We describe an experiment for production of high harmonic x-ray radiation from Thomson backscattering of an ultra-short high power density laser by a relativistic electron beam at the PLEIADES facility at LLNL. In this scenario, electrons execute a ``figure-8'' motion under the influence of the high-intensity laser field, where the constant characterizing the field strength is expected to exceed unity: $a_{L}=eE_{L}/m_{e}c\omega_{L}\geq1$. With large $a_{L}$ this motion produces high harmonic x-ray radiation and significant broadening of the spectral peaks. This paper is intended to give a layout of the PLEIADES experiment, along with progress towards experimental goals. 334 2005 Particle Accelerator Conference /home/httpd/docserver/releases/20080613005430/public/paper/file/636/lim_2005_636.pdf lim_2005_636.pdf 3 636 3 2005 636 2007-10-16T15:52:35-07:00 2005