Theoretical analysis of Wolter/LSM X-ray telescope systems

A ray tracing analysis has been performed for the spectral slicing zoom X-ray telescope for configurations in which a convex layered synthetic microstructure (LSM) optic is placed in front of the prime focus or a concave LSM optic is placed behind the prime focus. The analysis has considered the geometrical shape of the LSM optic to be either a hyperboloid, sphere, ellipsoid or constant optical path aspheric element for two configurations of the glancing incidence X-ray telescope: the ATM Experimental S-056 Wolter I system and the Stanford/MSFC Wolter-Schwarzchild nested system. For the different systems the RMS blur circle radii, the point spread function (PSF), the full width half maximum (FWHM) of the PSF have been evaluated as a function of field angle and magnification of the secondary to determine resolution of the system. The effects of decentration and tilt of the selected LSM element on the performance of the system have been studied to determine mounting and alignment tolerances

Theoretical design and analysis of the layered synthetic microstructure optic for the dual path X-ray telescope

A ray tracing analysis was performed for several configurations for the inner channel of the dual path X-ray telescope, which is proposed to use the second mirror of the Stanford/MSFC Wolter-Schwarzchild telescope and a normal incident layered synthetic microstructure (LSM) mirror to form a secondary image near the front of the telescope. The LSM mirror shapes considered were spherical, ellipsoid, hyperboloid, and constant optical path length (OPL) aspheric. Only the constant OPL case gave good axial resolution. All cases had poor off axis resolution as judged by the RMS blur circle radius

Weak Lensing of the Cosmic Microwave Background by Foreground Gravitational Waves

Weak lensing distortion of the background cosmic microwave background (CMB) temperature and polarization patterns by the foreground density fluctuations is well studied in the literature. We discuss the gravitational lensing modification to CMB anisotropies and polarization by a stochastic background of primordial gravitational waves between us and the last scattering surface. While density fluctuations perturb CMB photons via gradient-type deflections only, foreground gravitational waves distort CMB anisotropies via both gradient- and curl-type displacements. The latter is a rotation of background images, while the former is related to the lensing convergence. For a primordial background of inflationary gravitational waves, with an amplitude corresponding to a tensor-to-scalar ratio below the current upper limit of $\sim$ 0.3, the resulting modifications to the angular power spectra of CMB temperature anisotropy and polarization are below the cosmic variance limit. At tens of arcminute angular scales and below, these corrections, however, are above the level at which systematics must be controlled in all-sky anisotropy and polarization maps with no instrumental noise and other secondary and foreground signals.Comment: 11 pages, 4 figures; Revised version updates the numerical calculation for several corrections to the analytical formulation of lensing by foreground gravitational waves. Main conclusions unchanged. Version accepted for publication in Phys. Rev.

Theoretical analysis of segmented Wolter/LSM X-ray telescope systems

The Segmented Wolter I/LSM X-ray Telescope, which consists of a Wolter I Telescope with a tilted, off-axis convex spherical Layered Synthetic Microstructure (LSM) optics placed near the primary focus to accommodate multiple off-axis detectors, has been analyzed. The Skylab ATM Experiment S056 Wolter I telescope and the Stanford/MSFC nested Wolter-Schwarzschild x-ray telescope have been considered as the primary optics. A ray trace analysis has been performed to calculate the RMS blur circle radius, point spread function (PSF), the meridional and sagittal line functions (LST), and the full width half maximum (PWHM) of the PSF to study the spatial resolution of the system. The effects on resolution of defocussing the image plane, tilting and decentrating of the multilayer (LSM) optics have also been investigated to give the mounting and alignment tolerances of the LSM optic. Comparison has been made between the performance of the segmented Wolter/LSM optical system and that of the Spectral Slicing X-ray Telescope (SSXRT) systems

Calculation of wing response to gusts and blast waves with vortex lift effect

A numerical study of the response of aircraft wings to atmospheric gusts and to nuclear explosions when flying at subsonic speeds is presented. The method is based upon unsteady quasi-vortex-lattice method, unsteady suction analogy, and Pade approximate. The calculated results, showing vortex lag effect, yield reasonable agreement with experimental data for incremental lift on wings in gust penetration and due to nuclear blast waves

Calculation of wing response to gusts and blast waves with vortex lift effect

A numerical study of the response of aircraft wings to atmospheric gusts and to nuclear explosions when flying at subsonic speeds is presented. The method is based upon unsteady quasi-vortex lattice method, unsteady suction analogy and Pade approximant. The calculated results, showing vortex lag effect, yield reasonable agreement with experimental data for incremental lift on wings in gust penetration and due to nuclear blast waves

Velocity profiles in strongly turbulent Taylor-Couette flow

We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio $\eta$ between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the {\em qualitative} trends are the same -- down-bending for large wall distances and (properly shifted and non-dimensionalized) angular velocity profile $\omega^+(r)$ being closer to a log-law than (properly shifted and non-dimensionalized) azimuthal velocity profile $u^+_{\varphi}(r)$ -- {\em quantitative} deviations are found for large wall distances. We attribute these differences to the Taylor rolls and the height dependence of the profiles, neither of which are considered in the theoretical approach