Abstract
Pulse radiator in free space is a suitable example to use for deriving the energy separation formulae because all the energies are finite and their performances with respect to the source can be examined rigorously. By analogy with the electromagnetic energy concepts in the classical charged particle theory and using the relationships derived from the Maxwell equations, the total electromagnetic energy of a pulse radiator is divided into three parts. The first part is the Coulomb-velocity energy. It disappears immediately after the source has disappeared. The second part also disappears a short while later after the source has disappeared. It is called the macroscopic Schott energy in this book because its behavior is similar to the Schott energy in the charged particle theory. The third part is the radiative electromagnetic energy which keeps propagating in free space till it encounters other sources. The energy separation formulae for time harmonic waves are also available. The results in time domain and frequency domain are completely in consistent because they are respectively derived from the time domain Maxwell equations and the frequency domain Maxwell equations directly. It is also verified with the Hertzian dipole both in frequency domain and in time domain.
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References
Kong JA (2008) Electromagnetic wave theory. EMW Publishing, Cambridge, MA
Collin RE (1991) Field theory of guided waves, 2nd edn. IEEE Press, New York
Stratton JA (1941) Electromagnetic theory. McGraw-Hill, New York
Xiao GB, Liu R (2023) Explicit definitions for the electromagnetic energies in electromagnetic radiation and mutual coupling. Electronics 12(9):4031
Xiao GB (2023) The Schott energy and the reactive energy in electromagnetic radiation and mutual coupling. Phys Scr 98:015512
Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, New York
Schott GA (1912) Electromagnetic radiation and the mechanical reactions arising from it. Cambridge University Press, Cambridge
Rowland DR (2010) Physical interpretation of the Schott energy of an accelerating point charge and the question of whether a uniformly accelerating charge radiates. Eur J Phys 31:1037–1051
Grøn Ø (2011) The significance of the Schott energy for energy-momentum conservation of a radiating charge obeying the Lorentz-Abraham-Dirac equation. Am J Phys 79(1):115–122
Nakamura T (2020) On the Schott term in the Lorentz-Abraham-Dirac equation. Quantum Beam Sci 4:34
Vandenbosch GAE (2013) Radiators in time domain—Part I: electric, magnetic, and radiated energies. IEEE Trans Antennas Propag 61(8):3995–4003
Vandenbosch E (2013) Radiators in time domain—Part II: finite pulses, sinusoidal regime and Q factor. IEEE Trans Antennas Propag 61(8):4004–4012
Poynting JH (1884) On the connexion between electric current and the electric and magnetic inductions in the surrounding field. Proc Royal Soc London 38:168–172
Emanuel AE (2007) About the rejection of Poynting vector in power systems analysis. J Electr Power Qual Util 8(1):43–48
Kinsler P, Favaro A, McCall MW (2009) Four Poynting theorems. Eur J Phys 30(5):983–993
Aharonov Y, Bohm D (1959) Significance of electromagnetic potentials in the quantum theory. Phys Rev 115:485
Tonomura A, Osakabe N, Matsuda T et al (1986) Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave. Phys Rev Lett 56:792
Xiao GB (2022) An interpretation for Aharonov-Bohm effect with classical electromagnetic theory. Preprint at https://doi.org/10.48550/arXiv.2201.12292
Xiao GB, Xiong C, Huang S et al (2020) A new perspective on the reactive electromagnetic energies and Q factors of antennas. IEEE Access 8(8999565):173790–173803
Xiao GB (2020) Electromagnetic energy balance equations and Poynting Theorem Preprint. https://doi.org/10.36227/techrxiv.12555698.v1
Xiao GB, Hu Y and Xiang S (2020) Comparison of five formulations for evaluating Q factors of antennas. Paper presented at IEEE MTT-S international conference on numerical electromagnetic and multiphysics modeling and optimization, Hangzhou, China, 7–9 Dec 2020
Chu LJ (1948) Physical limitations on omni-directional antennas. J Appl Phys 19(12):1163–1175
McLean JS (1996) A re-examination of the fundamental limits on the radiation Q of electrically small antennas. IEEE Trans Antennas Propag 44(5):672–676
Rao SM, Wilton DR (1991) Transient scattering by conducting surfaces of arbitrary shape. IEEE Trans Antennas Propag 39(1):56–61
Tian X, Xiao GB, Xiang S (2014) Application of analytical expressions for retarded-time potentials in analyzing the transient scattering by dielectric objects. IEEE Antennas Wireless Propag Lett 13:1313–1316
Rao SM, Wilton DR, Glisson AW (1982) Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans Antennas Propag 30(3):409–418
Huang S, Xiao GB, Hu Y, Liu R, Mao JF (2021) Multi-branch Rao-Wilton-Glisson basis functions for electromagnetic scattering problems. IEEE Trans Antennas Propag 69(10):6624–6634
Xiao GB (2022) Calculating the energies of a pulse radiator with marching-on in time algorithm. Paper presented at IEEE international symposium on antennas and propagation, Denver, USA, 10–15 Jul 2022
Carpenter CJ (1989) Electromagnetic energy and power in terms of charges and potentials instead of fields. IEE Proc A 136(2):55–65
Endean VG, Carpenter CJ (1992) Electromagnetic energy and power in terms of charges and potentials instead of fields. IEE Proc A 139(6):338–342
Collin RE, Rothschild S (1964) Evaluation of antenna Q. IEEE Trans Antennas Propag 12(1):23–27
Fante RL (1969) Quality factor of general antennas. IEEE Trans Antennas Propag 17(2):151–155
Rhodes DR (1977) A reactance theorem. Proc R Soc London A 353(1672):1–10
Yaghjian AD, Best SR (2005) Impedance, bandwidth, and Q of antennas. IEEE Trans Antennas Propag 53(4):1298–1324
Vandenbosch GAE (2010) Reactive energies, impedance, and Q factor of radiating structures. IEEE Trans Antennas Propag 58(4):1112–1127
Gustafsson M, Jonsson BLG (2015) Antenna Q and stored energy expressed in the fields, currents, and input impedance. IEEE Trans Antennas Propag 63(1):240–249
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Xiao, G. (2024). Pulse Radiator in Free Space. In: Electromagnetic Sources and Electromagnetic Fields. Modern Antenna. Springer, Singapore. https://doi.org/10.1007/978-981-99-9449-6_6
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DOI: https://doi.org/10.1007/978-981-99-9449-6_6
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