ABSTRACT
Veksler in his first paper [1.1] on phase stability in 1944 proposed a modification of the cyclotron for electrons, which is now called the microtron. This machine has a constant and homogeneous magnetic field and a constant accelerating rf voltage usually with wavelength A ~ 10 cm, i.e. it is the microwave band that gives the name of this machine. The same idea had already been mentioned in 1939 in the USA (by Alvarez, as it was cited in [1.2]) and in Japan in 1945 (by Itoh and Kobayashi [1.3]), but Veksler was the first one to publish. The first estimate of the phase and energy region where stable acceleration is possible was made in [1.3]. A few years after Veksler’s original publication the race-track microtron was suggested by Schwinger (cf Schiff 1946
[L4])·The electron trajectory in a microtron is a system of circles, increasing in diameter, with a common tangent point where the accelerating cavity is placed — Fig. 1.1. The revolution period of electrons in the microtron after n transits across the accelerating cavity is
(1.1) where En is the total electron energy at π-th revolution and В is the magnetic field strength. Thus, the time required to complete one revolution is proportional to the total energy of the particle and an increase in period from one revolution to the next is directly proportional to the energy gain, i.e.
