TERMINATION OF IDEAL COS m phi WINDING
L. Jackson Laslett, S. Caspi, M. Helm · University of North Texas Digital Library (University of North Texas) · 1986
Configurations are proposed, and illustrated, for terminating the 'cosine {phi}' windings of an ideal iron-free dipole magnet so as to preserve the quality of the internal field integrated (vs. z) through the entire magnet. The end windings are placed on a surface of the same radius as that on which the conductors lie in the central (2-D) portion of the structure. The desired pure dipole quality of the integrated field then is assured by requiring that the z-component of current, after projection onto the y-z plane, shall have in that plane a density distribution whose integral is independent of y. As a result of the analysis, end-winding configurations that satisfy this requirement are proposed in which each conductor filament follows through the transition region a locus whose y-z projection is of the form z(y;Y{sub 0}) = f(y{sub 0}) - f(y-y{sub 0}), with f(0) = 0, wherein Y{sub 0} serves as an index to identify the location of the filament in the central (2-D) portion of the structure. Simple solutions of this nature are indicated in which the function f has the form f(y-y{sub 0}) = k (y-y{sub 0}{sup p}/a) for windings on the surface of a cylinder of radius {und a}, with p < 1 (and preferably p {le} 1/2) to ensure a smooth transition into the end region. The straightforward extension of these results to configurations for the production of integrated fields of higher multipolarity also is indicated.