New general beam dynamics formulation for the program Dynac

Until recently beam dynamics programs for electrons and ions have been fundamentally different because longitudinally the energy can change much more quickly with respect to the rest mass for electrons than for ions. A program, DYNAC, was proposed with the aim to treat long accelerating elements as currently used in superconducting systems for any type of particle. To obtain high accuracy, keeping a relatively simple formalism, DYNAC is now using a new concept of equivalent accelerating fields. Many examples have been treated (different fields and particles) and results will be presented including the comparison with an elaborate step by step integration method with a realistic electromagnetic field