Optimization method for orbit correction in accelerators

Abstract

We present a method to minimize the corrector strengths required to reduce the RMS beam orbit. Any least square correction method will usually lead to undesirably strong corrector settings. The method, we are presenting, minimizes the total kick vector by finding the eigensolutions of the equation X/spl I.oarr/=A/spl thetaspl circ/, where X/spl I.oarr/ is the orbit change vector /spl thetaspl circ/ is the kick vector and A is the response matrix. Since A is not necessarily a symmetric or even square matrix we symmetrize the matrix by using A/sup T/A instead. Eigenvectors with corresponding small eigenvalues generate negligible orbit changes. Hence, in the optimization process the kick vector is made orthogonal to the eigenvectors. The physical interpretation of the eigenvectors will be discussed. We will illustrate the application of the method to the NSLS X-ray and UV storage rings. From this illustration 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 beamlines and insertion devices. >