Sec. 21.1] THE CYCLOTRON 477 



where m = mass of particle 



v = linear velocity 



e = charge of particle 



H = magnetic field strength 



n = number of traversals of gap 



V = peak radio-frequency voltage 



<p = phase of particle: angular position from gap when V = 

 The angular velocity of the accelerated particle is independent of energy 

 and linear velocity, provided that the relativistic increase in mass is negligible. 

 The period of rotation is then constant, and its magnitude is given by 



_ 2-Ktnc 



The frequency of the particle, as well as that of the oscillating electric field, 

 is, correspondingly, constant with a magnitude given by 



1 ell , 



T 2irtnc 



The highest energy to which a particle can be accelerated is determined, aside 

 from the limitation imposed by the relativistic increase in mass, by the mag- 

 netic field strength and the maximum orbital radius. 



_ e' 2 R 2 H 2 



Imc 1 



where R = maximum radius 

 c = velocity of light 

 If the frequency and peak voltage applied to the dee are kept constant and 

 only the magnetic field is altered for the acceleration of particles of different 

 mass, the maximum energy to which the particles can be accelerated for a 

 given radius is directly proportional to the mass. 



iVax = lirhnu-R' 2 



After the particles have been accelerated to the maximum energy and 

 radius, extraction of the beam is accomplished, for energies up to 50 mev at 

 least and possibly higher, by electrostatic deflection of the particles from their 

 normal orbit. A long curved plate located a quarter or third of the distance 

 along the periphery of the orbit is operated at a sufficiently high negative 

 potential to deflect the beam out of its normal orbit and into the region where 

 the magnetic field begins to fall off rapidly. In this way the beam can be 

 directed into a tangentially located target chamber and if necessary brought 

 out of the vacuum tank through an aluminum-foil window. 



