Eigenvector method for optimized orbit correction

摘要

The task of the orbit correction is to find the kick vector (Theta) for a given measured orbit vector (right vector X). The authors are presenting a method, in which the kick vector is expressed as a linear combination of the eigenvectors. An additional advantage of this method is that it yields the smallest possible kick vector to correct the orbit. They will illustrate the application of the method to the NSLS X-ray and UV storage rings and the resulting measurements. It will be evident, that the accuracy of this method allows the combination of the global orbit correction and local optimization of the orbit for beam lines and insertion devices. The eigenvector decomposition can also be used for optimizing kick vectors, taking advantage of the fact that eigenvectors with corresponding small eigenvalues generate negligible orbit changes. Thus, one can reduce a kick vector calculated by any other correction method and still stay within the tolerance for orbit correction. The response matrix A is defined by the equation (right vector X) = A(right vector (Theta)), where (right vector (Theta)) is the kick vector and is the resulting orbit vector. Since A is not necessarily a symmetric or even a square matrix the authors symmetrize it by using A(sup T)A. Then they find the eigenvalues and eigenvectors of this A(sup T)A matrix. The physical interpretation of the eigenvectors for circular machines is discussed.