Dispersion function and closed orbit distortion in accelerator rings

Dispersion Function Distortion (DFD) affects accelerator operation and thus deserves attention, somehow as Closed Orbit Distortion (COD) does. Consequently, DFD correction schemes under computer control have been successfully developed and adopted in many rings such as PEP. It was realized during the author's study on the problem, however, that the existing DFD correction schemes ignore those terms that arise from bending magnets and their edges. Being of first order of correcting strength, the terms are significant in small rings, though really not important in big machines. This reminds of what has been noticed in the chromaticity calculation. A comparison between this note and the existing schemes shows a difference in DFD sensitivity matrix that is significant for sub-GeV machines and appears not negligible even for SPEAR. Many storage rings at energy around 0.7 to 3 GeV are being proposed, constructed or operated everywhere as synchrotron radiation generators. Vertical DFD correction should be an important part of their operation, because vertical DFD enlarges beam height and hence reduces light source brightness. This is the purpose the author had in mind when beginning to study the problem. In addition, a correct DFD analysis along with COD analysis can hopefully help spot magnet misalignments and remove them