A theoretical description of vortex dynamics in thin flat samples is derived and is found to compare favorably with experimental results. In perpendicular applied magnetic field the vortex penetration is delayed significantly due to the presence of a potential barrier of geometrical origin. This novel geometrical barrier effect results in hysteretic magnetization and in the existence of an irreversibility line in the absence of bulk pinning. Among the unique characteristics of the barrier are a vortex concentration in the center of the sample and a zero-field peak in the magnetization loops.

The vortex-lattice phase transitions in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ crystals with various oxygen stoichiometry are studied using local magnetization measurements. Three new findings are reported: The first-order phase transition line at elevated temperatures shifts upward for more isotropic overdoped samples. At lower temperatures another sharp transition is observed that results in enhanced bulk pinning in the second magnetization peak region. The two lines merge at a multicritical point at intermediate temperatures forming apparently a continuous phase transition line that is anisotropy dependent.

A design for a compact x-ray light source (CXLS) with flux and brilliance orders of magnitude beyond existing laboratory scale sources is presented. The source is based on inverse Compton scattering of a high brightness electron bunch on a picosecond laser pulse. The accelerator is a novel high-efficiency standing-wave linac and rf photoinjector powered by a single ultrastable rf transmitter at X-band rf frequency. The high efficiency permits operation at repetition rates up to 1 kHz, which is further boosted to 100 kHz by operating with trains of 100 bunches of 100 pC charge, each separated by 5 ns. The entire accelerator is approximately 1 meter long and produces hard x rays tunable over a wide range of photon energies. The colliding laser is a $\mathrm{Yb}:\mathrm{YAG}$ solid-state amplifier producing 1030 nm, 100 mJ pulses at the same 1 kHz repetition rate as the accelerator. The laser pulse is frequency-doubled and stored for many passes in a ringdown cavity to match the linac pulse structure. At a photon energy of 12.4 keV, the predicted x-ray flux is $5\times 10^{11}\mathrm{photons}/\mathrm{second}$ in a 5% bandwidth and the brilliance is $2\times 10^{12}\mathrm{photons}/(\sec {\mathrm{mm}}^2{\mathrm{mrad}}^{2}0.1\%)$ in pulses with rms pulse length of 490 fs. The nominal electron beam parameters are 18 MeV kinetic energy, 10 microamp average current, 0.5 microsecond macropulse length, resulting in average electron beam power of 180 W. Optimization of the x-ray output is presented along with design of the accelerator, laser, and x-ray optic components that are specific to the particular characteristics of the Compton scattered x-ray pulses.

The vortex matter phase diagram in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ crystals is investigated by introducing very low doses of point and correlated disorder. We conclude that at least three distinct phases are present. The ordered low-field quasilattice phase has a finite shear modulus which vanishes at the first-order melting or sublimation transition at elevated temperatures. At lower temperatures the quasilattice transforms into a disordered solid as field is increased above the second magnetization peak. This disorder-driven transition shifts to lower fields with increased point disorder. The first-order transition displays corresponding downward curvature in the vicinity of the critical point.