The Stability of Electron Orbits in the Synchrotron

Abstract

The motion of an electron in a synchrotron (or betatron) is analyzed as its motion in an axially symmetric magnetic field under the action of external torques provided by an r-f field and radiation reaction acting about the axis of symmetry. The process of transition from betatron to synchrotron action is examined in detail and a criterion is established for the condition of "locking-in" of the electrons to the r-f wave which drives them synchronously. The typical stages of synchrotron operation are discussed and it is shown that the requirements for successful, stable operation should not be difficult to realize.