Accelerated Particles in an AVF Cyclotron with a One or a Two Dee System

A general analytical theory is given, describing the motion of accelerated particles in an AVF cyclotron with a one or a two Dee-system. A Hamiltonian is formulated for the horizontal motion of these particles. Especially on the first turns, where the energy gain per turn is not small with respect to the particle energy, the structure of the Dees has much influence. For high harmonic acceleration, the motion in the radial phase space may even become unstable. A coupling exists between radial and longitudinal motion. In a few examples the applicability of the formulated theory is illustrated.