1. ACCELERATION BY TIME VARYING FIELDS

1. 1 Time varying magnetic field: the betatron concept The betatron accelerator is the only circular machine which uses a time varying magnetic field to accelerate the particle. It is typically an induction accelerator. Notice that induction linear accelerators are also used. The betatron, as shown on Fig. 1, is a very simple machine which consists of a magnet fed by an alternating current at a frequency usually between 50 to 200 Hz. The magnet poles which surround the vacuum chamber where particles circulate are truncated cones. In this machine the magnetic field is used for guiding the particles on a circular trajectory as well as for acceleration. Fig. 1 The betatron scheme The variable magnetic field produces an electric field component according to Maxwell's equations: E = − gradV − ∂A∂t B = µH = curl A In the present case where there is no scalar potential, and according to the field symmetry, one has: V =