326 research outputs found
Fel Oscillators with Tapered Undulators: Inclusion of Harmonic Generation and Pulse Propagation
We review the theory of FEL oscillators operating with tapered undulators. We
consider the case of a uniform tapering and introduce a parameter which
characterizes the effect of the tapering on the gain and on the saturation
intensity. We analyze the effect of the tapering on the FEL dynamics by
including the pulse propagation effects too. We analyze the importance of
tapering as a tool to model the optical pulse shapes and to control the higher
harmonic intensities
Operator solutions for fractional Fokker-Planck equations
We obtain exact results for fractional equations of Fokker-Planck type using
evolution operator method. We employ exact forms of one-sided Levy stable
distributions to generate a set of self-reproducing solutions. Explicit cases
are reported and studied for various fractional order of derivatives, different
initial conditions, and for different versions of Fokker-Planck operators.Comment: 4 pages, 3 figure
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
Imaginary Phases in Two-Level Model with Spontaneous Decay
We study a two-level model coupled to the electromagnetic vacuum and to an
external classic electric field with fixed frequency. The amplitude of the
external electric field is supposed to vary very slow in time. Garrison and
Wright [{\it Phys. Lett.} {\bf A128} (1988) 177] used the non-hermitian
Hamiltonian approach to study the adiabatic limit of this model and obtained
that the probability of this two-level system to be in its upper level has an
imaginary geometric phase. Using the master equation for describing the time
evolution of the two-level system we obtain that the imaginary phase due to
dissipative effects is time dependent, in opposition to Garrison and Wright
result. The present results show that the non-hermitian hamiltonian method
should not be used to discuss the nature of the imaginary phases in open
systems.Comment: 11 pages, new version, to appear in J. Phys.
Pathway to a Compact SASE FEL Device
Newly developed high peak power lasers have opened the possibilities of
driving coherent light sources operating with laser plasma accelerated beams
and wave undulators. We speculate on the combination of these two concepts and
show that the merging of the underlying technologies could lead to new and
interesting possibilities to achieve truly compact, coherent radiator devices
Deep Saturated Free Electron Laser Oscillators and Frozen Spikes
We analyze the behavior of Free Electron Laser (FEL) oscillators operating in
the deep saturated regime and point out the formation of sub-peaks of the
optical pulse. They are very stable configurations, having a width
corresponding to a coherence length. We speculate on the physical mechanisms
underlying their growth and attempt an identification with FEL mode locked
structures associated with Super Modes. Their impact on the intra-cavity
nonlinear harmonic generation is also discussed along with the possibility of
exploiting them as cavity out-coupler.Comment: 28 page
SASE FEL Storage Ring
We explore the possibility of operating a SASE FEL with a Storage Ring. We
use a semi-analytical model to obtain the evolution inside the undulator by
taking into account the interplay on the laser dynamics due to the induced
energy spread and to the radiation damping. We obtain the Renieri's limit for
the stationary output power and discuss the possibility of including in our
model the effect of the beam instabilities.Comment: 5 page
A new class of sum rules for products of Bessel functions
In this paper we derive a new class of sum rules for products of the Bessel
functions of first kind. Using standard algebraic manipulations we extend some
of the well known properties of . Some physical applications of the
results are also discussed. A comparison with the Newberger[J. Math. Phys.
\textbf{23} (1982) 1278] sum rules is performed on a typical example.Comment: Published in Journal of Mathematical Physics, 9 pages, no picture
umbral methods combinatorial identities and harmonic numbers
We analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations
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