496 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 23 



but would maintain a constant average energy while performing phase 

 oscillations about the equilibrium phase. However, if the magnetic field is 

 increased adiabatically, i.e., an infinitesimal increase in H during one cycle of 

 the particles, the phase oscillations will still remain stable but the circulating 

 electron group as a whole must receive a net increase in energy from the 

 electric field at each transit of the gap if the angular frequency is to remain 

 constant. The ultimate energy is not limited by the radius as in the cyclo- 

 tron, since here it remains nearly constant, but rather by radiative losses 

 from the electrons at very high energies. An energy can, in principle, be 

 reached for which the energy loss by radiation just equals the energy derived 

 per cycle from the electric field. 



In principle, the structure of the synchrotron magnet is similar to the core 

 of a large transformer. The yoke is built up from thin laminated plates of 

 iron to reduce excessive heating and loss from eddy currents. The annular 

 pole pieces similarly are constructed of thin laminations bonded with a non- 

 conducting material and shaped to give the requisite bowed field required for 

 focusing. The varying magnetic field is produced by coils wound on the 

 upper and lower pole pieces and energized at the desired frequency by dis- 

 charges from banks of condensers. 



Structural details of a synchrotron built for the Atomic Energy Comission 

 at the University of California are shown in Figs. 135 and 136. 



23.2. Motion of Particles, a. Synchronous Orbits. The condition for a 

 synchronous orbit is satisfied when the electron rotates in resonance with the 

 electric field at an angular velocity given [1,2] by 



eH ecH 

 m s c E s 



Alternatively, this gives the equilibrium energy at a particular value of H. 

 The angular position of an electron with respect to the gap when the dee 

 voltage is zero is referred as the phase <p. In the synchronous orbit, the 

 phase is constant and results in an energy gain per turn of eV sin <p, where V 

 is the peak radio-frequency dee voltage. The equilibrium or synchronous 

 phase, which can be determined from the conservation of energy, is given 

 [1,3] by the expression 



eV sin <p s = AE S + L s — 2irr s Vi 



. . _, 2t ec dH 



where AE S = — — —rr — energy gain per turn 

 oi dt 



L = radiation loss per turn 

 r = (E 2 — m 2 c 2 )/300H = equilibrium radius 

 Vi = voltage due to changing magnetic flux. This contribution is 

 usually small after synchrotron operation has started 



