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The Surrounding Field Compensation (SFC) system described in this work is installed around the four-layer Mu-metal magnetic shield of the neutron electric dipole moment spectrometer located at the Paul Scherrer Institute. The SFC system reduces the DC component of the external magnetic field by a factor of about 20. Within a control volume of approximately 2.5mx2.5mx3m, disturbances of the magnetic field are attenuated by factors of 5-50 at a bandwidth from 10-3 Hz up to 0.5Hz, which corresponds to integration times longer than several hundreds of seconds and represent the important timescale for the neutron electric dipole moment measurement. These shielding factors apply to random environmental noise from arbitrary sources. This is achieved via a proportional-integral feedback stabilization system that includes a regularized pseudoinverse matrix of proportionality factors which correlates magnetic field changes at all sensor positions to current changes in the SFC coils. [ABSTRACT FROM AUTHOR]

An analytic solution to the magnetostatic inverse problem in the framework of vector spherical harmonic basis functions is presented. This formalism is used for the design of a spherical magnetic field compensation system and its performance is compared with an already existing rectangular coil system. The proposed set of spherical coils with 15 degrees of freedom achieves a shielding factor of 1000 or better in a large part of the volume enclosed by the coils for a dipolar type external perturbation. [ABSTRACT FROM AUTHOR]