Patent ID: 7196603

Claim:
A method for designing a coil, comprising: selecting a geometry for the coil; selecting a region of interest for a magnetic field produced by the coil; defining a stream function for the current density distribution of the coil, wherein the stream function is a sum of sinusoidal functions, wherein each sinusoidal function comprises an amplitude, and wherein the stream function is defined as follows: S ⁡ ( x , y ) = ∑ i ⁢ A i ⁢ sin ⁡ ( i . π ⁢ ⁢ x a ) · ∑ j ⁢ B j ⁢ sin ⁡ ( j . π ⁢ ⁢ y b ) / ( i , j ) where A i and B j are Fourier coefficients representing the amplitudes of the sinusoidal functions in the x and y directions, respectively, and a and b are dimensions of the coil in the x and y directions, respectively; and numerically optimizing the amplitudes of the sinusoidal functions to produce a magnetic field of selected characteristics in the region of interest.