“…In a recent leport [18] a technique was implemented to recoid measuiements of single-shot, spatially lesolved spectra of betatron x-rays with high spectral resolution, by the use of an x-ray CCD Images analyzed by pei forming a histogram of single-pixel absorption events (SPAE) [21] produced x-ray spectra with an unprecedented lesolution of 225 eV, FWHM, and a range of over 10 keV A source emitting iron k shell x-ray lines was used to provide a calibration of the energy per pixel count Preliminary data show two important features not previously lesolved The first is iron and chromium fluorescence lines associated with the interaction of electrons and x-rays with the stainless steel of the vacuum chamber, and the second is the betation continuum The ratio of the amplitude of the fluoiescence lines to that of the betatron continuum was found to vaiy significantly with changes in the accelerator parameters, calling into question the validity of previous spectral analyses, based on filter packs, which cannot distinguish between these two components ELECTRO-OPTIC DIAGNOSTICS Electro-optic (EO) sampling has become a widely-used technique for the measurement of electron-bunch durations and temporal structure In this technique, either the relativistic Coulomb fields of the electron bunch or coheient transition radiation (CTR) in the THz frequency band emitted by the electron bunch traversing a dielectric boundary is used to induce birefringence in an elcctro-optically active crystal, such as gallium phosphide (GaP) or zinc tellunde (ZnTe) An optical probe, timed to overlap with these strong electric fields, is used to sample the temporal profile of the fields, from which the duration of the electron bunch can be deduced This technique is very powerful because it can be used in configurations that are non-or weakly-interacting with the electron bunch, allowing it to be used in conjunction with other diagnostics In addition, it provides the high tempoial resolutions required for measuring the sub picosecond electron bunches produced m LPAs The EO sampling process can be split into two conceptual parts generation of the temporally-varying birefringence, and sampling of the birefringence Three prominent methods for each will be discussed Generating the birefringence. In the first method (Direct Coulomb Sampling), the EO crystal is placed near to the path of the accelerated electrons, so that the Coulomb fields penetrate it, resulting m a transient birefringence An optical probe pulse, propagating parallel to the beam line overlaps the induced fields in the crystal, and is imprinted with the temporal profile of these fields Due to lelativistic contraction, the Coulomb field profiles will be longitudinally compressed by an amount dependent on the electron energy The field temporal profile will thus be a convolution of the charge profile with the longitudinal extent, x e = y/cy, of the electron Coulomb fields, where y is the transverse distance from the beam axis Provided the electrons are sufficiently energetic (y large) and the crystal is sufficiently close (y small), the field profile will represent the bunch profile well In general, however, a polychromatic electron bunch will have a field profile (at the crystal) significantly different than its charge profile, with the lower energy electrons having a longer longitudinal field-extent than the high energy components At a distance of 1 mm, foi example, the convolution factor will be approximately 1 7 ps for a 1 MeV component while it will be about 1 7 fs for a 1 GeV component In addition, since the field-strength scales as y, the EO signal will be strongly biased towards the high energy component of the electron bunch In scenarios where it is the behavior of the high-energy component that is of interest, such as in the FEL application, this bias can be advantageous, whereas if it is the actual longitudinal charge distribution that is ...…”