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

Abstract

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.

Effect of radiation-reaction on charged particle dynamics in a focused electromagnetic wave

“…It is under this approximation transverse variation may be neglected as compared to longitudinal variation in amplitude. This is the simplest way to model a focused light wave and has been used in some earlier works 9 , 10 , 26 . Following these references we have modelled the vector potential of a focused light wave as , where a ( z )is the spatially dependent amplitude of the vector potential, z being the direction of propagation and which depends only on the phase , is product of an oscillatory part and a pulse shaping envelope (for a wave train is unity).…”

“…It is under this approximation transverse variation may be neglected as compared to longitudinal variation in amplitude. This is the simplest way to model a focused light wave and has been used in some earlier works 9,10,26 . Following these references we have modelled the vector potential of a focused light wave as…”

“…( 9) and p z is evaluated using Eq. (10) taking ζ (φ) to be a purely sinusoidal function of φ . Multiplying both sides by , Eq.…”

“…For slow spatial variation of the vector potential, using adiabatic approximation, an approximate expression for showing its dependence on particle position was obtained (for calculations of with higher orders of approximation, see Ref. 10 ). It was found that the particle gains energy (along with forward momentum), when it is kept in the defocused region of the light wave.…”