Table of Solenoids with Sixth-Order Error and Near-Maximum Power Efficiency

Abstract

In a sixth-order solenoid of type I (or II), the field errors of second and fourth orders are compensated by a notch in the outer (or inner) cylindrical surface. The power efficiency EF≡G/0.1792, where the Fabry factor G is defined in the same way as for an uncompensated cylindrical coil with the same least radius, and 0.1792 is the largest possible value of G for any such coil. The efficiency of a sixth-order solenoid is defined to be ``near maximum'' when EF has a value no less than 98% of the maximum for any compensated coil of the same type and normalized volume V. The 2% tolerance permits the choice of an experimental coil to be influenced by properties that may be more sensitive to changes in geometry than is EF. Coils of type I are relatively long, with a maximum EF of 0.692 at V≅200. In type II coils, the diameter often exceeds the length, and the maximum EF is 0.884 at V≅300. Separate tables with V1/2 as argument list 100 solenoids of each type, with geometry, field strength, EF, and axial limits for field variations of 0.1% and 1.0%. All radial depths are so adjusted that the layer counts for the midplane and end sections are proportional to a pair of small integers. Though the 0.03% limits of a typical coil of type I could enclose the 1.0% limits of a type II coil of the same volume, the field error of the type II coil is less than 0.02% at the axial 1.0% limit of the same coil without the correcting notch.