Stability limits of the phase oscillations in a microtron

Abstract

The finite-difference equations existing in the literature for phase oscillations in a microtron are discussed first. It turns out that these equations are incorrect. A technique is then developed to analyse the effect of computing the stability limits with the aid of these equations. It is shown that the resulting phase stable regions really constitute a wrong result. Finally, a new treatment of the phase oscillations in microtron is given. The stability limits are derived from the general theory of phase oscillations. The results are: 1. 1) The range of equilibrium phase angles extends from 0° (corresponding to a peak voltage across the gap V′ = m 0 c 2/ e) up to 90° (corresponding to very high peak voltages). 2. 2) The bucket area is an increasing function of the peak voltage. 3. 3)At high peak voltages stable oscillations are connected with large radial excursions from the synchronous orbit.