Global orbit corrections
Global orbit corrections
There are various reasons for preferring local (e.g., three bump) orbit correction methods to global corrections. One is the difficulty of solving the mN equations for the required mN correcting bumps, where N is the number of superperiods and m is the number of bumps per superperiod. The latter is not a valid reason for avoiding global corrections, since, we can take advantage of the superperiod symmetry to reduce the mN simultaneous equations to N separate problems, each involving only m simultaneous equations. Previously, I have shown how to solve the general problem when the machine contains unknown magnet errors of known probability distribution; we made measurements of known precision of the orbit displacements at a set of points, and we wish to apply correcting bumps to minimize the weighted rms orbit deviations. In this report, we will consider two simpler problems, using similar methods. We consider the case when we make M beam position measurements per superperiod, and we wish to apply an equal number M of orbit correcting bumps to reduce the measured position errors to zero. We also consider the problem when the number of correcting bumps is less than the number of measurements, and we wish to minimize the weighted rms position errors. We will see that the latter problem involves solving equations of a different form, but involving the same matrices as the former problem.
mark.phillips@unt.edu
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