Calculation of an Enclosed Cylindrically Symmetric Green's Function and Its Comparison to Field Measurements

An analytic representation for the field from an arbitrary current distribution (either expandable in a Fourier series or for a current distribution that varies as sin2kz over one period) with cylindrical symmetry and enclosed within conducting inner and outer walls is derived. The Green's function applicable to the dc field from a single loop lying between two perfectly conducting cylinders is first calculated. The inversion from measured magnetic field to current distribution, which can be obtained in principle from the Green's function, is done in detail only for the previously mentioned current distributions. For most experimental parameters, the Green's function is so sharply peaked, one can assume a periodic current distribution for long current layers (length-to-diameter ratio > 2). The predicted magnetic field amplitude and field shapes were experimentally verified on the Astron machine.