New exact solutions of the Dirac and Klein–Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

Abstract

Abstract.The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n m < 1, have been studied. In the Dirac case the found exact solutions [21] are expressed in terms of new complex polynomials, and in the Klein-Gordon case they are expressed in terms of Ince polynomials [22]. In each case these solutions form a doubly infinite discrete set, parametrized by quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation (which may be considered as a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma). This solutions describe a high-contrast periodic structure of the particle density on the plasma length scale, and they may have relevance in the study of novel acceleration mechanisms.

Classical and quantum particle dynamics in univariate background fields

“…(For linear polarization one finds instead the Hill equation, some exact solutions of which have recently been investigated in detail in [18][19][20].) Despite the apparent simplicity of the classical theory, the quantum theory exhibits an intricate nonperturbative structure for k 2 ≠ 0 [40,54].…”

“…In order to gain analytical insights, confirm numerical results, and improve experimental predictions, we must go beyond the plane wave model [16][17][18][19][20][21][22][23]. This task is as challenging as it is open-ended.…”

Electron acceleration in underdense plasmas described with a classical effective theory

“…In this scheme the electrons are accelerated by the strong electromagnetic field of Gaussian laser pulses, as presented by Sohbatzadeh and Aku (2011); Sohbatzadeh et al (2006). Even in the frame of relativistic quantum mechanical description Varró (2014) has recently shown that there exist closed analytic solutions of the wave equations (Dirac and Klein-Gordon equations) if one takes into account the effect of the plasma through a phenomenological index of refraction (n m ). Needless to say, such an approach may also be meaningful in the classical (non-quantum) regime, where the index of refraction is contained in the Lorentz force.…”

Effective photon mass and exact translating quantum relativistic structures

“…For instance, consider the discussion of higher harmonic solutions of the KGE with a large n, in the context of a charged particle propagation under strong laser fields in underdense plasmas. 51 Possible experimental realization of the confining EM fields would involve high-intensity-laser-driven Z pinches as described in Ref. 52.…”