Electromagnetic Radiation: Variational Methods, Waveguides and Accelerators
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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angle angular approximation arbitrary asymptotic Bessel functions boundary condition cavity characteristic impedance charge density circular guide components conductor consider constant coordinates corresponding cross section current density cutoff wavelength cutoff wavenumber cylinder cylinder coordinates deﬁned derived differential equation dominant mode E-mode function eigenfunctions eigenvalue electric and magnetic electric field electromagnetic electron energy density expression ﬁeld ﬁnd ﬁrst Fourier frequency Green’s function H mode half plane harmonic Hence Lagrangian linear longitudinal lower limit magnetic field matrix Maxwell equations mode functions momentum normal obtained orthogonal particle plane wave potential Poynting vector propagation quantities radiation radius Rayleigh’s principle region relation result satisﬁes Schwinger solution stationary symmetry tangential theorem tion transformation transmission line transverse triangle unit length vanishes variational principle vector velocity voltage wave equation waveguide z-axis zero