Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves

Abstract

We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations are solved for these cases and approximations analysed. For the magnetic node solution (homogeneous, time-dependent electric field), the modified Volkov wavefunction which arises from a high-energy approximation is found to be inaccurate for all energies and the solution itself unstable when photon emission (nonlinear Compton scattering) is included. For the zero initial transverse canonical momentum case, in both quantum and classical cases, forbidden parameter regimes, absent in the plane wave model, are identified.For quantum electrodynamical (QED) calculations in a strong laser background, a general method to deal with the interaction between laser fields and charged particles is to employ the laser-dressed particle-state solution of the relevant relativistic quantum dynamical equation (Dirac for fermions and Klein-Gordon (KG) for scalars). However, only for a very limited number of background fields has the exact solution been obtained analytically. The most widely used "Volkov states" are the solutions to the Dirac and KG equations in a planewave electromagnetic background (reviews can be found in [1][2][3][4]). These form the basis of the plane wave model. In this model, QED processes with highly relativistic incoming particles in an arbitrary laser field background are well-approximated by calculating the same processes in a plane-wave background. This is supposed valid when the electromagnetic invariants are much smaller than the classical and quantum nonlinearity parameters [5].Due to the high degree of spatial focussing required to reach extreme field intensities in experiment, there has been recent interest in going beyond the plane wave model. Univariate, transverse but non-lightlike backgrounds have been studied for the case of k 2 > 0 (an electric vacuum) [6-11] and k 2 < 0 (a magnetic vacuum) [6,12,13]. Motivation for calculating QED in non-lightlike backgrounds stems from interest in quantum processes in dispersive media such as crystals [14] and plasmas [15] but also strong magnetic backgrounds such as found in astrophysical objects like magnetars [16].The constructive interference that accompanies coherent addition of multiple laser pulses has often been suggested as a mechanism to reach the high field intensities * b.king@plymouth.ac.uk required to trigger electron-positron cascades in an experiment [17,18]. On the one hand, the magnetic node of a standing wave is a particularly popular background for simulations [19][20][21][22][23], which rely upon the locally constant field approximation [24,25] within the plane wave model. On the other hand, there is a rich particle dynamics even when just two plane waves are combined to form a standing wave (this has recently been investigated classically when radiation reaction is incorporated [26]). High-energy approxi...

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