The Localized Waves (LW) are nondiffracting ("solitonlike") solutions to the wave equations, and are known to exist with subluminal, luminal and superluminal peakvelocities V. For mathematical and experimental reasons, the ones that called more attention were the "Xshaped" superluminal waves. Such waves are associated with a cone, so that one may be tempted let us confine ourselves to electromagnetism to look for links between them and the Cherenkov radiation[1]. However, the Xshaped waves belong to a very different realm: For instance, they can be shown to exist, independently of any media, even in the vacuum, as localized nondiffracting pulses propagating rigidly with a peakvelocity[2] V>c. In this paper we dissect the whole question on the basis of a rigorous formalism, and of clear physical considerations. [In particular we show, by explicit calculations based on Maxwell equations only, that, at variance with what was previously assumed by some authors: (i) the "Xwaves" exist in all space, and in particular inside both the front and the rear part of their double cone (which has nothing to do with Cherenkov's); (ii) they are to be found not heuristically, but by use of strict mathematical (or experimental) procedures, without any ad hoc assumptions; (iii) the ideal Xwaves, as well as the plane waves, are endowed with infinite energy, but finiteenergy Xwaves may be easily constructed (even without recourse to spacetime truncations): And at the end of this article, by following a new technique, we construct finiteenergy exact solutions, totally free from backwardtraveling waves; (iv) the Xwaves' most interesting property lies in the circumstance that they are LWs, endowed with a characteristic selfreconstruction property, which promises important practical applications (in part already realized, starting with 1992), quite independently of the superluminality or not of their peakvelocity; (v) insistence in attempting a comparison of Cherenkov radiation with Xwaves would lead one to an unconventional sphere: that of considering the rather different situation of the (Xshaped, too) field generated by a superluminal pointcharge, a nonorthodox question actually exploited in previous papers[3]: We show here explicitly that in such a case the pointcharge would not lose energy in the vacuum, and that its field would not need to be continuously fed by incoming sidewaves (as it is the case, on the contrary, for an ordinary Xwave).]
Cherenkov Radiation versus Xshaped Localized Waves
RECAMI, Erasmo;
20100101
Abstract
The Localized Waves (LW) are nondiffracting ("solitonlike") solutions to the wave equations, and are known to exist with subluminal, luminal and superluminal peakvelocities V. For mathematical and experimental reasons, the ones that called more attention were the "Xshaped" superluminal waves. Such waves are associated with a cone, so that one may be tempted let us confine ourselves to electromagnetism to look for links between them and the Cherenkov radiation[1]. However, the Xshaped waves belong to a very different realm: For instance, they can be shown to exist, independently of any media, even in the vacuum, as localized nondiffracting pulses propagating rigidly with a peakvelocity[2] V>c. In this paper we dissect the whole question on the basis of a rigorous formalism, and of clear physical considerations. [In particular we show, by explicit calculations based on Maxwell equations only, that, at variance with what was previously assumed by some authors: (i) the "Xwaves" exist in all space, and in particular inside both the front and the rear part of their double cone (which has nothing to do with Cherenkov's); (ii) they are to be found not heuristically, but by use of strict mathematical (or experimental) procedures, without any ad hoc assumptions; (iii) the ideal Xwaves, as well as the plane waves, are endowed with infinite energy, but finiteenergy Xwaves may be easily constructed (even without recourse to spacetime truncations): And at the end of this article, by following a new technique, we construct finiteenergy exact solutions, totally free from backwardtraveling waves; (iv) the Xwaves' most interesting property lies in the circumstance that they are LWs, endowed with a characteristic selfreconstruction property, which promises important practical applications (in part already realized, starting with 1992), quite independently of the superluminality or not of their peakvelocity; (v) insistence in attempting a comparison of Cherenkov radiation with Xwaves would lead one to an unconventional sphere: that of considering the rather different situation of the (Xshaped, too) field generated by a superluminal pointcharge, a nonorthodox question actually exploited in previous papers[3]: We show here explicitly that in such a case the pointcharge would not lose energy in the vacuum, and that its field would not need to be continuously fed by incoming sidewaves (as it is the case, on the contrary, for an ordinary Xwave).]File  Dimensione del file  Formato  

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