3-DIMENSIONAL PURE PERMANENT-MAGNET UNDULATOR DESIGN THEORY

Expressions for fields due to a point charge in 3D and due to a line c harge in 2D are compared. : Extensions to dipoles are made with emphas is on the relationship between dipole orientation and field component magnitudes. Differences between the effects on fields of dipole rotati ons in 2D and in 3D are highlighted and formulas for maximizing indivi dual field components are given. A final macrogeometry extension is ma de and a closed-form expression is developed to calculate the field du e to an arbitrary 3D configuration of permanent magnet (PM) blocks. Th e field optimization theory is applied to the design of the ALS ellipt ically polarizing undulator (EPU). Utilizing 3D held enhancement, peak on-axis field in practical designs can be increased typically by 5% t o 40% or more over their 2D counterparts. The theory is generally appl icable to any pure (i.e., no soft magnetic material) PM design.