Sec. 21.5] THE CYCLOTRON 487 



This limitation, inherent in a combination of fixed magnetic and constant- 

 frequency electric fields, can be removed either by slowly increasing the 

 magnetic field or by slowly reducing the electric-field frequency to match 

 the particle's angular velocity during the period of acceleration [10-13]. The 

 first method is impracticable in the magnetic structure required for the 

 cyclotron. The second alternative, however, has proved successful and has 

 been used for the acceleration of deuterons to ~ 200 mev [14,15] correspond- 

 ing to a mass increase of 10 per cent. The dee-voltage frequency is slowly 

 decreased over the period of time required by an ion starting from the center 

 to reach the maximum radius. The per cent frequency modulation required 

 depends on the mass of the ion and the maximum energy to which it is accele- 

 rated. Exact correspondence between the changing rotational frequency and 

 the modulation frequency, or more correctly, their instantaneous rates of 

 change, is not necessary since it has been shown that a slight mismatch in 

 the two frequencies leads to oscillations about the equilibrium phase which 

 are stable for an adiabatically changing field frequency. Precise control 

 of the field, therefore, is not an important factor to contend with, and the 

 field frequency need only approximate the instantaneous rotational frequency 

 of the particle given by 



f - foB 

 3 ' ' (1 + E)H 



where f = resonant frequency at low energies. 

 E — energy of particle in units of Mcr 

 H = magnetic field strength at center 

 H = magnetic field strength at radius where energy is E 



An example of the frequency-modulated cyclotron is shown in Figs. 127 

 and 128, illustrating the 184-in. cyclotron of the University of California. 

 Modulation is accomplished with a rotating condenser mounted at the end 

 of the dee stem [15,16]. 



Unlike the conventional cyclotron, the beam in this modified form must 

 be pulsed. Ions are injected during an interval of a few microseconds only 

 at the beginning of the modulation cycle when the electric-field frequency is 

 in resonance with the particle's rotational frequency at low energies. Aside 

 from frequency modulation and a pulsed beam, the characteristics and struc- 

 ture of the synchro-cyclotron are similar to the conventional cyclotron. 

 The ultimate energy that can be reached is now dependent wholly on prac- 

 tical considerations. 



Modulation of the field frequency can be accomplished by varying either 

 the inductance or capacitance of the resonant dee circuit. Several mechani- 

 cal systems have been successfully developed which provide frequency 



