Design and Field Measurements of Printed-Circuit Quadrupoles and Dipoles

Air-core printed-circuit (PC) quadrupoles and dipoles have been developed for the University of Maryland electron ring, currently under construction. The quadrupoles and dipoles are characterized by very small magnetic fields (about 15 G at the aperture edge) and small aspect ratios (length/diameter  <1). We review the theory behind the design of the PC lenses and bending elements, and present general expressions for estimating the values of integrated field and integrated field gradient as functions of design parameters. The new quadrupole magnet represents an improvement over an earlier version which was based on an empirical approach. Further, we summarize the results of multipole content of the magnet fields as measured with a rotating coil apparatus of special construction. The results are compared with calculations with an iron-free magnetics code and are related to different types of errors in the manufacture and assembly of the PC magnets.