Interstellar Propagation of Electromagnetic Signals

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1 Interstellar Propagation of Electromagnetic ignals

2 Interstellar Propagation of Electromagnetic ignals Henning F. Harmuth Formerly of The Catholic University of America Washington, D.C. and Konstantin A. Lukin Institute of Radiophysics and Electronics Academy of ciences of Ukraine Kharkiv, Ukraine pringer cience+business Media, LLC

3 IBN IBN (ebook) DOI / pringer cience+business Media New York Originally published by Kluwer AcademiclPlenum Publishers in 2000 oftcover reprint ofthe hardcover lst edition ro A C.I.P. record for this book is available from the Library of Congress. All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanicai, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

4 To the memory of Max Planck ( )

5 Preface Almost all information about the universe beyond the atmosphere of the Earth is received via electromagnetic waves. Generally we observe the amplitude and frequency of these waves-after making a Fourier decomposition to permit the use of the concept frequency. This is equivalent to the observation of the voltage and frequency of an electromagnetic wave arriving from a power station and totally different from the observation or reception of electromagnetic waves arriving by telephone or radio. In terms of information theory we receive information at the rate zero. Although this statement is exaggeratednobody waits infinitely long to receive the infinitely extended sinusoidal waves assumed by a Fourier decomposition-it states correctly that the observation of amplitude or power and frequency of electromagnetic waves yields very little information compared with the detection of electromagnetic signals. An electromagnetic signal is a propagating electromagnetic wave that is zero before a certain time and has finite energy. ignals are represented mathematically by functions or signal solutions that are zero before a certain time and quadratically integrable. uch signal solutions satisfy the causality law and the conservation law of energy while periodic, indefinitely extended sinusoidal solutions or functions satisfy neither. All observable or producable electromagnetic waves begin at a certain time and have finite energy. Hence, they are all signals even though we often approximate them with periodic functions. Electromagnetic theory has been based on Maxwell's equations for about a century. There is no need to elaborate the successes but from 1986 on we find publications claiming that Maxwell's equations generally do not have solutions that satisfy the causality law. Two scientists working independently and using different approaches arrived at the same result, which gives it great credibility. The mathematical investigations that uncovered the lack of causal solutions are necessarily complicated, otherwise it would not have taken a century to find this shortcoming of Maxwell's equations. The causality law is of little interest for power transmission but signal transmission without causality law is a contradiction in terms. It was found that the problem could be corrected by adding a term for magnetic dipole currents to Maxwell's equations. Electric dipole currents were always part of Maxwell's equations but they were called polarization currents and this choice of words obscured the unequal treatment of electric and magnetic dipoles. Having a theory that permits signal solutions one wants to apply it. The study of electromagnetic signals propagating in seawater or their use in the stealth technology were obvious applications. But the study of signals propagating for Billions of years from some star or galaxy to Earth is of much greater scientific interest and value. If the empty space were indeed empty there would be nothing to study. But the empty space contains low-density gases, primarily atomic hydrogen, and dust. They produce no observed effect for the distances of the solar system. For galactic distances we find an effect on the electromagnetic waves received from pulsars. Although these waves are signals we VII

6 have not yet observed the beginning of a wave radiated by a pulsar. What we observe are sequences of pulses with predictable time variation and intervals. Whenever a received wave is predictable it transmits-according to information theory-no information, but merely confirms what is already known. Great effects on electromagnetic signals are caused by atomic hydrogen when the propagation distance reaches Billions of light years. At such distances the energy of at least a supernova explosion is required to produce an observable signal. The relative rarity of supernovas is compensated by the fact that almost all of the universe is at distances of more than one Billion light years, which permits us to observe a fair number of supernovas at large distances. The repeated scattering of electromagnetic signals by interstellar gas and dust produces black body radiation without the help of a singular event like the Big Bang. Much work will be required before we will know to what extend the observed black body radiation can be explained by repeated scattering. The investigation of electromagnetic signals in this book applies to radio waves since we use a classical theory without quantization. The extension to the waves of visible light requires the quantization of the corrected Maxwell equations, which is a work in progress. The authors want to thank Dr.Nasser J. Mohamed-hihab of the Department of Electrical and Computer Engineering, Kuwait University, for his contribution to the endless computations required for this book. VlIl

7 Contents LIT OF FREQUENTLY UED YMBOL xi 1 Introduction 1.1 Dipole Current Densities in Maxwell's Equations Ohm's Law for Induced Electric Dipoles with Mass Magnetic Ohm's Law for Magnetic Dipoles with Mass Dipoles and Quadrupoles Created in Vacuum Observation of Dipole Currents Approximation of ignal Functions by Exponential FWlctions 37 2 Electric Field trength Due to Electric Excitation 2.1 Derivation of the Partial Differential Equation 2.2 Electric Field trength for Eigenfunction Excitation 2.3 Algebraic Equation of ixth Order 2.4 olution of Differential Equation of ixth Order 2.5 Plots of the Electric Field trength for p < 1/2 2.6 Plots of the Electric Field trength for p > 1/ Associated Field trengths 3.1 Associated Magnetic Field trength Integration Constants for Electric Excitation Plots of the Associated Magnetic Field trength for p < 1/ Plots of the Associated Magnetic Field trength for p > 1/ Field trengths Due to Magnetic Excitation Plots for the Associated Electric Field trength Excitation Functions With Finite Rise Time 4.1 Electric Excitation Function for p < 1/2 4.2 Electric Excitation Function for p > 1/2 4.3 Peak Amplitudes of the Precursor '4.4 Excitation by inusoidal Pulses 4.5 Excitation by Rectangular Pulses Equations are numbered consecutively within each of ections 1.1 to 6.7. Reference to an equation in a different section is made by writing the number of the section in front of the number of the equation, e.g., Eq.{2.1-50) for Eq.(50) in ection 2.1. Illustrations and tables are numbered consecutively within each section, with the number of the section given first, e.g., Fig.1.2-3, Table References are listed by the name of the author{s), the year of publication, and a lowercase Latin letter if more than one reference by the same author{s) is listed for that year. IX

