Patent ID: 7492158

Claim:
A method for determining construction parameters of magnet structures designed to generate magnetic fields in predetermined volumes of space, comprising the steps of: a) defining a predetermined volume of space in which a magnetic field is to be generated; b) defining a nominal strength and a profile of a nominal desired magnetic field in said predetermined volume of space; c) mathematically defining the nominal desired magnetic field on a surface of and/or in said predetermined volume of space by calculating a series of coefficients using a polynomial expansion of a magnetic field-describing function; and d) determining a size, a geometry and a relative position in space of a magnet structure designed to generate said nominal desired magnetic field, with respect to the predetermined volume of space in and on which the nominal desired magnetic field is defined; the magnetic field being expressed by the coefficients of the polynomial expansion in ellipsoidal harmonics; wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps; measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N; constructing Lamé functions from dimensions of the semiaxes up to an order of N−1; calculating normalization coefficients γ n p according to the function γ n p = 8 ⁢ ∑ i = 1 N ⁢ ω i C ⁢ ω i L ⁡ ( F n p ⁡ ( x i L ) ⁢ G n p ⁡ ( x i C ) - G n p ⁡ ( x i L ) ⁢ F n p ⁡ ( x i C ) ) , where F n p (x i L ) and G n p (x i C ) are related to the ellipsoidal harmonics of degree n and order p as determined in Gauss-Chebychev abscissas x i C and Gauss-Legendre abscissas x i L , and where ω i C and ω i L represent respective weights; and calculating expansion coefficients α n p by using the function α n p = 2 γ n p ⁢ ∑ i = 1 N / 2 ⁢ ∑ j = 1 N ⁢ ω i C ⁢ ω i L ⁢ B ⁡ ( x i C , x i L ) ⁢ ( F n p ⁡ ( x i L ) ⁢ G n p ⁡ ( x i C ) - G n p ⁡ ( x i L ) ⁢ F n p ⁡ ( x i C ) ) , where N represents the order of approximation and B represents the magnetic field expressed in ppm and normalized with respect to an assumed value of the magnetic field at the center of the ellipsoid.