Sensitivity of a Laser Driven Grating Linac to Grating Errors*

The effect of grating errors on transverse beam stability is analyzed. We,characterize grating errors by random groove displacements and find that transverse displacements due to such errors approach limiting values of the same order as the grating displacements themselves. It therefore appears that transverse stability requirements will not impose unusually stringent precision requirements on the grating structure. INTRODUCTION As described by Palmer,I the grating structure for a laser driven grating linac requires shaped groove spacings of the order of one half the laser wavelength and an overall length of several hundred meters. Random errors in the grooves are surely inevitable, and in view of the vast number of grooves, the effect of such errors upon beam stability must be assessed. We provide here an estimate of the relation between the magnitude of these errors and that of the mean deviation from the nominal orbit which these errors induce, FORMULATION OF THE PROBLEM We begin with a brief description of the strong focussing design discussed elsewhere in these proceedings.1'2 The field components in synchronism with the electrons are written * Work supported in part by the Department of Energy, contracts DE-AC03-76SF00515 (SLAC) and DE-AT03-81ER40029 (UCSD). IPermanent address. (Presented at the Laser Acceleration of Particles Workshop, Los Alamos, New Mexico, February 18-23, 1982.)