Three-dimensional relativistic model of a bound particle in an intense laser field

Relativistic high-power laser–matter interactions

“…Nevertheless, expressions in closed form for the transition amplitude are restricted to the Born approximation for the Coulomb field of the ionic core. Finally, in the theory of relativistic direct strong field ionization we should mention also an exact solvable model of a Klein-Gordon particle in a separable short-range potential [102].…”

Effective photon mass and exact translating quantum relativistic structures

“…As an alternative to the traditional Volkov assumption, the quantum state contains a stringent dependence on the radial coordinate, mediated by the scalar potential /ðrÞ appearing in the fundamental equation (26). The procedure can work only in a plasma medium, which implies a non-zero photon mass.…”

“…(64) assuming decaying boundary conditions, plus the use of the dispersion relation (7), the KGE (13), the radial equation (26), the definition (27), and the normalization condition (34). In such way, we finally derive the simple expression…”

“…(6) represents an exact solution for the KGE for a charged scalar in the presence of a transverse plasma wave, provided the traveling envelope function w in Eq. (15) is defined in terms of RðrÞ; SðhÞ satisfying the uncoupled linear system of second-order ordinary differential equations (25) and (26). The corresponding static EM field is…”

“…Examples are provided by the analysis of the Zitterbewegung (trembling motion) of Klein-Gordon particles in extremely small spatial scales, and its simulation by classical systems, 16 the KGE as a model for the Weibel instability in relativistic quantum plasmas, 17 the description of standing EM solitons in degenerate relativistic plasmas, 18 the KGE as the starting point for the wave kinetics of relativistic quantum plasmas, 19 the KGE in the presence of a strong rotating electric field and the QED cascade, 20 the Klein-Gordon-Maxwell multistream model for quantum plasmas, 21 the negative energy waves and quantum relativistic Buneman instabilities, 22 the separation of variables of the KGE in a curved space-time in open cosmological universes, 23 the resolution of the KGE equation in the presence of Kratzer 24 and Coulombtype 25 potentials, the KGE with a short-range separable potential and interacting with an intense plane-wave EM field, 26 electrostatic one-dimensional propagating nonlinear structures and pseudo-relativistic effects on solitons in quantum semiconductor plasma, 27 the square-root KGE, 28 hot nonlinear quantum mechanics, 29 a quantum-mechanical free-electron laser model based on the single electron KGE, 30 and the inverse bremsstrahlung in relativistic quantum plasmas. Very often, the treatment of charged particle dynamics described by the Klein-Gordon or Dirac equations assumes a circularly polarized electromagnetic (CPEM) wave, [31][32][33][34][35][36][37][38][39][40] mainly due to the analytical simplicity.…”