8 5 Electromagnetic ignals in Astronomy 5.1 Information Obtained from Electromagnetic Waves 5.2 Main Lobe of ignals for Various Distances 5.3 Precursor of ignals for Various Distances 5.4 inusoidal Pulses at Various Distances 5.5 Rectangular Pulses at Various Distances Appendix 6.1 Numerical Evaluation for p < 1/2 6.2 Numerical Evaluation for p > 1/2 6.3 Evaluation of Certain mall Terms for p < 1/2 6.4 Evaluation of Certain mall Terms for p > 1/2 6.5 Associated Magnetic Field trength for p < 1/2 6.6 Associated Magnetic Field trength for p > 1/2 6.7 Relation Between D and E or Band H REFERENCE AND BIBLIOGRAPHY INDEX x

9 LIT OF FREQUENTLY UED YMBOL B C = X lob Cp = 1.98 X D E,E EE EH e F f fo ge gm H,H HE HH j J L = JLdL2 m mo mmo No p P = TmplTp q = TplT Q. QJL qm R r = TmplTs s, sp (t) t T v Z =.Jil1E Vs/m 2 mls - As/m2 Vim Vim Vim As Vim -l s-l A/m2 V/m2 Aim Aim Aim kgm2 m 2 kg kg Am2 m-3 Asm Vs m m VI Am VIAm s s mls V/A magnetic flux density vacuum velocity of light Eq.(2.3-12) electric flux density electric field strength electric field strength due to electric excitation electric field strength due to magnetic excitation electric charge effective electric field strength, Eq.(1.2-5) frequency Eq.(2.3-1) electric current density, Eq.(1.2-2) magnetic current density, Eq.(1.3-7) magnetic field strength magnetic field strength due to electric excitation magnetic field strength due to magnetic excitation complex unit (i is an integer variable) inertial moment of rotation, Eq.(1.3-11) Eq.(2.2-17) mass rest mass magnetic dipole moment, Eq.(1.3-11) particles per unit volume electric dipole moment p2 + O'pTmp/f. ~ p2, Eq.(3.1-15) p2 + 2spTsI/-L ~ p2, Eq.(3.5-16) hypothetical magnetic charge, Eq.(1.3-30) half length of a bar magnet; Fig distance conductivity for hypothetical magnetic monopole current, Eq.(1.3-2) conductivity for magnetic polarization current, Eqs.(1.3-7), (2.1-6) unit step function; Eq.(2.2-1) time variable time interval velocity wave impedance xi

10 Q1, Q2, Q ~ Q e f3 = vic = ge/9c 11 to 16 E = X E ( TJ TJo = 27rTJ e {) K A Al to A6 /-1 = 47r X 10-7 /-1r Ill, 1l2, 1l3, 114 I l ~ 1l2', 1l3, 114 ~ e ~ m 7r = (J (Jp = NOe2Tmp/m T, T1, T2, T3, T4 TIe, T2e, T3e, T4e T1m,T2m, T3m, T4m Tmp Tp Ts Tmp/Tp = P Tmp/Ts = r Tp/T = q W = 27rf As/Vm Vs/Am kg/s kgm/s A/Vm A/Vm -l Eqs.(2.1-68), (2.1-48), (2.1-32) electric polarizability, Eq.(1.2-5) normalized velocity or current density Eqs.(2.3-37), (2.4-4) permi tti vi ty small number used in integration limits normalized distance; Eq.(2.4-3) normalized wave number, Eq.(2.4-3) Eq.(2.3-13) normalized time; tit, Eq.(1.2-21) angle wave number Eq.( ) Eq.( ) permeability relative permeability normalized frequency; Eqs.(3.3-1), (3.3-2), (3.5-2), (3.5-3) normalized frequency; Eqs.(3.1-1),(3.1-2) constant referring to electric losses, Eq. (1. 2-1) magnetic friction constant for rotation, Eq.(1.3-13) conductivity of electric monopole current conductivity for electric polarization current time constants time constants; Eqs.(2.1-68), (2.1-70) time constants; Eqs.(2.1-32), (2.1-48), (3.1-1), (3.1-2) time constant related to losses time constant related to dipole generation time constant of exponential excitation function; Eq.(2.2-2) normalized time constant normalized time constant normalized time constant circular frequency XII

11 Interstellar Propagation of Electromagnetic ignals

CHAPTER 9 ELECTROMAGNETIC WAVES

CHAPTER 9 ELECTROMAGNETIC WAVES Outlines 1. Waves in one dimension 2. Electromagnetic Waves in Vacuum 3. Electromagnetic waves in Matter 4. Absorption and Dispersion 5. Guided Waves 2 Skip 9.1.1 and 9.1.2