Method for designing open magnets and open magnetic apparatus for use in MRI/MRT probes

A method for constructing an open magnetic apparatus for providing a volume of substantially homogenous magnetic field, the apparatus having an axis of symmetry passing therethrough, the method comprising the steps of:

• providing an open ferromagnetic yoke having a first yoke surface and a second yoke surface opposed to said first yoke surface, said second yoke surface is shaped like a mirror image of said first yoke surface with respect to a mid-plane equidistant from said first yoke surface and said second yoke surface, said symmetry axis is perpendicular to said mid-plane;
• providing a first magnetic assembly attached to said first yoke surface, said first magnetic assembly includes
• a first ferromagnetic pole-piece substantially parallel to said mid-plane and having an outer radius, said axis of symmetry passing through the center of said first pole-piece, said first pole-piece is radially symmetric along any axis perpendicular to said axis of symmetry and passing through said center of said first pole-piece, said first pole-piece having a first surface facing said volume and a second surface facing said first yoke surface, and
• a first magnetic structure disposed between said second surface of said first pole-piece and a surface formed by a projection on said first yoke surface of said second surface of said first pole-piece in a direction parallel to said axis of symmetry, said first magnetic structure having a first magnetization vector directed substantially parallel to said axis of symmetry, and
• at least a first substantially annular ferromagnetic collimator concentric with said first pole-piece and having an inner radius larger than said outer radius of said first pole-piece, said at least first collimator is radially separated from said first pole-piece by a first gap, said at least first collimator having a fourth surface facing said volume and a fifth surface facing said first yoke surface, and
• at least a second magnetic structure disposed between said fifth surface of said at least first collimator and a surface formed by a projection on said first yoke surface of said fourth surface of said first collimator in a direction parallel to said axis of symmetry, said second magnetic structure having a second magnetization vector directed substantially parallel to said axis of symmetry;
• and
• providing a second magnetic assembly opposed to said first magnetic assembly and attached to said second yoke surface, said volume is disposed in the open region defined between said first magnetic assembly and said second magnetic assembly, said second magnetic assembly includes,
• a second ferromagnetic pole-piece substantially parallel to said mid-plane and having an outer radius substantially equal to said outer radius of said first pole-piece, said axis of symmetry passing through the center of said second pole-piece, said second pole-piece is radially symmetric along any axis perpendicular to said axis of symmetry and passing through said center of said second pole-piece, said second pole-piece having a fifth surface facing said volume and a sixth surface facing said second yoke surface, and
• a third magnetic structure disposed between said sixth surface of said second pole-piece and a surface formed by a projection on said second yoke surface of said sixth surface of said second pole-piece in a direction parallel to said axis of symmetry, said third magnetic structure having a third magnetization vector substantially equal to said first magnetization vector, and
• at least a second substantially annular ferromagnetic collimator concentric with said second pole-piece and having an inner radius substantially equal to said inner radius of said at least first collimator and larger than said outer radius of said second pole-piece, said at least second collimator is radially separated from said first pole-piece by a second gap, said at least second collimator having a seventh surface facing said volume and an eighth surface facing said second yoke surface, and
• at least a fourth magnetic structure disposed between said eighth surface of said at least second collimator and a surface formed by a projection on said second yoke surface of said eighth surface of said second collimator in a direction parallel to said axis of symmetry, said at least fourth magnetic structure having a fourth magnetization vector substantially equal to said second magnetization vector,
• wherein said first pole-piece and said second pole-piece are selected from a cylindrical pole piece, an annular pole-piece, a regular polygonal pole-piece and a regular polygonal annular pole-piece, and said at least first collimator and said at least second collimator are selected from an annular collimator and a regular polygonal annular collimator.

A method for designing an open yoked magnetic apparatus providing a volume of substantially homogenous magnetic field, the volume having radial symmetry with respect to an axis of symmetry passing therethrough, said volume has a center point, said center point is located on a mid-plane, said mid-plane is perpendicular to said axis of symmetry and symmetrically bisects said volume, the method comprising the steps of:

• providing a first set of parameters defining the desired dimensions of said volume and the desired magnitude of the magnetic field within said volume;
• providing an integer number N representing the number of high order harmonics of said magnetic field which are to be compensated;
• providing a second set of dimensional parameters defining a plurality of K ferromagnetic members concentrically arranged around said axis of symmetry and radially symmetric with respect to any axis perpendicular to said axis of symmetry, said plurality of K ferromagnetic members includes a substantially disc-like or annular pole-piece and K-1 substantially annular collimators, each of said plurality of K ferromagnetic members is associated with a magnetic structure of a plurality of K magnetic structures such that the K-th magnetic structure is disposed between the K-th ferromagnetic member and a portion of a surface of a ferromagnetic yoke of said yoked magnetic apparatus;
• computing from said second set of dimensional parameters a matrix M.sub.jK comprising N-K matrix elements, wherein each of said matrix elements m.sub.jK represents the contribution of said K-th magnetic structure to a j-th harmonic coefficient a.sub.j wherein said harmonic coefficient a.sub.j represents the coefficient of the jth term of higher than zeroth order terms of the magnetic field expansion equation for the magnetic field formed by a magnetic structure of said plurality of K magnetic structures and by said pole-piece, said magnetic structure is disposed between said pole-piece and a portion of said surface of said yoke;
• computing from said matrix M.sub.jK and from the values of the high order coefficients a.sub.j a plurality of K remanence values, each of the remanence values J.sub.K of said plurality of K remanence values represents the average remanence value for the K-th magnetic structure;
• checking whether the absolute value of all of said remanence values J.sub.K is smaller than or equal to a maximal remanence value J.sub.MAX, said maximal remanence value J.sub.MAX representing the maximal remanence value of the magnetic material available for constructing said magnetic apparatus,
• performing a solution stability check to verify that the solution based on said second set of parameters is a stable solution within the tolerance range of the magnetic material available for constructing said magnetic apparatus;
• checking whether any of said K ferromagnetic members is magnetically saturated;
• and
• accepting said solution based on said second set of parameters if none of said K ferromagnetic members is magnetically saturated.