The self-force and the self-energy (Coulomb-velocity energy) of an electron moving along a rectilinear trajectory in the vacuum is analyzed numerically. It is illustrated for the first time that when the velocity of the electron approaches the light velocity in the vacuum, the Coulomb-velocity energy approaches infinitely large, so is the self-force that calculated with the Lorentz force formula. Consequently, electrons cannot be accelerated to move faster than the light in the vacuum using electric accelerators because infinite large external force may be required to make the electron cross the electromagnetic barrier of the light velocity in the vacuum. Based on the observation, the Bertozzi experiment is re-interpreted, which shows that the velocity limit is due to the intrinsic behavior of the electron that can be clearly explained with the classical Maxwell’s theory. It is obviously not so definite that this behavior of the electron is due to the effect of special relativity as claimed in text books. Therefore, the outcome of the Bertozzi experiment may be not an unquestionable experimental support to the Einstein’s theory of special relativity. It is natural to consider that neutral particles may move faster than the light velocity in the vacuum because they do not face the infinite electromagnetic self-force when they cross the electromagnetic barrier. Furthermore, a reasonable hypothesis can be made that superluminal electrons may be generated by the collision of high energy neutral particles in a collider or in the universe.

The electromagnetic fields of point sources with time varying charges moving in the vacuum are derived using the Liénard-Wiechert potentials. The properties of the propagation velocities and the Doppler effect are discussed based on their far fields. The results show that the velocity of the electromagnetic waves and the velocity of the sources cannot be added like vectors; the velocity of electromagnetic waves of moving sources are anisotropic in the vacuum; the transverse Doppler shift is intrinsically included in the fields of the moving sources and is not a pure relativity effect caused by time dilation. Since the fields are rigorous solutions of the Maxwell's equations, the findings can help us to abort the long-standing misinterpretations concerning about the classic mechanics and the classic electromagnetic theory. Although it may violate the theory of the special relativity, we show mathematically that, when the sources move faster than the light in the vacuum, the electromagnetic barriers and the electromagnetic shock waves can be clearly predicted using the exact solutions. Since they cannot be detected by observers in the region outside their shock wave zones, an intuitive and reasonable hypothesis can be made that the superluminal sources may be considered as a kind of electromagnetic blackholes.

I feel sorry that the manuscript is written in a hurry and most content of the synthesis of the linear arrays is similar to that discussed in C.A. Balanis book as pointed out by reviewers. However, I still post this manuscript on this server as I indeed derived it from the very beginning and I wish some part of them may be of usage for others, especially the 2-D cases and some of my considerations on this issue. The direct synthesis results are very good initial values for further optimization with a method in which the properties of the entire functions and the number of degrees of the freedom of far fields are made full use of.In this paper, the current distribution is expanded with Fourier series. Analysis shows that only a limited number of the harmonic components of the current can generate propagation fields and contribute to the far-field pattern. Most importantly, it is found that this part of the current can be directly obtained from the far-field without utilizing any optimization algorithm. The degree of freedom of the far-field can be exactly counted for a linear source or a rectangular planar source. Numerical examples verify that the method is very efficient for synthesizing large antenna arrays.

The Einstein's theory of special relativity is based on his two postulates. The first is that the laws of physics are the same in all inertial reference frames. The second is that the velocity of light in the vacuum is the same in all inertial frames. The theory of special relativity is considered to be supported by a large number of experiments. This paper revisits the two postulates according to the new interpretations to the exact solutions of moving sources in the laboratory frame. The exact solutions are obtained using the classic Maxwell's theory, which clearly show that the propagation velocity of the electromagnetic waves of moving sources in the vacuum is not isotropic; the propagation velocity of the electromagnetic waves and the moving velocity of the sources cannot be added like vectors; the transverse Doppler effect is intrinsically included in the fields of the moving sources. The electromagnetic sources are subject to the Newtonian mechanics, while the electromagnetic fields are subject to the Maxwell's theory. We argue that since their behaviors are quite different, it is not a best choice to try to bind them together and force them to undergo the same coordinate transformations as a whole, like that in the Lorentz transformations. Furthermore, the Maxwell's theory does not impose any limitations on the velocity of the electromagnetic waves. To assume that all objects cannot move faster than the light in the vacuum need more examinations. We have carefully checked the main experiment results that were considered as supporting the special relativity. Unfortunately, we found that the experimental results may have been misinterpreted. We here propose a Galilean-Newtonian-Maxwellian relativity, which can give the same or even better explanations to those experimental results.

A planar current is generally divided into a radiating part that generates propagation fields and a non-radiating part that generates evanescent fields. This paper proposes a direct method to reconstruct the radiating part of a planar source from its far fields based on their exact relationship. A standard reconstruction process is provided in which the far-fields are sampled at the peaks of each propagation mode. Analysis shows that the achievable reconstruction resolution of the source distribution is about half a wavelength. The paper also demonstrates that it is possible to reconstruct the source by sampling the far-fields on a plane or along a linear path. The performance of the reconstruction algorithm is illustrated with numerical examples.

