Problem 3.399

Since the period of revolution of electrons in a uniform magnetic field rapidly increases with the growth of energy, a cyclotron is unsuitable for their acceleration. This drawback is rectified in a microtron (Fig. 3.105 ) in which a change \(\Delta T\) in the period of revolution of an electron is made multiple with the period of accelerating field \(T_{0} .\) How many times has an electron to cross the accelerating gap of a microtron to acquire an energy \(W=\) \(=4.6 \mathrm{MeV}\) if \(\Delta T=T_{0}\), the magnetic induction is equal to \(B=107 \mathrm{mT},\) and the frequency of accelerating field to \(v=3000 \mathrm{MHz?}\)