Using the X-FEL to understand X-ray Thomson scattering for partially ionized plasmas

For the last decade numerous researchers have been trying to develop experimental techniques to use X-ray Thomson scattering as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. With the advent of the X-ray free electron laser (X-FEL) at the SLAC Linac Coherent Light Source (LCLS) we now have such a source available in the keV regime. One challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas. Most Thomson scattering codes used to model experimental data greatly simplify or neglect the contributions of the bound electrons to the scattered intensity. In this work we take the existing models of Thomson scattering that include elastic ion-ion scattering and the electron-electron plasmon scattering and add the contribution of the bound electrons in the partially ionized plasmas. Except for hydrogen plasmas almost every plasma that is studied today has bound electrons and it is important to understand their contribution to the Thomson scattering, especially as new X-ray sources such as the X-FEL will allow us to study much higher Z plasmas. Currently most experiments have looked at hydrogen or beryllium. We will first look at the bound electron contributions to beryllium by analysing existing experimental data. We then consider several higher Z materials such as Cr and predict the existence of additional peaks in the scattering spectrum that requires new computational tools to understand. For a Sn plasma we show that the bound contributions changes the shape of the scattered spectrum in a way that would change the plasma temperature and density inferred by the experiment.Comment: 13th International Conference on X-ray Lasers Paris, France June 10, 2012 through June 15, 201

Average-Atom Model for X-ray Scattering from Warm Dense Matter

A scheme for analyzing Thomson scattering of x-rays by warm dense matter, based on the average-atom model, is developed. Emphasis is given to x-ray scattering by bound electrons. Contributions to the scattered x-ray spectrum from elastic scattering by electrons moving with the ions and from inelastic scattering by free and bound electrons are evaluated using parameters (chemical potential, average ionic charge, free electron density, bound and continuum wave functions, and occupation numbers) taken from the average-atom model. The resulting scheme provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum, titanium, and tin plasmas. At high momentum transfer, contributions from inelastic scattering by bound electrons are dominant features of the scattered x-ray spectrum for aluminum, titanium, and tin.Comment: 22 pages, 10 figures Presentation at Workshop IV: Computational Challenges in Warm Dense Matter at IPAM (UCLA) May 21 - 25, 201

Single-stage experimental evaluation of tandem-airfoil rotor and stator blading for compressors. Part 1: Analysis and design of stages A, B, and C

A conventional rotor and stator, two dual-airfoil tandem rotors, and one dual-airfoil tandem stator were designed. The two tandem rotors were each designed with different percentages of the overall lift produced by the front airfoil. Velocity diagrams and blade leading and trailing edge metal angles selected for the conventional rotor and stator blading were used in the design of the tandem blading. Rotor inlet hub/tip ratio was 0.8. Design values of rotor tip velocity and stage pressure ratio were 757 ft/sec and 1.30, respectively

Dynamical stability of a doubly quantized vortex in a three-dimensional condensate

The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges of parameter values. The existence of alternating windows of stability and instability, respectively, is explained qualitatively and quantitatively using variational calculus and direct numerical solution. It is seen that the windows of stability are much smaller for a cigar shaped condensate than for a pancake shaped one, which is consistent with the findings of recent experiments.Comment: 23 pages, 11 figure