Stochastic and coherent acceleration of relativistic particles in a regular potential wavepacket perpendicular to a uniform magnetic field. Pt. 1

A promising physical process able to provide efficient particle acceleration in a plasma is the surfatron. In the basic picture a particle is accelerated without limit when it is trapped by a potential wave moving perpendicularly to a uniform magnetostatic field. In this paper we study surfatron acceleration due to a wave packet with waves evenly spaced in phase speed. Particles are accelerated by two mechanisms: diffusive acceleration due to the local instability leading to chaos and coherent acceleration due to trapping in the available subluminal waves. The probability of trapping in each wave is derived analytically and confirmed numerically. We account for the perturbations due to the other waves of the packet and find the arising of intermittency between chaos and regular motion. The consequences of this phenomenon are discussed. (orig.)