An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Frequency-domain statistics of the chaotic optical field of a high-gain, self-amplified free-electron laser and its correlation to the time-domain statistics

Recently, the temporal evolution of the amplitude and phase of the chaotic output from a self-amplified free-electron laser was determined. In this letter, we characterize the frequency dependence of the amplitude and phase of the output radiation and discuss the relationship between the characteristics of the spiky intensity structures observed in both the time and the frequency domains. The distribution of the rms time–bandwidth products for an ensemble of output pulses is presented. Experimental results are compared with simulation and theory. PACS 41.60.Cr; 42.50.Ar; 05.40.-a; 42.55.Vc     

Generating a quasiellipsoidal electron beam by 3D laser-pulse shaping

A generic 3D laser-pulse-shaping scheme is proposed towards the generation of a uniform ellipsoidal particle distribution, an ideal distribution due to the linear dependence of the space-charge force on the particle position. The shaping is accomplished via spatiotemporal coupling of the laser dynamics via chromatic aberration in an optical lens. Particle tracking simulations show that the electron beam initiated by such a laser pulse in a high-gradient radio-frequency photoinjector delivers very low emittance, ideal for beam-based light sources such as the x-ray free-electron laser.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.