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The multipole expansion, a ubiquitous tool in a variety of physical problems, can be formulated in spherical and Cartesian coordinates. By constructing an explicit map linking both formulations in isotropic media, we discover a lack of equivalence between both approaches in anisotropic media. In isotropic media, the Cartesian multipole tensor can be reduced to a spherical tensor containing significantly fewer entries. In anisotropic media, however, the loss of propagation symmetry prevents this reduction. In turn, non-harmonic sources radiate fields that can be projected onto a finite set of Cartesian multipole moments but require (possibly infinitely) many spherical moments. For harmonic sources, the link between both approaches presents a systematic way to construct the spherical multipole expansion from the Cartesian one. The lack of equivalence between both approaches results in physically significant effects wherever the field propagation includes the Laplace operator. We illustrate this issue on an electromagnetic radiation inverse problem in anisotropic media, including an analysis of a large-anisotropy regime. We show that the use of the Cartesian approach significantly increases the efficiency and interpretability of the model. The proposed approach opens the door to wider applications of the multipole expansion in anisotropic media, whose importance is rising in multiple physical systems., Comment: 16 pages, 5 figures

The recent development of high average, high peak power lasers has revived the effort of using lasers as a potential tool to influence natural lightning. Although impressive, the current progress in laser lightning control technology may only be the beginning of a new area involving a positive feedback between powerful laser development and atmospheric research. In this review paper, we critically evaluate the past, present and future of Laser Lightning Control (LLC), considering both its technological and scientific significance in atmospheric research., Comment: Revised version after first round of peer-review. Restructuration, adding more physics contextuality and pushed some tables in a newly created Appendix

Observations and theoretical principles indicate that electromagnetic waves, including light, propagate in dielectric media at speeds lower than those in free space, as eloquently expressed in Maxwell's equations featuring material-dependent permittivity and permeability. This study reveals that the observed slower propagation of waves in dielectric media arises from an interference between two types of waves: a forward-moving primary wave and a set of secondary waves induced by the primary wave's interaction with the medium. The forward-moving primary wave and secondary waves travel at the speed of light in vacuum. Notably, the reflected wave caused by the impedance discontinuity on the boundary of a dielectric medium is manifested by the induced secondary waves moving in the opposite direction to the primary wave. From a photonic point of view, photons will be moving back and forth below the slowly moving apparent front of the observed wave with the speed of light in vacuum. Ahead of this front the probability of finding photons is zero due to complete destructive interference of the waves in that region. From a photonic perspective, beneath the gradually advancing facade of the observed wave, photons move at the unyielding speed of light in vacuum. The likelihood of detecting photons ahead of the front diminishes to zero, a consequence of the thorough destructive interference manifesting within that specific region., Comment: 10 pages, 4 figures

X-rays have been observed in natural downward cloud-to-ground lightning for over twenty years and in rocket-triggered lightning for slightly less. In both cases, this energetic radiation has been detected during the stepped and dart leader phases of downward negative flashes. More recently, X-rays have also been reported during the dart leader phase of upward negative flashes. In this study, we present the observations of four upward positive lightning flashes from the S\"antis Tower (2.5 km ASL) in Switzerland. These consist of the simultaneous records of electric current passing through the tower, and electric field strength and X-ray flux 20 meters from the tower base. One of the flashes was captured by a high-speed camera operating at 24,000 frames per second, stills from which are also presented. We detected X-rays during the initial phase of upward negative leader propagation, which can be associated with the leader-stepping process from electric field and current waveforms. To the best of our knowledge, this is the first time that such measurements are reported in the literature. The obtained time-synchronised data confirm that the X-ray emissions detected are associated with the initial steps of the upward negative leader. The frequency and energy of X-ray pulses appear to decrease as a function of time, with pulses disappearing altogether within the first millisecond of the leader initiation. The X-ray pulse energy appears to increase with the maximum current-derivative and the electric field change of its associated leader step. These observations contribute to improving the currently lackluster understanding of upward lightning, which is a primary source of damage to tall structures such as telecommunications towers and wind turbines, as well as airplanes during take-off and landing.

