The FFAG accelerator, which was 80 thoroughly studied at MURA two decades ago, now shows great promise as a moderate cost means of achieving great intensities of spallation-bred neutrons. For this reason, it is being studied both at Argonne National Laboratory and at the Kernforzhungzanlage, Juelich. Although a great many isochronouz cyclotron versions of the FFAG principle exist, no ion zynchrotron versions have been built. The MURA codes designed to study FFAG accelerators were written in machine language for the IBM 704 Computer and are thus not usable today. The code here described was written to fill the gap. Following the author’s current passion, tt was written in Pascal in order to be easily followed and operable on a great variety of computers. Most of the development was done on the author’s Western Digital “Pascal Microengine”, which is able to compile the entire code in two minutes. Method FFAG synchrotrons have much stronger nonlinearitiez than the usual alternating-gradient synchrotron. In particular, an adequate study of the stability limits in the vertical plane requires the inclusion of some nonlinear terms--at least those that yield tune shifts with amplitude in the vertical plane. The methods used are basically those of the Oak Ridge National Laboratory cyclotron cpdes (e.g., #1482) as described by Welton Cl]. These have been extended to include third-order terms in the axial direction in order to be able to determine the axial acceptance. The ORNL methods are very fast and yield the exact motion in the median plane. In this FFAG code, six simultaneous equations are integrated to locate the closed orbit. Using the radial transfer matrix thus derived about a trial orbit, corrections are made and the process repeated until convergence is achieved. The error in closing is generally reduced by one to two orders of magnitude per iteration. Once the closed orbit is determined, four more equations are added in order to obtain the linear properties in the axial plane also. The extreme values of the Courant and Snyder amplitude functions are also determined. Having the closed orbit, nonlinearities may be analyzed in several ways. A great number of orbits may be run through one sector to provide fitting data for a canonical transformation program r.21. Single orbits Magnetic Field Representation The code treats scaling fields that are free of error. The magnetic field in the median plane is completely determined by giving the field index, k, the spiral angle, & , and the azimuthal profile of the magnetic field over one sector. The azimuthal profile is normally given as an irregular mesh. This mesh is fit with a series of (up to 400) cubic zpline functions such that the profile and its first two azimuthal derivatives are continuous at each mesh point, and the zplinez are periodic. With the periodic condition dropped, the splinez are determined by a Gaussian reduction algorithm that operates on a diagonally-dominant matrix whose non-zero elements can always be stored in an array of size 3, where n is the number of mesh points 131. The solution with the periodic condition imposed is determined by an iterative method that uses the reduced matrix to quickly converge on the desired solution. The azimuthal profile may also be given by mean8 of Fourier harmonics; however, the zpline representation is far faster. Only the median field is needed to obtain the exact motion in the median plane, and only the first radial and first azimuthal derivatives are needed to obtain the linearized motion in both planes about the closed orbit. To include higher order terms in the axial motion, we expand the axial component of the magnetic field as a power series in z; however, because of the symmetry condition, only even terms can exist in this expansion: