Design of thin windings to create magnetic fields of a given shape

A method is described for finding the density distribution of the current flowing over a surface of a given shape and then a configuration of windings to be placed on it that create in a specified region of space a magnetic field of a given shape. The possibilities of the method are demonstrated by the example of the design of windings to create a constant transverse axial-magnetic-field gradient. They ensure a field nonlinearity of 5% in a sphere whose radius is 30% greater than that of the rectangular frameworks placed over cylindrical surfaces that are usually employed. Use of the method to achieve the required accuracy in the creation of a magnetic field of a given configuration is described. 2 refs., 2 figs