In this dissertation, I have studied theoretical problems in statistical physics and electrodynamics of Bose particles, namely, mesoscopic effects in statistics of Bose- Einstein condensate (BEC) of atoms and electromagnetic waveguide effects of planar Bragg structures in Free Electron Lasers. A mesoscopic system of a trapped gas of Bose atoms is the most difficult for the theoretical analysis in quantum statistical physics since it cannot be studied by neither a quantum mechanics of the simple microscopic systems of one or very few atoms nor a standard statistical physics of the macroscopic systems that implies a thermodynamic limit. I present analytical formulas and numerical calculations for the moments and cumulants of BEC fluctuations in both ideal and weakly interacting gas. I analyze the universal scaling and structure of the BEC statistics in a mesoscopic ideal gas in the critical region. I present an exactly solvable Gaussian model of BEC in a degenerate interacting gas and its solution that confirms the universality and constraint-cut-off origin of the strongly non-Gaussian BEC statistics. I consider a two-energy-level trap with arbitrary degeneracy of an upper level and find an analytical solution for the condensate statistics in a mesoscopic ideal gas. I show how to model BEC in real traps by BEC in the two-level or three-level traps. I study wave propagation in the open oversized planar Bragg waveguides, in particular, in a planar metal waveguide with corrugation. I show that a step perturbation in a corrugation phase provides a high selectivity over transverse modes. I present a new Free Electron Laser (FEL) amplifier scheme, in which the radiation is guided by the planar Bragg structure with slightly corrugated walls and a sheet electron beam is traveling at a significant angle to the waveguide axis. By means of nonlinear analysis, I demonstrate that the proposed scheme provides an effective mode filtration and control over the structure of the output radiation and allows one to achieve amplification up to 30 dB in the existing FEL machines.

Thesis (M.S. in Applied Physics)--Naval Postgraduate School, December 2003. / Thesis advisor(s): William Colson, Robert Armstead. Includes bibliographical references (p. 67-68). Also available online.

This Thesis describes the development of hard X-ray zone plates intended for focusing radiation at X-ray free-electron lasers (XFELs). XFELs provide unprecedented brightness and zone plates which are put in the intense X-ray beam are at risk of being damaged. Therefore, it is crucial to perform damage tests in order to design zone plates which can survive the XFEL beam. Zone plates are diffractive nanofocusing optics and are regularly used at high brightness synchrotron beamlines in the soft and hard X-ray regime. The resolution of a zone plate is proportional to its outermost zonewidth and thus depends on the smallest feature that can be fabricated. State-of-the-art nanofabrication processes developed for zone plates are able to produce zonewidths down to 10 nm. However, for hard X-rays, the zone plates need to be of sufficient thickness to efficiently focus the radiation. Thus, the limit in the fabrication of hard X-ray zone plates lies in the high aspect-ratios. This Thesis describes two processes developed for high aspect-ratio nanostructuring. The first process uses tungsten as diffractive material. Aspect-ratios up to 1:15 have been accomplished. Furthermore, a mounting method of a central stop directly on the zone plate is also presented. The other fabrication process uses diamond, in which aspect-ratios of 1:30 have been demonstrated. Both processes rely on thin-film deposition techniques, electron-beam lithography, and reactive ion etching. Thanks to the materials’ excellent thermal properties these types of zone plates should be suitable for XFEL applications. Tungsten and diamond diffractive optics have been tested at an XFEL at Stanford (LCLS), and damage investigations were performed in order to determine the maximum fluence that could be imposed on the optics before degradation occured. The conclusion of these damage tests is that tungsten and diamond diffractive optics can survive the XFEL beam and could potentially be used in beamline experiments relying on nanofocused X-ray beams. Finally in this Thesis, characterization of two zone plates using an interferometer is presented, where it is also shown that the interferometric method can be used to pin-point beamline instabilities. / <p>QC 20150112</p>

Thesis (Ph. D. in Biomedical Engineering)--Vanderbilt University, Dec. 2004. / Title from title screen. Includes bibliographical references.

Thesis (M.S. in Applied Physics)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): William B. Colson. Includes bibliographical references (p. 79-81). Also available online.

The advances achieved using X-ray Free Electron Lasers such as the Linac Coherent Light Source (LCLS), have revolutionised the routine production of uniform solid-density plasmas. Pulses of X-rays above 1 keV and with durations shorter than 100 fs attaining intensities on target of around 10¹⁷ Wcm^-2 are now routinely created. Through simple single-photon photoionization events with atoms in ambient solid conditions, it is possible to create uniform samples that are simultaneously hot, dense, and highly ionized which may be easily modelled. This thesis describes measurements of the spectrally-resolved X-rays emitted from solid-density magnesium targets of varying sub-&mu;m thicknesses isochorically heated by an X-ray laser. The data exhibit a thickness-independent source function, allowing the extraction of a measure of the opacity to K-shell X-rays within well-defined regimes of electron density and temperature, extremely close to Local Thermodynamic Equilibrium conditions by fitting to the simple 1D slab solution of the equation of radiative transfer. The deduced opacities at the peak of the K-&alpha; transitions of the ions are consistent with those predicted by detailed atomic-kinetics calculations. The extracted opacities transpire to be robust to a plethora of variations in X-ray drive conditions, including the shape, pulse-length, and energy content. Furthermore the approximations in using the 1D slab solution are examined in detail and found to be good. A full three-dimensional model of the plasma is advanced which includes attenuation, line-of-sight effects, full longitudinal and transverse gradients, and photon time-of-flight effects. The results from this model are found to also agree with the simpler 1D slab solution. This novel method of elucidating opacities may complement other methods based on absorption and could be important for further benchmarking of opacities in solar-interior relevant conditions.

