Dimensioning of additional current paths to optimize the disturbance behavior of a superconducting magnet system

A superconducting magnet system for generating a magnetic field in a direction of a z axis in a working volume disposed about z=0, the magnet system being able to react inductively to a, within a magnet volume substantially homogeneous, disturbance field produced by a disturbance coil (D), the magnet system comprising:

• at least one current-carrying magnet coil (M);
• and
• at least one additional superconductingly closed current path (P1, . . . , Pn), which can react inductively to changes of the magnetic flux through the area enclosed by it, wherein the magnetic fields in the z direction generated by these additional current paths during operation and in response to induced currents do not exceed 0.1 Tesla in the working volume, wherein said magnet coil(s) (M) and said current path (P1, . . . , Pn) are designed such that, when the additional disturbance coil (D) produces a substantially homogeneous disturbance field in the magnet volume, a value β = 1 - g T · ( ( L cl - α ⁢ ⁢ L cor ) - 1 ⁢ ( L ← D cl - α ⁢ ⁢ L ← D cor ) g D )
• differs by more than 0.1 from a value β 0 = 1 - g T · ( ( L cl ) - 1 ⁢ L ← D cl g D )
• which would result if α=0,
• wherein:
• −α:
• is an average magnetic susceptibility in the volume of said magnet coil(s) (M) with respect to field fluctuations which do not exceed a magnitude of 0.1 T, with 0<α≦1, and
• gT=(gM, gP1, . . . , gPj, . . . , gPn),
• wherein
• gPj:
• is a field per ampere of said current path Pj in the working volume without field contributions of said current paths Pi for i≠j and said magnet coil(s) (M),
• gM:
• is a field per ampere of said magnet coil(s) (M) in the working volume without the field contributions of said current paths (P1, . . . ,Pn),
• gD:
• is a field per ampere of the disturbance coil (D) in the working volume without field contributions of said current paths (P1 , . . . ,Pn) and said magnet coil(s) (M),
• Lcl:
• is a matrix of inductive couplings between said magnet coil(s) and said current paths (P1, . . . ,Pn) and among said current paths (P1, . . . ,Pn),
• Lcor:
• is a correction for said inductance matrix Lcl, which would result with complete diamagnetic expulsion of disturbance fields from the volume of said magnet coil(s) (M),
• L77 Dcl:
• is a vector of inductive couplings of the disturbance coil (D) with said magnet coil(s) and said current paths (P1, . . . ,Pn), and
• L←Dcor:
• is a correction for said coupling vector L←Dcl, which would result with complete diamagnetic expulsion of disturbance fields from the volume of said magnet coil(s) (M).