The electromagnetic fields of a long dipole working without dispersive and dissipative losses are analyzed in the frequency domains. The dipole produces radiation in bursts of duration T/2 where T is the period of oscillation. The parameter studied in this paper is the energy, U, dissipated in a single burst of radiation of duration T/2. We have studied how U vary as a function of the charge associated with the current in the dipole and the ratio of the length of the dipole and its radius. We have observed a remarkable result when this ratio is equal to the ratio of the radius of the universe to the Bohr radius. Our results, based purely on the classical electrodynamics and general relativity, show that, as the magnitude of the oscillating charge (as defined by the root mean square) reduces to the electronic charge, the energy dissipated in a single burst of radiation reduces to hv, where v is the frequency of oscillation and h is the Planck constant. The importance of this finding is discussed. In particular, the results show that the existence of a minimum free charge in nature, i.e., electronic charge, is a direct consequence of the photonic nature of the electromagnetic fields. Furthermore, the presented findings allow to derive for the first time an expression for the vacuum energy density of the universe in terms of the other fundamental constants in nature, the prediction of which is consistent with experimental observations. This equation, which combines the vacuum energy, electronic charge and mass, speed of light, gravitational constant and Planck constant, creates a link between classical field theories (i.e., classical electrodynamics and general relativity) and quantum mechanics., Comment: arXiv admin note: substantial text overlap with arXiv:2112.07972

Electric currents circulating between charged clouds and the earth surface during lightning discharges are responsible for considerable damages and casualties. It is therefore important to develop better protection methods in addition to the traditional Franklin rod. Here we present the first demonstration that filaments formed by short and intense laser pulses can guide lightning discharges over considerable distances. We believe that this experimental breakthrough will lead to progress in lightning protection and lightning physics. An experimental campaign was carried out on the S\"antis Mountain in Northeastern Switzerland during the Summer of 2021 with a high repetition rate terawatt laser. The guiding of an upward negative lightning leader over a distance of 50 m was recorded by two separate high-speed cameras. The guiding of negative lightning leaders by laser filaments was corroborated in three other instances by VHF interferometric measurements, and the number of X-ray bursts detected during guided lightning events was significantly increased. While this research field has been very active for more than 20 years with many research groups around the world working to achieve this goal, this result demonstrates lightning guiding by lasers, which may lead to the development of a laser lightning rod. This work paves the way for new atmospheric applications of ultrashort lasers and represents a significant step forward in the development of a laser based lightning protection for airports, launchpads or large infrastructures., Comment: Laser-guided lightning. Nat. Photon. (2023)

The electromagnetic fields of linear radiating systems working without dispersive and dissipative losses are analyzed both in the time and the frequency domains. In the case of the time domain radiating system, the parameter studied is the action, A, associated with the radiation. The action is defined as the product of the energy and the duration of the radiation. In the case of the frequency domain radiating system, which produces radiation in bursts of duration T/2 where T is the period of oscillation, the parameter studied is the energy, U, dissipated in a single burst of radiation of duration T/2. In this paper, we have studied how A and U vary as a function of the charge associated with the current in the radiating system and the ratio of the length of the radiating system and its radius. We have observed remarkable results when this ratio is equal to the ratio of the radius of the universe to the Bohr radius. In the case of the time domain radiating system, we have observed that when the charge associated with the current propagating along the radiator reaches the electronic charge, the action associated with the radiation reduces to h/2*pi where h is the Planck constant. In the case of the frequency domain radiating system, we have observed that as the magnitude of the oscillating charge reduces to the electronic charge, the energy dissipated in a single burst of radiation reduces to h*v, where v is the frequency of oscillation. Interestingly, all these results are based purely on classical electrodynamics and general relativity. The importance of the findings is discussed. In particular, the fact that the minimum free charge that exists in nature is the electronic charge, is shown for the first time to be a direct consequence of the photonic nature of the electromagnetic fields. Furthermore, the presented findings allow to derive for the first time an expression for the dark energy density of the universe in terms of the other fundamental constants in nature, the prediction of which is consistent with experimental observations. This Equation, which combines together the dark energy, electronic charge and mass, speed of light, gravitational constant and Planck constant, creates a link between classical field theories (i.e., classical electrodynamics and general relativity) and quantum mechanics., Comment: 19 pages, 4 figures

A recent study pointed out that macroscopic dark matter (macros) traversing through the earth's atmosphere can give rise to hot and ionized channels similar to those associated with lightning leaders. The authors of the study investigated the possibility that when such channels created by macros pass through a thundercloud, lightning leaders may locked into these ionized channels creating lightning discharges with perfectly straight channels. They suggested the possibility of detecting such channels as a means of detecting the passage of macros through the atmosphere. In this paper, we show that macros crossing the atmosphere under fair weather conditions could also give rise to mini lightning flashes with current amplitudes in the order of few hundreds of Amperes. These mini lightning flashes would generate a thunder signature similar to or stronger than those of long laboratory sparks and they could also be detected by optical means. As in the case of thunderstorm assisted macro lightning, these mini-lightning flashes are also associated with straight channels. Moreover, since the frequency of mini lightning flashes are about three hundred times more frequent than the macro generated lightning flashes which were assisted by thunderstorms, they could be used as a means to look for the paths of macroscopic dark matter crossing the atmosphere., Comment: 11 pages, 5 figures