Fundamental Limits on Beam Stability at the Advanced Photon Source

Orbit correction is now routinely performed at the few-micron level in the Advanced Photon Source (APS) storage ring. Three diagnostics are presently in use to measure and control both AC and DC orbit motions: broad-band turn-by-turn rf beam position monitors (BPMs), narrow-band switched heterodyne receivers, and photoemission-style x-ray beam position monitors. Each type of diagnostic has its own set of systematic error effects that place limits on the ultimate pointing stability of x-ray beams supplied to users at the APS. Limiting sources of beam motion at present are magnet power supply noise, girder vibration, and thermal timescale vacuum chamber and girder motion. This paper will investigate the present limitations on orbit correction, and will delve into the upgrades necessary to achieve true sub-micron beam stability. INTRODUCTION: POWER SPECTRAL DENSITY An essential tool in the study of beam stabilization is the power spectral density. Simply put, the power spectral density is the mean square signal per unit frequency, whether the signal is measured in volts, microns, or furlongs per fortnight. Upon integration (or summation) over the available frequency band represented in a given data set, one arrives at the mean square signal in that band, the square root of which yields the rms signal. Shown in Equation (1) is the definition of a discrete Fourier transform pair for a time-sampled data set { x n } containing N samples, while Equation (2) is a statement derived from Parseval’s theorem, forming the basis for the definition of power spectral density (1):