Question

The original (uniform magnetic field) type of fixed frequency cyclotron was limited in energy because of the relativistic increase of mass of the accelerated particle with energy. What percentage increment to the magnetic flux density at extreme radius would be necessary to preserve the resonance condition for protons of energy 20 MeV? A cyclotron is powered by a 50,000 V, 5 Mc/s radio frequency source. If it. diameter is 1.524 m. what magnetic field satisfies the resonance conditions for (a) protons (b) deuterons (c) alpha-particles? Also what energies will these particles attain? In a synchrocyclotron, the magnetic flux density decreases from 15,000 G at the centre of the magnet to 14,300 G at the limiting radius of 206 cm. Calculate the range of frequency modulation required for deuteron acceleration and the maximum kinetic energy of the deuteron. (The rest mass of the deuteron is 3.34 x 10-24 g) Calculate the magnetic field, B and the Dee radius of a cyclotron which will accelerate protons to a maximum energy of 5 MeV if a radio frequency of 8 MHz is available. When a cyclotron shifts from deuterons to alpha particles it is necessary to drop the magnetic field slightly. If the atomic masses of 2H and He are 2.014102 amu and 4.002603 amu, what is the percentage decrease in field strength that is required? [Osmania University]

please do last problem with neat work

Answer 1

Condition is The cyclotron resonance wa 28/m Waland For deuterons, wd = 1x Bd for alpha particles, wa- 2x Ba ma resonance frequency is to meantar unaltered Wd awd If the remain Ben 5 2x (2,0141032) 1.006396 Ba 4.002603) 21 Fractional decrease of magnetic field (Be - Bd)/B4 = +0.006355 or percentage decrease = 0.635502