OPTIMAL LARMOR PRECESSION MAGNETIC-FIELD SHAPES - APPLICATION TO NEUTRON SPIN-ECHO 3-AXIS SPECTROMETRY

Resolution characteristics of neutron spectrometers using Larmor prece ssion of the neutron spin are limited by magnetic field homogeneities of a special type. The line integral of the modulus of the magnetic in duction B integral(L) \B\ dl along a neutron trajectory of length L is a measure of the amount of precession performed by the neutron. Hence it should be precisely the same for all neutron trajectories in a div erging beam. We present an analytical solution to the variational prob lem integral L \B\ dl = constant, for the case of cylindrical magnets (better than any lower symmetry geometry) coaxial to the beam axis. Th is solution describes the best irrotational (rot B = 0) field shape al ong the beam axis z. It can be obtained in practice by superposing a n umber of solenoids of different lengths. The optimal homogeneity is si gnificantly better than for a simple solenoid of comparable dimensions , the only magnets used until now. For realistic lengths L and beam ra dii r, it is however not good enough for very high-resolution measurem ents. We therefore introduce a technique to correct both for the resid ual inhomogeneities of optimized cylinder magnets and the line integra l variations due to path length differences resulting from finite angu lar beam divergence. Such corrections can only be done by introducing current distributions in the beam. Their optimal distributions can als o be calculated analytically. Until now only the residual inhomogeneit ies have been corrected by in beam currents. With the two concepts of optimal field shape (OFS) and path length corrections described here, the resolution properties of Larmor precession techniques can be pushe d to their intrinsic limits. As a further result of the correction tec hnique introduced here, wider angular divergences can be used, for exa mple using multi-detectors, resulting in substantially improved neutro n economy. Several neutron spin echo (NSE) spectrometers based on abov e ideas have in the meantime been constructed by different working pat ties. The experimental results confirm the calculations reported here; no significant polarization drop is observed at maximum field, For th e investigation of dispersive elementary excitations in solids where t he neutron energy change depends on the momentum transfer, a special t ype of gradient coils is needed. We describe their design for OFS prec ession magnets.