Classical dynamics of free electromagnetic laser pulses

Abstract

We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multiand single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a potential means for experimentally bounding the fundamental length scale in the generalized electrodynamics of Bopp, Landé and Podolsky.Keywords: Laser pulse, finite energy, Maxwell equations, Bopp-Landé-Podolsky Advances in laser technology have made possible the exploration of physical processes on unprecedented temporal and spatial scales. They have also opened up new possibilities for accelerating charged particles using lasermatter interactions. Multi-and single cycle high intensity (10 10 − 10 15 Watts/cm 2 ) laser pulses can be produced using Q-switching or mode-locking techniques [1]. Such pulses can accelerate charged particles such as electrons to relativistic speeds where radiation reaction and quantum effects may influence their dynamics. Lower intensity pulses have also been used as diagnostic tools for exploring the structure of plasmas in various states [2,3]. In order to interpret experimental data involving classical laser interactions with both charged and neutral matter, theoretical models [4][5][6][7] rely crucially on parameterizations of the electromagnetic fields in laser pulses, particularly in situations where traditional formulations using monochromatic or paraxial-beam approximations have limitations [8][9][10].In this Letter we discuss a viable methodology for parameterizing a particular class of propagating solutions to the source free classical Maxwell equations in vacuo that offers an efficient means to explore the classical effects of compact laser pulses on free electrons in dynamical regimes where quantum effects are absent. The parameterization is based on a remarkable class of explicit solutions of the scalar wave equation found by Ziolkowski [11][12][13][14][15] together with the behaviour of charged particle-pulse interactions over a broad parameter range without recourse to expensive numerical computation. Finally, we argue that such parameterizations can be used to find compact finite energy solutions to other linear wave equations. This is illustrated by showing that the generalized theory of Bopp [17], Landé [18] and Podolsky [19] admits such particular solutions that reduce to the Maxwell solutions when a fundamental length parameter in their theory tends to zero. Compact laser pulses in this theory might be used to explore properties of the theory by searching experimentally for bounds on this parameter.If a complex scalar field α satisfies α = 0 on spacetime and Π µν is any covariantly constant (degree 2) antisymmetric tensor field on spacetime (i.e. Π µν;δ = 0) for all µ, ν, δ...

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

“…The function ζ(t, ρ, z) is non-zero for all real t, ρ, z and hence both the real and imaginary parts of α(t, ρ, z) are bounded. To our knowledge, this constitutes a new source-free finite-energy solution for F to Bopp-Landé-Podolsky electrodynamics that does not arise in classical Maxwell electrodynamics [14].…”

“…The method of pre-potentials can be used to construct solutions to the source-free linear vacuum Maxwell system in Minkowski spacetime: using (7). We seek particular local complex solutions to (14) with the ansätz:…”

On gravitational chirality as the genesis of astrophysical jets

“…For gravitational wave spacetimes ψ is given by (8) for some choice of integers σ, m 1 and m 2 . For gravitational pulse spacetimes ψ is given by (12) for some choice of positive semi-definite integer m where ψ 0 = ∇ (η) dα and α is a spatially compact solution satisfying Lap (η) α = 0. In the context of astrophysical jet modelling, we have chosen (10) with strictly positive, real, dimensionless parameters κ, Q 1 and Q 2 .…”

Chirality in gravitational and electromagnetic interactions with matter

“…In particular, we construct families of new non-stationary metrics having propagating pulse-like characteristics with bounded components in three-dimensional spatial domains. The derivation of this class of solutions is based on a methodology used to construct single-or few-cycle laser pulse solutions to the vacuum Maxwell solutions in Minkowski spacetime [11]. To facilitate the construction of gravitational pulse-like solutions this methodology will be reviewed first.…”