Unipolar pulse of an electromagnetic field with uniform motion of a charge in a vacuum

Propagation of electromagnetic pulses with nonzero area in dissipative media

“…Hence, for small terms of the order of (ω p /ν tr ) 2 , the decrease of spatial area S Z (t) is consistent with the decrease of temporal area S T (z), given by equation (28). The apparent small difference is due to the fact that the phase speed of light in the medium differs slightly from c.…”

“…However, the existence of such pulses is still questionable (see, for example, the recent paper [27] and subsequent discussion [28]). The problem of temporal evolution of the pulse electric area during its propagation remains debatable [29,30].…”

Electromagnetic pulses with non-zero electric area in transition radiation

“…For this, it is necessary to use the full Maxwell equations. Estimations [25,26] show that the duration of the pulse is of the order of the time of charge movement in the region of the longitudinal localization of the electric area, i.e. L z /V.…”

“…The flat interface between the media is located at z = 0 (normal charge incidence on the interface). In this case, the electric charge density ρ(r, t) = qδ(x)δ(y)δ(z − Vt) and Maxwell's equations for the electric area are formulated as [25] rot…”

“…Although this value is the zero-frequency spectral component of the electrical strength, its difference from zero in no way means that the pulse has a static component [25] (by the very definition, a non-zero static component would lead to an infinitely large electrical area, and there is no any static component for pulses of finite duration). Under the name 'integral of the field over time' it appears in Jackson's monograph [26], in which it is shown that the electric area is inversely proportional to the speed of a charge uniformly moving in a vacuum.…”