Hand written solution required

Problem 1. In single-cell pillbox cavity, TM010 mode can be expressed as blow. He Ez b 2b d He = 7/1 (2.405 ) sin(WRFt) Ez = A/o (2.405 ) Cos(WRFt) 2.405c C The resonance frequency is fres = 27b 2.62b d) Assume that the gradient of the accelerating cavities increases by a factor of Vk if the resonant frequency of accelerating cavities is increased by a factor of k. When the RF cavities with the rf frequency of fRF= 11.7 GHz are chosen for the Next Linear Collider (NLC), estimate the length of linear accelerator required to reach the energy of 50 GeV with electrons injected at 1 GeV energy. Discuss your results