Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum

We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a real eigenvalue crosses the imaginary axis. For a model we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a pitchfork bifurcation of equilibria and the nonlinear stability of the bifurcating equilibria, again with respect to spatially localized perturbations.     

Dynamics of Multisection Semiconductor Lasers

We consider a mathematical model (the so-called traveling-wave system) which describes longitudinal dynamical effects in semiconductor lasers. This model consists of a linear hyperbolic system of PDEs, which is nonlinearly coupled with a slow subsystem of ODEs. We prove that a corresponding initial-boundary value problem is well posed and that it generates a smooth infinite-dimensional dynamical system. Exploiting the particular slow-fast structure, we derive conditions under which there exists a low-dimensional attracting invariant manifold. The flow on this invariant manifold is described by a system of ODEs. Mode approximations of that system are studied by means of bifurcation theory and numerical tools.     

Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.     

Pulsed laser deposition of atomically flat La1-xSrxMnO3 thin films using a novel target geometry

A new ablation target geometry is presented that was used to produce thin films of La_1-xSr_xMnO₃ grown heteroepitaxially on SrTiO₃ by pulsed reactive crossed-beam laser ablation. The films were grown in order to perform angle-resolved photoelectron spectroscopy, which demands that the surface be atomically flat. In situ and ex situ analysis shows that this condition was met, even after depositing to a thickness of over 100 nm. PACS 61.10.-i; 61.18.Bn; 68.47.Gh; 71.27.+a; 81.15.Fg     

Determination of Hydrogen Single Ion Activity Coefficients in Aqueous HCl Solutions at 25°C

The single ion activity coefficients of hydrogen and chloride ions in aqueous HCl solutions have been estimated at 25°C at concentrations up to 1 mol-kg^–1, using potentiometric measurements with ion-selective electrodes and appropriate calibration procedures. Two methods are described for an internal calibration of the electrodes in the extended Debye–Hückel concentration range. The results are compared to the conventional pH calibration with external buffer solutions. Since the latter calibration method does not account for the liquid junction potential E _J which arises at the reference electrode, the resulting activity coefficients are quite different in HCl solutions of higher concentration. These differences between internal and external calibration decrease significantly, when a correction for E _J is introduced into the conventional pH calibration. Hence, in solutions of higher ionic strength the accuracy of the conventional pH electrode calibration using buffer solutions is very limited, when exact H⁺ activities are required. The consistency of the results indicates that the liquid junction potentials in the examined systems calculated by the Henderson/Bates approximation are of reasonable precision.     

Possible application of X-ray optical elements for reducing the spectral bandwidth of an X-ray SASE FEL

A new design for a single pass X-ray Self-Amplified Spontaneous Emission (SASE) FEL is proposed. The scheme consists of two undulators and an X-ray monochromator located between them. The first stage of the FEL amplifier operates in the SASE linear regime. After the exit of the first undulator the electron bunch is guided through a non-isochronous bypass and the X-ray beam enters the monochromator. The main function of the bypass is to suppress the modulation of the electron beam induced in the first undulator. This is possible because of the finite value of the natural energy spread in the beam. At the entrance to the second undulator the radiation power from the monochromator dominates significantly over the shot noise and the residual electron bunching. As a result the second stage of the FEL amplifier operates in the steady-state regime when the input signal bandwidth is small with respect to that of the FEL amplifier. Integral losses of the radiation power in the monochromator are relatively small because grazing incidence optics can be used. The proposed scheme is illustrated for the example of the 6 nm option SASE FEL at the TESLA Test Facility under construction at DESY. As shown in this paper the spectral bandwidth of such a two-stage SASE FEL (Δλ/λ 5 × 10⁻⁵) is close to the limit defined by the finite duration of the radiation pulse. The average brilliance is equal to 7 × 10²⁴ photons/(s × mrad² × mm² × 0.1% bandw.) which is by two orders of magnitude higher than the value which could be reached by the conventional SASE FEL. The monochromatization of the radiation is performed at a low level of radiation power (about 500 times less than the saturation level) which allows one to use conventional X-ray optical elements (grazing incidence grating and mirrors) for the monochromator design.