Some Orbit Calculations for TRIUMF

This paper is a report of some studies made of orbit properties in the TRIUMF Cyclotron. We will describe a numerical technique for obtaining solutions of ill-conditioned linear equations, this has proved useful when trying to produce a desired field with 54 trim coil pairs using the method of least squares, and in calculating an isochronous field. We will also describe a phase dependent centring error which can distort the horizontal emittance of beams with positive phases, thus limiting the phase acceptance of a cyclotron; and tolerances for field imperfections imposed by certain resonances in TRIUMF will also be reported. These calculations are chiefly concerned with phenomena away from the immediate central region and consequently electric focusing forces have been ignored. Central region calculations that include electric fields will be reported elsewhere.