2011
DOI: 10.1088/0741-3335/53/12/125006
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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 der… Show more

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Cited by 21 publications
(17 citation statements)
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“…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.…”
Section: B Relativistic Classical Trajectory Monte Carlo Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…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.…”
Section: B Relativistic Classical Trajectory Monte Carlo Methodsmentioning
confidence: 99%
“…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.…”
Section: B Relativistic Classical Trajectory Monte Carlo Methodsmentioning
confidence: 99%
“…[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.…”
Section: B Classical Equations Of Motion For the Electronmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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 .…”
Section: Introductionmentioning
confidence: 99%