“…In this respect, one can find several mathematically equivalent transport equations (Maj and Bornatici 2002). Nevertheless, from a physical point of view, it is important to distinguish the effective energy dissipation from the (adiabatic) time-variation of the medium as suggested by the analogy with the adiabatically stretched pendulum (Katou 1981). Such a separation appears to be naturally present in Kravtsov's transport equation ( 4) where the effect of the effective energy dissipation is governed by ε (eff) A,ij ê * i êj (cf equation ( 35)), whereas the effect of the adiabatic time-variation is accounted for through the term (1/2ω)(∂ε (0) H,ij /∂t) ê * i êj .…”

Comparative analysis of two formulations of geometrical optics. The effective dielectric tensor

“…The wave-action density J σ (r, k; t) can thus be interpreted as a Liouville-type phase-space density associated with the wave propagation in the geometrical optics approximation. The conservation property expressed by (4) makes the wave-action density a more useful quantity than the corresponding wave-energy density W σ (r, k; t) = σ (k; r, t)J σ (r, k; t), which, instead, is not an invariant along the ray trajectories [10,13], in contrast with the incorrect claim made in [14].…”

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

“…We also assume that a wave is linear [14], and no collisions, ionization, or recombination take place [15]. In this case, the plasma dynamics should allow a Lagrangian formulation [16,17]; thus it is anticipated to comply with the general theorem of GO which states that the wave action is conserved in inhomogeneous nonstationary medium [18,19,20,21,22,23,24]. Previously, the theorem was independently rederived for a variety of oscillations [18,19,25,26,27,28], confirming the general treatment; particularly, space-charge waves in cold electron beams were considered, similar to Langmuir waves in cold plasmas [29,30,31].…”