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 $v=3000 \mathrm{MHz?}$