By B. Mueller
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E(z) is usually at least approximately an even function about a geometric center of the gap. 12) When E(z) is an even function about the geometric center of the gap, the electrical center and the geometric center coincide. When Eq. 13) L/2 −L/2 E(0, z) dz Then the transit-time-factor expression in Eq. 13) is the average of the cosine factor weighted by the field. The transit-time factor increases when the field is more concentrated longitudinally near the origin, where the cosine factor is largest.
Note that all of the first five TE11p modes now lie below the TM010 frequency. Calculate the RF surface resistance and skin depth of room-temperature copper at 400 MHz. 7 × 10−8 -m. 8. Calculate the RF surface resistance of superconducting niobium at 400 MHz. Assume a residual resistance Rresidual = 100 × 10−9 . What is the ratio of the RF surface resistance of superconducting niobium to that of room-temperature copper? 0 K. 9. Design a room-temperature cylindrical cavity that operates in the TM010 mode at 400 MHz with an axial electric field E0 = 1 MV/m, and a length = λ/2, where λ is the RF wavelength in free space.
The Feynman Lectures on Physics, Addison Wesley, 1963 Vol. 2, p. 18–11. , (1940) J. App. Phys. , (1941) J. App. Phys. 12, 129. Potentials that satisfy Eq. (14) are said to belong to the Coulomb gauge. Note that for this case, because φ = 0, Eq. (11) is also satisfied and the potentials belong simultaneously to the Lorentz and Coulomb gauges. , 1958 Topics in Electromagnetic Theory, John Wiley & Sons, New York, pp. , 1964 Electromagnetic Slow Wave Systems, John Wiley & Sons, New York, pp. 17–19.