The Theory of the Synchrotron

In accelerators of the type discussed by Veksler and McMillan (e.g., the synchrotron and synchro-cyclotron) the motion of particles can be described in terms of stable oscillations about a synchronous orbit. Expressions are worked out for the frequencies of these oscillations, and for the way in which their amplitudes are damped as the energy is increased. The effect of radiation losses on the damping is discussed. It is shown that the synchrotron can advantageously be operated as a betatron until the electron velocity is close to that of light; the dee voltage is then turned on and the machine works as a synchrotron for the remainder of the acceleration. The transition from betatron to synchrotron operation proved to be quite efficient. Formulae are given for the distortions of the orbits by azimuthal asymmetries of the magnetic field. The results are illustrated in terms of the California synchrotron.