Adiabatic formulation of charged particle dynamics in an inhomogeneous electro-magnetic field

Abstract

AbstractThe 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.