CHAPTER 23 

 THE SYNCHROTRON 



23.1. Description. The synchrotron, proposed independently by 

 McMillan [1] and Veksler [2], employs certain properties of both the cyclotron 

 and betatron to accelerate electrons to very high energies. Electrons, 

 injected with a velocity near that of light with an electron gun, are first 

 accelerated by betatron operation for which flux bars (Fig. 135) located 

 within the orbit provide the necessary time rate of change of flux through 

 the orbit due to the slowly increasing magnetic field. At a certain energy the 

 flux bars become saturated, the flux remains essentially constant thereafter, 

 and betatron operation ceases. At this time a constant radio-frequency 

 voltage is applied to the dee and the electrons are then accelerated to high 

 energies by cyclotron-like operation. Since electrons are injected with 

 nearly the velocity of light, the radius increases by only a few per cent during 

 subsequent acceleration. The magnetic field, pole pieces, and vacuum 

 chamber therefore are confined to a narrow annular region about the stable 

 orbit, as illustrated in Fig. 136. 



A principal characteristic of the synchrotron is its "phase stability." The 

 angular velocity of an electron traversing a circular trajectory normal to a 

 magnetic field is 



ell ecll 



u> = 



mc E 



where e = electronic charge 



m = relativistic electronic mass 



H = magnetic field strength 

 c = velocity of light 



E = total energy of electron, kinetic plus rest energy 

 As the energy and relativistic mass of the electron increases, the magnetic 

 field at the orbit must increase correspondingly if the electron is to remain in 

 or near resonance with the oscillating electric field applied to the dee. With 

 a magnetic field that increases slowly during the period of acceleration, oscilla- 

 tions in phase are stable and tend to be damped. In effect, the phase 

 stability causes the particles to remain in or near resonance with the electric 

 field, making only small departures from exact resonance. This can be 

 shown by the fact that an electron traversing the dee gap too early, i.e. at a 

 time when the dee voltage is low, receives a smaller impulse than an electron 



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