LINEAR PROGRAMMING Vs LEAST SQUARES METHOD IN DETERMINING THE BEST TRIM COIL CURRENTS FOR THE NRL CYCLOTRON

A description is given of a linear programming method which has been used in determining the best trim coil currents to produce the isochronous field needed to accelerate particular ions to a particular energy. The results using this sub­ routine are compared with those using a least squares method. Although the least squares method had given good results, it contained a certain arbitrariness in choosing which trim coil to set at the limiting current value when two or more of the best trim coil currents fell outside the allowable limits. It was hoped that the linear programming method might give better results, since the requirement that all currents be less than certain values can be inCluded among the constraints of the problem. The two methods are compared in terms of the deviation from isochronism of the field produced. It was found that in cases where the general fit in either case was good, there was little difference between the methods, but when the general fit was poor, the least squares method gave over-all, less deviation from the calculated isochronous field.