This thesis presents results from two strands of work towards realizing a free-electron laser (FEL) driven by electron bunches generated by a laser-wakefield accelerator (LWFA). The first strand focuses on selecting operating parameters for such a light source, on the basis of currently achievable bunch parameters as well as near-term projections. The viability of LWFA-driven incoherent undulator sources producing nanojoule-level pulses of femtosecond duration at wavelengths of 5 nm and 0.5 nm is demonstrated. A study on the prospective operation of an FEL at 32 nm is carried out, on the basis of scaling laws and full 3-D time-dependent simulations. A working point is selected, based on realistic bunch parameters. At that working point saturation is expected to occur within a length of 1.6 m with peak power at the 0.1 GW-level. This level, as well as the stability of the amplification process, can be improved significantly by seeding the FEL with an external radiation source. In the context of FEL seeding, we study the ability of conventional simulation codes to correctly handle seeds from high-harmonic generation (HHG) sources, which have a broad bandwidth and temporal structure on the attosecond scale. Namely, they violate the slowly-varying envelope approximation (SVEA) that underpins the governing equations in conventional codes. For this purpose we develop a 1-D simulation code that works outside the SVEA. We carry out a set of benchmarks that lead us to conclude that conventional codes are adequately capable of simulating seeding with broadband radiation, which is in line with an analytical treatment of the interaction. The second strand of work is experimental, and focuses on on the use of coherent transition radiation (CTR) as an electron bunch diagnostic. The thesis presents results from two experimental campaigns at the MPI für Quantenoptik in Garching, Germany. We present the first set of single-shot measurements of CTR over a continuous wavelength range from 420 nm to 7 μm. Data over such a broad spectral range allows for the first reconstruction of the longitudinal profiles of electron bunches from a laser-wakefield accelerator, indicating full-width at half-maximum bunch lengths around 1.4 μm (4.7 fs), corresponding to peak currents of several kiloampères. The bunch profiles are reconstructed through the application of phase reconstruction algorithms that were initially developed for studying x-ray diffraction data, and are adapted here for the first time to the analysis of CTR data. The measurements allow for an analysis of acceleration dynamics, and suggest that upon depletion of the driving laser the accelerated bunch can itself drive a wake in which electrons are injected. High levels of coherence at optical wavelengths indicate the presence of an interaction between the bunch and the driving laser pulse.

X-rays have been widely exploited to unravel the structure of matter since their discovery in 1895. Nowadays, with the emergence of new X-ray sources with higher intensity and very short pulse duration, notably X-ray Free Electron Lasers, the number of experiments that may be considered in the X-ray regime has increased dramatically, making the characterization of gas phase atoms and molecules in space and time possible. This thesis explores in the theoretical analysis and calculation of X-ray scattering atoms and molecules, far beyond the independent atom model. Amethod to calculate inelastic X-ray scattering from atoms and molecules is presented. The method utilizes electronic wavefunctions calculated using ab-initio electronic structure methods. Wavefunctions expressed in Gaussian type orbitals allow for efficient calculations based on analytical Fourier transforms of the electron density and overlap integrals. The method is validated by extensive calculations of inelastic cross-sections in H, He+, He, Ne, C, Na and N2. The calculated cross-sections are compared to cross-sections from inelastic X-ray scattering experiments, electron energy-loss spectroscopy, and theoretical reference values. We then begin to account for the effect of nuclear motion, in the first instance by predicting elastic X-ray scattering from state-selected molecules. We find strong signatures corresponding to the specific vibrational and rotational state of (polyatomic) molecules. The ultimate goal of this thesis is to study atomic and molecular wavepackets using time-resolved X-ray scattering. We present a theoretical framework based on quantum electrodynamics and explore various elastic and inelastic limits of the scattering expressions. We then explore X-ray scattering from electronic wavepackets, following on from work by other groups, and finally examine the time-resolved X-ray scattering from non-adiabatic electronic-nuclear wavepackets in the H2 molecule, demonstrating the importance of accounting for the inelastic effects.

Approved for public release, distribution is unlimited / The Free Electron Laser has the potential to become a revolutionary weapon system. Deep magazines, low cost-per-shot, pinpoint accuracy, and speed of light delivery give this developing weapon system significant advantages over conventional systems. One limiting factor in high energy laser implementation is thermal blooming, a lensing effect which is caused by the quick heating of the atmosphere, so that the laser beam does not focus on the desired spot, thereby degrading the effectiveness of the laser on target. The use of multiple beam directors focusing on a target from a single platform may mitigate thermal blooming by allowing half of the laser's energy to travel through a given volume of air, so that they only overlap very near the target. Less energy traveling through a given volume of space means less heating, and therefore lessens the effects of thermal blooming. Also, simulations of FEL's were conducted modifying parameters such as the number of undulator periods, electron beam focus, the normalized Rayleigh length, and mirror output coupling, in order to determine optimum design parameters. New parameters for the next proposed FEL were simulated to examine the effect of mirror tilt on laser power and extraction as well. / Lieutenant, United States Navy

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