Analyzing the uniformity of the generated magnetic field by a practical one-dimensional Helmholtz coils system

Using the Helmholtz coils system is one of the most suitable approaches which have been introduced for generating uniform magnetic fields. In this paper, uniformity of the generated magnetic field by a practical one-dimensional (1D) Helmholtz coils system has been analyzed, mathematically. For this purpose, relationships between the magnetic field uniformity and different practical unavoidable mismatches have been extracted. The theoretical analysis clearly demonstrates the effect of assembly misalignments and manufacturing mismatches on the magnetic field achieved by a practical 1D Helmholtz coils system. The given analyses have been confirmed by the experimental results which are in good agreement with the calculated values. This analysis and the experimental results illustrate that to achieve a very high uniform magnetic field, practical assembly misalignments, and manufacturing mismatches must be as small as possible, and the background magnetic field distortion must be avoided, too. The results of this work are important in the design of instruments and systems where Helmholtz coils are used.