Fundamental studies on electron dynamics in exact paraxial beams with angular momentum

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Classical electromagnetic radiation with orbital angular momentum (OAM), described by nonvanishing vector and scalar potentials (namely, Lorentz gauge) and under Lorentz condition, is considered. They are employed to describe paraxial laser beams, thereby including non-vanishing longitudinal components of electric and magnetic fields. The relevance of the latter on electron dynamics is investigated in the reported numerical experiments. The lowest corrections to the paraxial approximation appear to have a negligeable influence in the regimes treated here. Incoherent Thomson scattering (TS) from a sample of free electrons moving subject to the paraxial fields is studied and investigated as a beam diagnosis tool. Numerical computations elucidate the nature and conditions for the so called trapped solutions (electron motions bounded in the transverse plane of the laser and drifting along the propagation direction) in long quasi-steady laser beams. The influence of laser parameters, in particular, the laser beam size and the non-vanishing longitudinal field components, essential for the paraxial approximation to hold, are studied. When the initial conditions of the electrons are sufficiently close to the origin, a simplified model Hamiltonian to the full relativistic one is introduced. It yields results comparing quite well quantitatively with the observed amplitudes, phase relationships and frequencies of oscillation of trapped solutions (at least for wide laser beam sizes). Genuine pulsed paraxial fields with OAM and their features, modeling true ultra-short pulses are also studied for two cases, one of wide laser beam spot (100 p.m) and other with narrow beam size of 6.4 p.m. To this regard, the asymptotic distribution of the kinetic energy of the electrons as a function of their initial position over the transverse section is analyzed. The relative importance of the transverse structure effects and the role of longitudinal fields is addressed. By including the full paraxial fields, the asymptotic distribution of kinetic energy of an electron population distributed across the laser beam section, has a nontrivial and unexpected rotational symmetry along the optical propagation axis.
© 2022 by the authors. I.P. acknowledges support from Ministerio de Ciencia, Innovacion y Universidades (Spain) under Projects RTI2018-100835-B-I00 (MCIU/AEI/FEDER, UE) and RTI2018-096967-B-I00. R.F.A.-E. acknowledges support from Ministerio de Ciencia, Innovacion y Universidades (Spain) under Project PGC2018-094684-B-C21 (contract partially funded by FEDER). L.R. acknowledges support from Laserlab V (Grant Agreement No. 871124, European Union Horizon 2020 INFRAIA research and innovation program), from IMPULSE (Grant Agreement No. 871161, European Union Horizon 2020 INFRADEV research and innovation program), and from Junta de Castilla y Leon Grant No. CLP087U16. R.F.A.-E. and F.C. are associate members of Instituto de Biocomputacion y Fisica de los Sistemas Complejos, Universidad de Zaragoza, Zaragoza, Spain.
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