FFT calculation of magnetic fields in air coils

The magnetostatic field produced by an air coil that possesses one-dimensional periodicity can be expressed as a one-dimensional discrete convolution of two functions. The first function expresses the field produced by a single turn of the coil. The second is a shape function; it expresses the spatial position and strength of current of each turn of the coil. The discrete convolution of these two functions gives the magnetostatic field produced by the coil. This result can be interpreted with linear system theory. Under this interpretation, the first function, the response from a single turn, can be thought of as the impluse response function of a hypothetical linear system or "black box." The second function, the expression of position and current strength can be thought of as the input signal to the black box. The advantage of this approach is that it allows the application of highly developed methods of linear system theory to air-coil problems. This paper presents one application of linear system theory to an air-coil calculation, the use of the Fast Fourier Transform (FFT) in computing magnetostatic fields from air coils. A program is described which uses FFT convolution to perform this calculation.