A new particle acceleration method that is based on betatron acceleration is proposed for cyclic accelerators; however, in contrast to the betatron, the acceleration process can be repeated without loss of the previously gained energy. This is achieved by an appropriate radial change of the orbits. Use is being made of an azimuth-independent vector potential with components that are different functions of time. Explicit calculations are made in first-order perturbation theory. Accelerated are any magnetically guided charged particles independently of charge sign, particle mass and energy, cyclotron and betatron frequencies, and phases, also simultaneously. Large acceleration rates may be achievable, as well as a ratchet-like performance. Possible applications and implications are discussed. r Particles of a given charge q may be accelerated by applying an electric fieldẼ. For example, static or stationary electric fields produced by an electric potential F that is static or a vector potentialà varying in time, respectively, are used to producẽ E in the cases of a van de Graaff and a betatron, respectively: the particles gain energy while running down F or feel the electric field connected with building upÃ, respectively. As F andà are limited, so is the maximum energy achievable. In the betatron case there are no restrictions in frequencies and phases: neither for the revolutions with the cyclotron frequency o nor for the oscillations around the stationary orbit in the form of radial and axial betatron oscillations with the betatron frequencies o r and o z , respectively. This shall be called phase-free acceleration.If particles are to be accelerated up to high energies, an alternating electric fieldẼ (AC field, or, at higher frequencies, also called RF field) is applied. The common recipe is to let the particles on their trajectory feel the field when it is in its accelerating phase and shield them against the field when it would be, without shielding, in its decelerating phase. This implies a phase ARTICLE IN PRESS www.elsevier.com/locate/nima 0168-9002/$ -see front matter r
