Design, optimization, and purity of permanent magnet helical wigglers for free-electron lasers

A helical wiggler field can be produced inside a cylindrical waveguide by properly distributing and orienting an array of permanent magnets within an annular shell surrounding the waveguide. The design and optimization of such wigglers is considered herein, along with assessments of the strength and spectral purity achievable under practical constraints of equality and uniformly magnetized rare-earth cobalt magnets. Starting with the optimum continuum magnetization, a design is derived that differs from Halbach's primarily in that it includes axially directed components of magnetization. A comparison of the two approaches to helical wiggler design is made in terms of the field strength and purity each can achieve under similar constraints. The optimized design is shown to generate stronger and purer helical wiggler fields than Halbach's version for typical parameters. A modified design that uses many small magnets and does not fill the annular space is suggested and evaluated.