Laser wakefield acceleration of electrons holds great promise for producing ultra-compact stages of GeV scale, high quality electron beams for applications such as x-ray free electron lasers and high energy colliders. Ultra-high intensity laser pulses can be self-guided by relativistic plasma waves over tens of vacuum diffraction lengths, to give >1 GeV energy in cm-scale low density plasma using ionization-induced injection to inject charge into the wake at low densities. This thesis describes a series of experiments which investigates the physics of LWFA in the self-guided blowout regime. Beginning with high density gas jet experiments the scaling of the LWFA-produced electron beam energy with plasma electron density is found to be in excellent agreement with both phenomenological theory and with 3-D PIC simulations. It is also determined that self-trapping of background electrons into the wake exhibits a threshold as a function of the electron density, and at the densities required to produce electron beams with energies exceeding 1 GeV a different mechanism is required to trap charge into low density wakes. By introducing small concentrations of high-Z gas to the nominal He background the ionization-induced injection mechanism is enabled. Electron trapping is observed at densities as low as 1.3 x …

Large extra dimensions (LED) have been proposed to account for the apparent weakness of gravitation. These theories also indicate that the postulated massive Kaluza-Klein (KK) gravitons may be produced by nucleon-nucleon bremsstrahlung in the course of core collapse of supernovae. Hannestad and Raffelt have predicted energy spectra of gamma ray emission from the decay of KK gravitons trapped by the gravity of the remnant neutron stars (NS). These and other authors have used EGRET data on NS to obtain stringent limits on LED. Fermi-LAT is observing radio pulsar positions obtained from radio and x-ray catalogs. NS with certain characteristics are unlikely emitter of gamma rays, and emit in radio and perhaps x-rays. This talk will focus on the blind analysis we plan to perform, which has been developed using the 1st 2 months of all sky data and Monte Carlo simulations, to obtain limits on LED based on about 1 year of Fermi-LAT data. Preliminary limits from this analysis using these first 2 months of data will be also be discussed.