Philippe Francken

R-matrix-Floquet theory of multiphoton processes

A unified theory is developed to analyse both the multiphoton ionization of atoms and laser-assisted electron-atom collisions. It combines the R-matrix method with the Floquet theory, is nonperturbative and is applicable to any atom. It takes advantage of the natural R-matrix division of configuration space into two regions, which allows us to choose the most appropriate form of the interaction Hamiltonian in each region and also to use the Hermitian Floquet theory in the internal region. Our theory is illustrated by the calculation of multiphoton ionization rates for a one-dimensional model.

Theoretical study of electron–atom collisions in intense laser fields

We discuss various important aspects of the theory of multiphoton free–free transitions. First we show, in the simple framework of potential scattering, the necessity for a description of the laser field to take into account the actual experimental conditions such as beam focusing and pulsed and multimode operations. We then generalize the study to the collisions of fast electrons with atoms in intense laser fields and show how the dressing of the atomic states by the external radiation field can affect the scattering cross sections. Finally, we consider the role played by statistical fluctuations of the laser field. To this end, we develop the pre-Gaussian model of laser noise and show how this formalism can be included in the theory of multiphoton free–free transitions.

On the spectrum of the iteration operator associated to the finite element preconditioning of Chebyshev collocation calculations

Abstract An analytical investigation is performed of the spectrum of the iteration operator associated to the finite element preconditioning of Chebyshev collocation calculations, on a one-dimensional Dirichlet model problem. Use is made of the techniques developed by Haldenwang et al. for the finite difference preconditioning of the same problem. In the latter case the eigenvalues may be obtained as the diagonal elements of an upper-triangular matrix. This is not possible with finite element preconditioning, where the corresponding operator splits into two parts, one of which only is upper-triangular. Discarding the non-triangular part of the operator (which vanishes asymptotically for large values of N , partition size), this procedure yields an approximate expression of the eigenvalues in good agreement with the properties given earlier by Deville and Mund.

Multiphoton free-free transitions in stochastic laser fields: the Kubo-Anderson master equation approach

We present a new treatment of potential scattering of charged particles in a stochastic laser field whose amplitude or phase noise is modelled by an N-state Kubo-Anderson process. Our theoretical method, based on the resolution of a Kubo-Anderson master equation, provides a fully nonperturbative treatment of the field fluctuations. The effect of laser noise on the scattering cross-sections is analysed as a function of the magnitude of the field fluctuations.

Random telegraph noise in laser-assisted collisions

We present a treatment of potential scattering of a charged particle in a laser field undergoing jumplike fluctuations in amplitude, phase or frequency. Our method allows the inclusion of these three types of noise in a unified way for the case of random telegraph and, more generally, of pre-Gaussian statistics. The broadening of the lines corresponding to the various multiphoton processes is analysed as a function of the characteristic parameters of the model.