Sec. 21.2] 



THE CYCLOTRON 



481 



arises from the bowed magnetic field near the edge of the gap, providing 

 horizontal components in the magnetic field, as shown in Fig. 131.* Ions 

 that have wandered out of the median plane are continuously forced back by 

 interaction of their vertical velocity components with the horizontal field 



MEDIAN PLANE 



Fig. 130. Electric field focusing effect on ions in a cyclotron. The figure illustrates the 

 potential distribution in the gap between dee's. Due to the lenslike contour of the field, 

 particles in trajectories lying outside the median plane are deflected back toward the plane. 



component in the same way that the particle is constrained to move in a 

 circular or spiral orbit by the vertical component of the field. 



Both the electrostatic and magnetic focusing effects provide the requisite 

 restoring force to ensure the stability of oscillations of the orbits about the 

 median plane and the normal orbit. When the magnetic field possesses 



CIRCULAR ORBITS 

 DEFLECTED TOWARD 

 MEDIAN PLANE 



POLE PIECE 



Fig. 131. Magnetic focusing effect on ion trajectories of large radius in the cyclotron. 

 Cross-sectional view of magnetic field shows bowed lines of force near periphery which 

 deflect particles toward median plane. 



perfect radial symmetry, free oscillation can occur with both vertical and 

 radial components and only with periods equal to or longer than the rotational 

 period of the particle. Free oscillations in cyclotrons are neither damped 

 nor forced once they are excited. 



Oscillations in phase, i.e., the angular position of the particle with respect 

 to the gap when the dee voltage is zero, are stable for certain orbits. A 

 particle arriving at the gap early or late is retarded or advanced accordingly 



