Laser vacuum acceleration can be optimized significantly by applying a static magnetic field which is along the direction of laser magnetic field. This setup can cause a charged particle to be of a periodic, oscillatory-rising velocity, and significantly high kinetic energy. Moreover, the contribution from the motion vertical to accelerating electric field is fully taken into account and is found to be essential to efficient acceleration.

A new scheme of particle acceleration is verified by the investigation on single-body dynamics of charged particle in a compound field setup. This compound field setup contains a linear polarized laser field and a DC electric field which is along the direction of laser magnetic field. This setup can cause a charged particle to be of aperiodic motion and significantly high kinetic energy. Moreover, the contribution from the motion vertical to accelerating electric field is fully taken into account and is found to be essential to efficient acceleration. The efficiency of such a setup in acceleration is higher than that of a single laser.

The relativistic motion of a charged particle is studied in an inhomogeneous field of finite duration laser pulse. An inhomogeneity in a laser field is due to the spatial variation of laser intensity. Such a variation in laser intensity is characteristic of focused and de-focused laser beams. In the presence of an inhomogeneity, the problem becomes non-integrable and hence particle dynamics can not be derived exactly. In the present work considering a slow variation in the laser intensity, it is shown that the particle dynamics is associated with an adiabatic invariant. It is further found that the adiabatic invariant itself evolves and in a typical example changes such that the adiabaticity parameter attains a value of order unity. Thus higher orders of invariance are required for specifying the particle dynamics in terms of an adiabatic invariant. An adiabatic formalism is derived using the Lie transform perturbation method for calculating the higher orders of invariance and to obtain the evolution of the adiabatic invariant. The estimates of energy gained by a particle considering focused laser field are obtained by solving the equation of motion numerically. On comparing the results of a numerical experiment with theoretical predictions, it is found that the energy estimates improve on taking into account higher orders of invariance predicted by the present theory.