Related papers: On Generalized Free Electron Laser Equation
The Euler-Poisson equations para determinar the rotation matrix of a rigid body can be solved without using of particular parameterization like the Euler angles. For the free Lagrange top, we obtain and discuss a general analytic solution,…
We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser (XFEL). We consider practically important case when XFEL is optimized for maximum gain. Such an optimization allows to reduce…
This paper is dedicated to finding the solutions of the equation of the loaded modified Korteweg-de Vries. By the way, it is shown to find the solutions via $(G'/G)$-expansion method that is one of the most effective ways of finding…
The method of zero range potential (ZRP) for one-electron problems is reviewed. In the absence of an external electromagnetic field, the notion of a ZRP is introduced from different points of view and for an arbitrary dimension of space.…
It is argued that in the paper by A.A. Garcia-Diaz and G. Gutierrez-Cano [Phys. Rev. D 100, 064068 (2019)] on nonlinear electrodynamics coupled to general relativity, along with some interesting results and useful observations, many…
It is shown that that the Volume free electron laser is a self-phase-locking system. Equations are derived that describe both the phase-locking process and the dependence of generation on the times of bunches' entering into the VFEL…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the…
A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A…
A method for computation of the matrix Mittag-Leffler function is presented. The method is based on Jordan canonical form and implemented as a Matlab routine.
In this work at first the relation the Mittag-Lefler function to the exponential is given. The results are applied to the construction of the solution of Cauchy problem for ordinary linear operator differential equations with constant…
In this paper, we present a covariant formalism that connects solutions to force-free electrodynamics in the non-null case and foliations of spacetime. In doing so, we are also able to derive an expression of the general non-null current…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
Calculating the electromagnetic field of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. While the correct field has been obtained many times and through various…
The process of nonlinear electron emission from a metal surface under the action of femtosecond laser pulse with moderate intensity $\sim10^{11}$~W/cm$^2$ is considered. One-dimensional model is formulated, taking into account the advantage…
The cumulant expansion is a powerful approach for including correlation effects in electronic structure calculations beyond the GW approximation. However, current implementations are incomplete since they ignore terms that lead to partial…
A generalization of the Dirac field equation in three-dimensional Minkowski space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$ symmetry is considered. Constraints that ensure a correct physical interpretation of the…
The variational equation for the mean square displacement of the electron in the polaron worldline approach to quenched QED can be cast into a form which closely resembles the classical Abraham-Lorentz equation but without the conceptual…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…