Acceleration of relativistic electrons by an intense focused laser radiation combined with a static homogeneous almost collinear magnetic field

Interaction of electrons with a focused laser field combined with a static magnetic field is considered. The gain of energy acquired by the electron after crossing the laser focus is found. Optimal conditions for efficient acceleration of electrons are determined. The efficiency of acceleration is shown to be maximal in the case of almost, but not exactly, coinciding directions of a static magnetic field and of propagation of the laser radiation (almost collinear geometry). A small optimal angle between these two directions is shown to be on the order of the inverse relativistic factor 1/γ. An optimal ratio of the `transverse to longitudinal' electron energy in a static magnetic field and optimal conditions of light focusing are found. The optimized electron energy gain Δε_opt is shown to be a linear function of γ. It is shown that Δε_opt can be rather large at a moderately high intensity of the laser radiation in the focus