Electromagnetic Radiation: Variational Methods, Waveguides and Accelerators

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Springer Science & Business Media, Jun 18, 2006 - Science - 347 pages
Julian Schwinger was already the world’s leading nuclear theorist when he joined the Radiation Laboratory at MIT in 1943, at the ripe age of 25. Just 2 years earlier he had joined the faculty at Purdue, after a postdoc with OppenheimerinBerkeley,andgraduatestudyatColumbia. Anearlysemester at Wisconsin had con?rmed his penchant to work at night, so as not to have to interact with Breit and Wigner there. He was to perfect his iconoclastic 1 habits in his more than 2 years at the Rad Lab. Despite its deliberately misleading name, the Rad Lab was not involved in nuclear physics, which was imagined then by the educated public as a esoteric science without possible military application. Rather, the subject at hand was the perfection of radar, the beaming and re?ection of microwaves which had already saved Britain from the German onslaught. Here was a technology which won the war, rather than one that prematurely ended it, at a still incalculable cost. It was partly for that reason that Schwinger joined this e?ort, rather than what might have appeared to be the more natural project for his awesome talents, the development of nuclear weapons at Los Alamos. He had got a bit of a taste of that at the “Metallurgical Laboratory” in Chicago, and did not much like it. Perhaps more important for his decision to go to and stay at MIT during the war was its less regimented and isolated environment.

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Contents

Contents
1
Waveguides and Equivalent Transmission Lines
103
Rectangular and Triangular Waveguides 133
132
Circular Cross Section
154
Reflection and Refraction
179
Spherical Harmonics 2 1 Connection to Bessel Functions 2 2 Multipole Harmonics 2 3 Spherical Harmonics 2 4 Multipole Interactions 2 5 Problems f...
189
63
244
79
274
Diffraction
295
80
300
84
310
Quantum Limitations on Microwave Oscillators 329
328
89
340
Appendix Electromagnetic Units
347
Index
353
Copyright

Synchrotron Radiation
281

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Page x - Department of Special Collections, University Research Library, University of California at Los Angeles (Leyda Collection).
Page 249 - ... eliminated (/ = — iBV), All of the results just derived are generalizations of well-known lowfrequency theorems. The essential difference is that at low-frequency there exist regions (coils, condensers) containing only magnetic or electric energy. This is not possible when the dimensions of the region are comparable with the wavelength.
Page 249 - The relation between the reactance (susceptance) matrix and the difference between magnetic and electric energy is one of the most fundamental equations of the theory for it forms the basis of a variational principle. Since the class of waveguide problems which can be solved rigorously is very limited, the variational formulation is important in almost all calculations. This variational principle can be derived as follows: From Eq. (60) we can write...
Page 5 - V • (A x B) = (V x A) - B - (V x B...
Page 88 - Equation (1.5) signifies that the tangential component of the electric field is continuous across the boundary, whereas the tangential component of the magnetic field is discontinuous by an amount equal to the surface current density.
Page 275 - ... moving in a circular orbit of radius r in a uniform magnetic field of strength H.
Page 37 - M is distributed uniformly over the surface of a sphere of radius a the potential is constant inside of the surface, and its value is Fi = M/a.
Page 39 - Solve for the above potentials in some gauge, and find the asymptotic radiation field. Now what is the relationship between E and B? Construct the spectral-angular distribution of the radiated power. How do it change under the duality transformation (1.219)?
Page 147 - ... the trilinear coordinates of a point are the perpendicular distances from the origin to the three lines drawn through the point parallel to the sides of the triangle. A coordinate is...

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