Related papers: On Generalized Free Electron Laser Equation
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present…
A quantum model of a free-electron laser is considered for the many electron system. An exact expression for the evolution of the laser amplitude is obtained in the framework of the coherent state consideration. Reliable conditions for the…
Schrodinger equation for a charged particle interacting with the plane wave electromagnetic field is solved exactly. The exact analytic solution and the perturbative solution up to second order are compared.
This report is a primer introduction on the sources of coherent syncrotron radiation from FELs compared to conventional lasers. Even though the underlying mechanisms are different, FELs can be considered a laser source to all effects. In…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
We examine the experimental requirements for realizing a high-gain Quantum free-electron laser (Quantum FEL). Beyond fundamental constraints on electron beam and undulator, we discuss optimized interaction geometries, include coherence…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate…
We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…
Correct quantization of free electromagnetic field is proposed
In this paper a differential equation with noninteger order was used to model an anomalous luminescence decay process. Although this process is in principle an exponential decaying process, recent data indicates that is not the case for…
We present a nonlinear theory for relativistic X-ray free electron lasers in the quantum regime, using a collective Klein-Gordon (KG) equation (for relativistic electrons), which is coupled with the Maxwell-Poisson equations for the…
The FEL gain formulas for non-resonant case are studied. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that…
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The…
A generalization of the Wigner function for the case of a free particle with the ``relativistic'' Hamiltonian $\sqrt{{\bf p}^2+m^2}$ is given.
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…