Matrix method for analysis of network accuracy based on the beam dynamic theory

Starting the development of the alignment system, surveyors have faced several questions in respect to the degree of accuracy, the length of the region of relative accuracy, the optimal smoothing curve not resulting in the orbit distortion, and the scheme of measurements and appropriate instruments. Aiming to give answers to these questions, matrix method was practically applied for VEPP-4 alignment system. By the analysis of elements of the matrix A, the particular elements to be aligned with higher accuracy and the places where special attention should be paid to the positioning of the vacuum chamber and other equipment were able to be determined. The matrix of the orbit distortion A enabled to perform an analysis of the sensitivity of the magnet system to certain Fourier frequencies in a distribution of the quad displacements. The spectral sensitivity of magnet system for harmonics was much reduced when the matrix A was replaced by A-I. It was found that the surveyor can determine the orbit distortion and reduce the number of elements requiring alignment by applying the matrix method in the realignment process. (M.N.)