17 - Neutron and Charged Particle Magnetic Optics

Abstract

This chapter begins with charged particle motion in an axial symmetric magnetic field. The paraxial ray equation and Busch's theorem are derived from the least-action principle. Presented are multipole magnetic fields and magnetic lenses, and the focusing-defocusing quadrupole, magnetic lens pair for charged particles. Derived are the neutron trajectory in an applied sextupole magnetic field, and the magnetic field gradient focusing of neutrons. Discussed is the 1-D focusing of neutrons by a row of cylindrical magnetic lenses. The use of paired sheets of opposite magnetic charges are shown to model magnetic fields for rectangular, permanent magnets. A 1-D periodic magnetic field is shown to act as a gravitational trap for ultracold spin-up neutrons. Finally, the electron trajectory in wigglers and undulator photon sources is derived, and the emitted X-ray wavelength, bandwidth, cone angle, and power from an undulator are presented.