Accelerator with

a constant gradient of the field - the family ring particle accelerators, including, inter alia, synchro trony, mikrotrony, betatrony and synchrotrony protic (with a weak focusing). Their common feature is the reduction of the magnetic field along the radius of the electromagnet. In the cyclic magnetic field accelerating acting (Lorentz force) perpendicular to the direction of centripetal force acts as a force to the particle flight trajectory, which is a circle of radius r: which leads to the following formula: The dependence shows that a particle moving faster moves along larger radius.