Lattice design for a very high brightness x-ray storage ring Mentors: Ivan Bazarov and Richard Talman Extremely bright x-rays are being produced in large accelerators called storage rings when the trajectory of ultra-relativistic electrons is deflected by the strong magnetic field of a wiggler or undulator. These intense x-rays are used by scientists from many disciplines to study problems as diverse as determining the structure of proteins, to visualizing chemical reactions on atomic scale, to characterizing dislocations in high quality semiconductors, to analyzing rare paintings to reveal their age and underlying brushstroke technique, helping identify or verify the artist. The single most important quantity characterizing the x-rays (for most applications) is their brilliance, a measure of "pure" photons that can be delivered to samples. In order to produce high brilliance, it is essential for the electron beam to have a small "emittance" which is the product of its intrinsic size and its angular divergence. The emittance in turn is determined by the sequence of magnets that comprise the storage ring (its dipoles and quadrupoles), called the magnet lattice. The goal of this REU project is to refine the magnet lattice design of an upgrade to the existing Cornell Electron Storage Ring (CESR), which will become the brightest source of hard x-rays in the United States.