Field Processing Methods Developed for a Separated-Sector Cyclotron

This paper describes three numerical techniques which were developed during beam orbit studies undertaken for the separated-sector cyclotron of the NAC project. The techniques are concerned with the numerical manipulation of field map data. Firstly, a method is given for interpolating the field and calculating its derivatives more accurately than is possible by conventional methods, in regions where the field varies rapidly and the data are not closely spaced. The technique consists of fitting a suitable analytical function f(x) to the field distribution Bi = B(xi) so as to minimize the fourth differences of the distribution Bi - f(xi). The distribution Bi - f(xi) is then smooth enough for conventional methods to be applied. Secondly, we describe a method for isochronizing field map data, the method being applicable to magnets which have trim-coils with edge contours similar to the shapes of the equilibrium orbits within the sectors. Thirdly, we discuss a modification of an alternative isochronization technique, this method being applicable to magnets with trim-coils having edges which are arcs of circles concentric about the centre of the cyclotron.