An equivalent nonuniform transmission line model for electromagnetic radiation in free space is developed. By properly defining a voltage and a current associated with the transverse component of the mode fields, a kind of Telegraphers’ equation is derived for each spherical harmonic mode. Based on the equivalent distribution inductance and capacitance, the local characteristic impedance and phase velocity are derived. For each spherical mode, a cutoff spherical surface and an associated cutoff radius are introduced to separate the space into an evanescent region and a propagating region. A spherical mode field will decay approximately exponentially in the evanescent region and experience local reflection in the propagating region. The proposed model may provide an intuitive illustration for the radiation process in free space. This work is also part of my efforts in revisiting the issue of electromagnetic radiation and mutual coupling. Although the concepts I proposed, like the macroscopic Schott energy and this NTL model, may look strange and different from the conventional formulations, I believe they can provide intuitive and insightful interpretattion to the issue of EM radiation.

The direct array factor synthesis method is extended in this paper. Two parallel current sheets are used for synthesizing array factors with non mirror-symmetrical radiation patterns in the two sides of the sources.  Analysis shows that the synthesized current distributions are affected by the distance between the two current sheets.  Numerical results demonstrated that the method is efficient for synthesizing large scale antenna arrays with non mirror-symmetrical footprints.

I have made some revisions according to the advices of other researchers and submitted a new version of the theory (v4). I also have added a supplementary material for the the new version, including some detailed explanations and derivations. In the proposed theory, the total electromagnetic energy of a radiator is separated into three parts: a Coulomb-velocity energy, a radiative energy, and a macroscopic Schott energy. The Coulomb-velocity energy is considered to be attached to the sources as the same in the charged particle theory. It becomes zero as soon as its sources have disappeared. The radiative energy leaves the radiator and propagates to the surrounding space. The macroscopic Schott energy continues to exist for a short time after the sources have disappeared. It is a kind of oscillating energy and is considered to be responsible for energy exchange between the reactive energy and the radiative energy, performing like the Schott energy in the charged particle theory. As the Poynting vector describes the total power flux density related to the total electromagnetic energy, it should include the contributions of the real radiative power and a pseudo power flow caused by the fluctuation of the reactive energy. The energies involved in the electromagnetic mutual coupling are interpreted in a similar way. In the theory, all energies are defined with explicit expressions in which the vector potential plays an important role. The time domain formulation and the frequency domain formulation of the theory are in consistent with each other. The theory is also verified with Hertzian dipole. Numerical examples demonstrate that the theory may provide insightful interpretation for electromagnetic radiation and mutual coupling problems.

A revised version.  The main derivation is reorganized, some denotations are changed. In the proposed theory for analyzing the electromagnetic radiation and electromagnetic mutual couplings in vacuum, the electromagnetic energy associated with a source is separated into three parts: a Coulomb-velocity energy, a radiative energy and a macroscopic Schott energy. At the instant that the sources disappear, the Coulomb-velocity energy disappers simultaneously; a short time later, the total macroscopic Schott energy becomes zero, while the radiative energy keeps propagating and the total radiative energy becomes constant. By applying the Lienard-Wiechert potentials to a moving charge, this paper illustrates that the macroscopic Schott energy is corresponding to the Schott energy in the charged particle theory.

A theory for analyzing the radiative and reactive energies for pulse radiators in free space is presented. With the proposed definition of reactive energies and radiative energies, power balance at arbitrarily chosen observation surfaces are established, which intuitively shows that the Poynting vector contains not only the power flux density associated with the radiative energies, but also the influence of the fluctuation of the reactive energies dragging by the sources. A new vector is defined for the radiative power flux density. The radiative energies passing through observation surfaces enclosing the radiator are accurately calculated. Numerical results verifies that the proposed radiative flux density is more proper for expressing the radiative power flux density than the Poynting vector.

Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power balance in a system, it is not so convenient in some situations to use it for evaluating the electromagnetic energies. The energy balance issue for time varying fields is revisited in this paper, and a set of energy balance equations are introduced, and a modified method for evaluating power flux is proposed.

It is required to calculate the stored reactive energy of an antenna in order to evaluate its Q factor. Although it has been investigated for a long time, some issues still need further clarification. The main difficulty involved is that the reactive energy of an antenna tends to become infinitely large when integrating the conventionally defined energy density in the whole space outside a small sphere containing the antenna. The reactive energy is usually made to be bounded by subtracting an additional term associated with the radiation fields. However, there exists no well-accepted accurate definition for this additional term that is valid for all cases. By re-checking the definition of reactive energies, a new formulation is proposed in this paper which can separate the reactive energy and the radiation energy explicitly based on source-potentials. The clearly defined reactive energy is bounded without necessity to subtract that additional term, and the resultant formulae are easy to implement.