Three Dimensional Properties of Magnetic Beam Transport Elements

Analytical and experimental methods to describe precisely, in three dimensions, the magnetic fields of beam transport elements will be discussed. The influence of the fringing field on beam optical properties and magnet design will be presented. With appropriate boundary conditions the field components are expressed in terms of the magnetic potential to arbitrarily high orders with empirical coefficients and are grouped in a form to avoid the divergence of higher order terms. As an accurate description of the true field is obtained, a very precise trajectory can be computed for a known momentum. In addition, the more useful inverse problem of finding the momentum of a particle with known input and output trajectory coordinates is attacked. The trajectory solution is expressed as the sum of an analytical part plus perturbation terms. The first order solution for the momentum is easily obtained and the convergence of the subsequent perturbation calculations is very rapid even for extreme rays. The value of this method, with its precise treatment of fringing fields, is emphasized by treating in detail a wide angle spectrometer (120-in. wide, 36-in. long, 24-in. gap). The perturbation technique shows promise that an accurate instantaneous read-out of the momentum can be obtained by employing a modest number of perturbation corrections stored in the memory of the computer.