By Emily Joy Drake
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Given the magnetic field, the radial electric field can be obtained from the differential form of Faraday’s law as Er = I0 e j(ωt−kz) µ0 c/2πr. Likewise, we find that a wave traveling in the −z direction has components I0 e j(ωt+kz) , Bθ = I0 e j(ωt+kz) µ0 /2π r, and Er = −I0 e j(ωt+kz) µ0 c/2πr. Adding these two waves produces a standing wave satisfying the boundary condition that the tangential electric field Er vanishes on the end walls at z = 0 and . 29) , p = 1, 2, 3, . . We note that the complex j factor in Eq.
The orbit of the betatron is circular, and that of the induction linac is straight. , (1924) Ark. Mat. Fys. 18, (No. 30), 1–4. , (1928) Arch. Electrotech. 21, 387. (1994) For a discussion of this and other work by Wider¨oe, see P. Waloschek, The Infancy of Particle Accelerators-Life and Work of Rolf Wider¨oe, DESY 94–039, Deutsches Elektronen-Synchrotron, Notkestrasse 85–22603, Hamburg, March. O. , (1930) Science 72, 376. H. , (1931) Phys. Rev. 38, 2021. H. , (1934) Phys. Rev. 46, 539. , (1946) Phys.
36) comprise a complete solution to Maxwell’s equations together with the remaining components Bz , Br , and Eθ , which are zero, as can be shown by direct substitution. 4 Transit-Time-Factor Models We can improve on the approximation for T in Eq. 15) by accounting for penetration of the field into the axial bore holes of drift tubes. Field penetration into the drift tubes reduces T, because it reduces the concentration of the field near the center of the gap. We assume that the electric field at the drift-tube 39 40 2 RF Acceleration in Linacs bore radius (r = a) is constant within the gap and zero outside the gap within the metallic walls, as shown in Fig.