Search Results (7 total)

Nonlinear harmonic generation can be a very useful and important phenomenon for single-pass free-electron lasers (FELs) operating in the high-gain regime. Strong bunching at the fundamental wavelength and its associated higher harmonic content allow significant radiation at shorter wavelengths to be emitted without serious effects upon the output power at the fundamental. Here, we analyze the relative sensitivities to beam quality variations of the output fundamental and harmonic powers for a visible-wavelength FEL operating in the high-gain regime.

We exploit the Fokker-Planck equation to investigate the longitudinal phase-space dynamics of a FEL amplifier operating with a storage ring. We study both standard and optical-klystron configurations and prove that in both cases the damping times of the electron longitudinal modes are modified by the system operating conditions. In particular, they decrease with increasing laser power when the input laser is tuned at the resonant frequency.

We use the split-operator technique (SOT) to solve evolution equations of the Liouville type. The method we propose is based on an iterative application of the evolution operator, associated with the equation under study, on the initial distribution. The SOT approximation of the evolution operator leads to analytical expressions that can be easily programmed. We discuss the validity of the method, solving the Liouville equation governing the longitudinal phase-space dynamics of an e beam undergoing free-electron-laser interaction and the phase-space evolution of a quartic anharmonic oscillator.

A prebunched electron beam can be exploited to reduce the rise time of a free-electron laser (FEL) oscillator, or to provide the start-up signal for an amplifier. We discuss the dynamical behavior of FEL’s operating with prebunched electron beams, and analyze different regimes of operation, from low signal up to saturation. We also include short pulses effects, discussing the modifications occurring in the FEL pulse propagation equation and analyzing the relevant small signal dynamics.

A model for even "superconductor" nuclei is proposed and developed. In this model the ground state is approximated by the component of a Bardeen-Cooper-Schrieffer (BCS) state corresponding to a fixed particle number. The low-lying excited states are then obtained by diagonalizing the nuclear Hamiltonian in the space spanned by the particle-hole elementary excitations and, for J=0, by the ground state itself. Expressions for the matrix elements of the electromagnetic operators are also given. In the final section, the results obtained from this model for some even tin isotopes are compared with the experimental results and the corresponding results of an ordinary BCS-Tamm-Dancoff approximation. Thus, we are able to give a direct evaluation of the effects of the particle-number nonconservation in the Tamm-Dancoff approximation.

A modified Tamm-Dancoff approximation for spherical superconductor nuclei is formulated. The approximation consists in diagonalizing the nuclear Hamiltonian in the space spanned by the components of zero-and two-quasiparticle excitations corresponding to a fixed particle number ("projected states"). Thus, spurious states arising from the Bogoliubov-Valatin canonical transformation, which are present in the usual Tamm-Dancoff approximation, are completely eliminated. Matrix elements between "projected states" are evaluated by the Bayman projection method of the generating functions. The model is applied to the calculation of the low-lying excited states of the tin isotope with A=116, and the results are compared with the corresponding ones obtained in the Tamm-Dancoff approximation. Our conclusion is that the effect of the particle-number nonconservation is important mainly for the energies of the highest levels. This becomes particularly clear for the J=0 case.

A microscopic theory of the low-lying states of even-even spherical nuclei is developed in which eigenvectors are linear combinations of two- and four-quasiparticle excitations. The quasiparticles are defined by the Bogoliubov-Valatin canonical transformation. The method is called the quasiparticle second Tamm-Dancoff (QSTD) approximation, since no ground-state correlations are included. It is found that the spurious kets due to the particle-number nonconservation must be absolutely projected out of the secular matrices before their diagonalization. Such a procedure is described and applied. Formulas are given for the electromagnetic transition probabilities. The theory is applied to the study of the 2⁺, 4⁺, and 0⁺ states of the even tin isotopes. The single-particle radial wave functions employed are those of a Saxon-Woods potential and of a harmonic-oscillator potential. The two-nucleon residual interaction potential is spin-dependent and of zero range. Satisfactory numerical agreement with the observed 2⁺ and 4⁺ low-lying levels is obtained with the Saxon-Woods wave functions for a reasonable strength constant of our zero-range force. Appreciable admixtures of the four-quasiparticle creation components are found even in the lowest lying levels. Poor agreement is obtained for the 0⁺ states, for which a more refined theory is necessary (rather unreasonable values of the strength constant of the zero-range potential are required to fit the 0⁺ data). Generally, markedly worse 2⁺ results are obtained if we replace the Saxon-Woods wave functions with harmonic-oscillator wave functions.