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Models attempting an analytical description of free-electron laser (FEL) devices have been proposed in the past. They provided interesting results, leading either to a deeper understanding of the FEL dynamics and to semi-analytical formulae, useful for the preliminary design of self amplified spontaneous emission and oscillator FELs. Most of these models work well until the level of mild saturation. In this paper, we comment on the so-called logistic model and a more recent analysis describing the FEL evolution in terms of Jacobi elliptic functions. Both models are shown to be suited to describe the evolution from the low signal to the onset of saturation. We attempt therefore an extension of these theoretical formulations using a delayed logistic model, capable of including characteristic features like the post saturation power oscillations. [ABSTRACT FROM AUTHOR]

We consider a free electron laser oscillator employing an exotic undulator provided by a figure-8, a device having the orthogonal field component oscillating with a period one-half of the radial component. The harmonic spectrum of such an oscillator device is fairly reach. We have indeed emission on odd and even harmonics with orthogonal polarizations. The intracavity nonlinear coherent harmonic generation follows the harmonic undulator spectrum and in addition allows the possibility of obtaining robust and very short pulses at different wavelengths. [ABSTRACT FROM AUTHOR]

We review the theory of ontogenetic tumor growth by discussing different evolution equations which account for the relevant dynamics. It is shown that most of the equations proposed can be treated from a unitary point of view. We extend the West ontogenetic evolution model to cancer growth and show that the relevant predictions agree with the experimental data from breast and prostate cancer. We finally prove that aging effects can be easily included in the theoretical scheme proposed. [ABSTRACT FROM AUTHOR]

We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses. [ABSTRACT FROM AUTHOR]

Semianalytical formulas have been used to model the pulse propagation dynamics of low gain free electron laser oscillators. Most of the scaling relations, including pulse propagation effects, are limited to the low gain regime. We discuss the problem of oscillator devices operating with small signal gain coefficients larger than 1. We comment on the relevant physical aspects and show that gain and saturated power can be reproduced by a set of simple formulas, analogous to those employed for the low gain case. [ABSTRACT FROM AUTHOR]

In this paper we present an analysis of the intracavity harmonic generation in free electron laser amplifier operating with short pulses. Various features are investigated. We discuss, in particular, the dependence of the harmonic power and of the width of the associated pulses on the cavity mismatch. It is shown that very short and robust pulses can be generated by suitably setting the cavity desynchronism. [ABSTRACT FROM AUTHOR]

The dynamical behavior of high gain free-electron lasers, operating with segmented undulators in the self-amplified spontaneous emission regime, is studied using a set of semianalytical formulas, which reproduce the induced energy spread, the bunching coefficients, and the field evolution along the longitudinal coordinate. The proposed technique is applied to the design of segmented free-electron laser devices, employing undulators with helical or linear polarization. The case of biharmonic sections is discussed too, as well as the possibility of extending the analysis to this “exotic” case. [ABSTRACT FROM AUTHOR]

We reconsider the derivation of semianalytical expressions providing the most significant aspects of the high-gain free-electron laser dynamics. We obtain new expressions for the growth of the laser power, of the e-beam-induced energy spread, and of the higher-order nonlinearly generated harmonics. The procedure we employ, based on theoretical ansatz and fitting methods, allows the determination of crucial quantities like the expected harmonic output power and its dependences on the e-beam parameters. [ABSTRACT FROM AUTHOR]

The distribution of points ( r, r), n = 0, 1, 2,...whose coordinates are terms at distance s of the pseudorandom sequence generated by the Wichmann and Hill method is studied. It is known that for many congruential generators critical values of the distance s exist such that these points, far from being uniformly distributed, are concentrated on very few lines. An algorithm is described for computing the critical distances within the Wichmann-Hill sequence and the results obtained are compared with those of other linear congruential generators. [ABSTRACT FROM AUTHOR]

Partitions of pseudo-random sequences generated by congruential schemes are investigated for use on computer systems where multiple processing units run in parallel for the solution of a Monte Carlo problem. A special partition is suggested which ensures independence between the units working simultaneously, and yields reproducible sequences. The analysis performed has brought out the existence of strong autocorrelations between terms located far apart in the sequences, dependent only on the congruential nature of the generators. The study of these correlations - carried out in a number theoretic framework - points out that only small fractions of the sequences can be safely used. [ABSTRACT FROM AUTHOR]