  We demonstrate neutron beam focusing by axisymmetric mirror systems based on
a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a
system, known as a Wolter mirror configuration, is commonly used in x-ray
telescopes. The axisymmetric Wolter geometry allows nesting of several mirror
pairs to increase collection efficiency. We have implemented a system
containing four nested Ni mirror pairs, which was tested by focusing a
polychromatic neutron beam at the MIT Reactor. In addition, we have carried out
extensive ray-tracing simulations of the mirrors and their performance in
different situations. The major advantages of the Wolter mirrors are nesting
for large angular collection, and aberration-free performance. We discuss how
these advantages can be utilized to benefit various neutron scattering methods,
such as imaging, SANS, and time-of-flight spectroscopy.
