Experimental confirmation of transverse focusing and adiabatic damping in a standing wave linear accelerator

The measurement of the transverse phase-space map, or transport matrix, of a relativistic electron in a high-gradient, radio-frequency linear accelerator (rf linac) at the UCLA photoinjector is reported. This matrix, which indicates the effects of acceleration (adiabatic damping), first-order transient focusing, and ponderomotive second-order focusing, is measured as a function of both rf field amplitude and phase in the linac. The elements of the matrix, determined by observation of centroid motion at a set of downstream diagnostics due to deflections induced by a set of upstream steering magnets, compare well with previously developed analytical theory [J. Rosenzweig and L. Serafini, Phys. Rev. E 49, 1599 (1994)]. The determinant of the matrix is obtained, yielding a direct confirmation of trace space adiabatic damping. Implications of these results on beam optics at moderate energy in high-gradient linear accelerators such as rf photoinjectors are discussed.