Analysis of magnetic fields and circuits in separators with plane-parallel and plane-meridian symmetry

We present, for the first time, an analytic method of making plane-meridian magnetic field and magnetic circuit calculations. The analytic expressions for the magnetic force, field strength, flux, potential difference, etc., are derived semiempirically. They make possible a transition from the plane-parallel configuration to the plane-meridian one. The method takes into account the magnetic resistance of a steel. We compare all the results of calculations with appropriate experimental values and evaluate the corresponding errors. We also present a method for complete calculation of a separator's magnetic system. We describe an approximate method of finite size effects in multipole magnetic systems with axial pole disposition. Using the method of conformai mapping, we derive an analytic expression for the magnetic field in the inner domain of separators with radial pole disposition. We also define a precise limit when a multipole system with radial pole disposition coincides with a multipole system with axial pole configuration and show that, in this limit, analytic expressions obtained independently for both cases coincide. Taking into account the analytic expressions published earlier, we thus complete the description of the magnetic fields belonging to this class of magnetic systems.