2018
DOI: 10.1088/1751-8121/aaa304
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Travelling waves and a fruitful ‘time’ reparametrization in relativistic electrodynamics

Abstract: We simplify the nonlinear equations of motion of charged particles in an external electromagnetic field that is the sum of a plane travelling wave F µν t (ct−z) and a static part F µν s (x, y, z): by adopting the light-like coordinate ξ = ct−z instead of time t as an independent variable in the Action, Lagrangian and Hamiltonian, and deriving the new Euler-Lagrange and Hamilton equations accordingly, we make the unknown z(t) disappear from the argument of F µν t . We study and solve first the single particle e… Show more

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Cited by 15 publications
(67 citation statements)
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“…As fas as we now, such general solutions have not appeared in the literature before Ref. [1]. We next analyze a few special cases (the first two have already appeared in the literature).…”
Section: Dynamics Under a A µ Independent Of The Transverse Coordinatesmentioning
confidence: 85%
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“…As fas as we now, such general solutions have not appeared in the literature before Ref. [1]. We next analyze a few special cases (the first two have already appeared in the literature).…”
Section: Dynamics Under a A µ Independent Of The Transverse Coordinatesmentioning
confidence: 85%
“…x(t) = cp(t) m 2 c 2 +p 2 (t) (1) in its general form is non-autonomous and highly nonlinear in the unknowns x(t), p(t).…”
Section: Introductionmentioning
confidence: 99%
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“…In section II we discuss the motion of electrons when R = ∞ (χ R ≡ 1) using an improved plane hydrodynamical model [11,12] (for shorter presentations see [13]) that allows to reduce the system of Lorentz-Maxwell and continuity partial differential equations (PDEs) into ordinary differential equations (ODEs), more precisely into a family of decoupled systems of arXiv:1803.02915v2 [physics.plasm-ph] 25 Mar 2018 non-autonomous Hamilton Equations in dim 1 in rational form. In the model we alternatively adopt the light-like coordinate ξ = ct−z or time t to parametrize the electron motion, the transverse and the light-like components p ⊥ e , p 0 e −cp z e ≡ mc 2 s e (instead of the longitudinal one p z e ) of the electron 4-momentum as unknowns, neglect pump depletion, control how long this is valid, how long the hydrodynamical picture holds, when and where it fails (by wave-breaking [4]).…”
Section: Introductionmentioning
confidence: 99%