Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration

Abstract

This study examines single-particle electron motions in both a plane electromagnetic wave and a Gaussian focus in vacuum. Exact, explicit analytic expressions for relativistic electron trajectories in a plane wave are obtained, using the proper time as a parameter, in the general case of arbitrary initial positions and velocities. It is shown that previous analyses can be completed using the proper-time parameter. The conditions under which localized oscillatory motions ('figure-of-eight' orbits) occur are derived from the new solutions. The general solutions are also connected with the figure-of-eight orbits by a Lorentz transformation. The analytic solutions for arbitrary initial conditions and an arbitrary initial field phase can be used to determine the ranges of electron ejection angle and emerging electron energy in a vacuum laser accelerator, in which electrons are ejected externally, and provide a basis for explaining the spectrum of nonlinear Thomson scattering radiation. Numerical solutions are used for electron motions in the focus of a Gaussian laser beam, and the mean motion allows one to test a new expression for the relativistic ponderomotive force. It is suggested that plane wave solutions can provide a basis for approximating the orbital motion of particles in Gaussian beams.

Favorable target positions for intense laser acceleration of electrons in hydrogen-like, highly-charged ions

“…For the simple case of free electrons interacting with a plane wave laser field, explicit exact analytic expressions for relativistic electron trajectories are presented in Ref. 58 for arbitrary initial positions and velocities. For a focused laser pulse, approximations and numerical integrations are necessary.…”

“…For a plane-wave laser field, analytic solutions have been given for free electrons (i.e., E C ¼ 0) with arbitrary initial position and momentum. 58 In general, when both the electromagnetic and Coulomb fields are present, these equations are integrated numerically using the Runge-Kutta method with self-adaptive steps. In classical mechanics, if some electrons move too close to the nucleus, they will very likely fall into the nucleus owing to the Coulomb singularity at r ¼ 0.…”

Nonlinear relativistic single-electron Thomson scattering power spectrum for incoming laser of arbitrary intensity

“…[12][13][14][15][16][17] See also Ref. 18 for a recent account of the exact solutions, which the authors of that work also deem important as a basis for the computation of Thomson scattering spectra.…”

“…As it is well known, incoherent and collective TS occur in certain regimes which are different from each other. 2 We remind that the classical equations of motion for a relativistic electron subject to an incoming (non-necessarily monochromatic) electromagnetic plane wave have been solved exactly in an analytical (although implicit) way, 12 which provided the basis for subsequent approximate studies of incoherent TS, [13][14][15][16][17][18] by using the Liénard-Wiechert radiated fields. 19 Recently, 20 the present authors extended those researches.…”

Net energy gain in direct laser acceleration due to enhanced dephasing induced by an applied magnetic field

“…Energy is periodically gained and lost with each cycle of oscillation, and if the adiabatic nature of this oscillation is not broken by some means then the electron may only gain an absolutely negligible amount of energy. Vacuum Laser Acceleration (VLA) faces essentially the same problem [27][28][29][30][31][32][33][34][35][36][37] . To be absolutely clear : net energy gain is the energy gained by the particle after the laser interaction has completely ceased, and this is quite distinct from the 'instantaneous' energy that the electron can acquire while the interaction with the laser pulse is on-going 10 .…”