Particle acceleration in extremely strong electromagnetic wave fields

The present paper can be seen in the context of work on the origin of high energy cosmic ray particles. The plane-wave formalism without radiation reaction based on the Lorentz equation is adequate for the description of particle dynamics if the wave amplitude is of moderate strength. Particle motion then is periodic in velocity space so that there is an upper limit to particle energy. We have shown that the plane-wave formalism without radiation reaction also is a powerful tool to define and to calculate important features of particle dynamics in spherical wave fields. Among these features are the acceleration boundary, the plasma border and the law of asymptotic energy. In extremely strong wave fields the influence of radiation forces has to be taken into account. Motion under the influence of the radiation reaction is no longer periodic in velocity space. Particles, at least in principle, can achieve unlimited values of energy. This may be relevant for the cosmic particle acceleration to extremely high energies as, for example, in cosmic jets associated with rotating magnetized configurations. One may also think of man made jets constituted of laser beams connecting natural or artificial satellites. It is the intention of this paper to present and to discuss some results, which may be of interest in the above mentioned context.<>