Optimization of the magnetic field homogeneity of circular and conical coil pairs.

The magnetic field generated by a pair of coaxial circular loops is analyzed in order to find the optimum separation between the loops for each value of a prescribed homogeneity. For the maximum heterogeneities considered here, 0.1%, 1%, and 10%, the optimum loop spacing is obtained following a graphical procedure so that the length of the homogeneous field region along the axis is the longest possible. This study is extended to regions near the axis and to the entire region surrounding the center, calculating the loop separation that produces the largest homogeneous volume. The field homogeneity of a pair of "Helmholtz" coaxial conical coils is also investigated to obtain the optimum spacing between the conical coils; the volumes calculated with the desired homogeneity are compared with those obtained with a single pair of optimum coaxial loops. A new arrangement is hereby proposed based on double conical coils with optimum separation between the coils and optimum aperture of the cones. Some of the proposed arrangements are carried out in the laboratory where the experimental results are in good agreement with the theoretical predictions.

[1]  F. Gascón,et al.  Magnetic field homogeneity of a conical coaxial coil pair. , 2017, The Review of scientific instruments.

[2]  Reza Beiranvand,et al.  Effects of the Winding Cross-Section Shape on the Magnetic Field Uniformity of the High Field Circular Helmholtz Coil Systems , 2017, IEEE Transactions on Industrial Electronics.

[3]  Félix Salazar Bloise,et al.  Solved Problems in Electromagnetics , 2016 .

[4]  Jake J Abbott,et al.  Parametric design of tri-axial nested Helmholtz coils. , 2015, The Review of scientific instruments.

[5]  Michal Ulvr,et al.  Precise Calibration Method for Triaxial Magnetometers Not Requiring Earth’s Field Compensation , 2015, IEEE Transactions on Instrumentation and Measurement.

[6]  Paul Bartlett,et al.  Toward an Automated Setup for Magnetic Induction Tomography , 2015, IEEE Transactions on Magnetics.

[7]  H. Zafar,et al.  Design and Analysis of a High-Power Electron Beam Source $(>\hbox{50}\ \hbox{KW/cm}^{2})$ Confined in a Highly Uniform Magnetic Field Region , 2012, IEEE Transactions on Plasma Science.

[8]  M. Crosser,et al.  On the magnetic field near the center of Helmholtz coils. , 2010, The Review of scientific instruments.

[9]  Celso Fabricio de Melo,et al.  Calibration of low frequency magnetic field meters using a Helmholtz coil , 2009 .

[10]  Andrew Gibson,et al.  Influence of balancing parameters in achieving magnetic field uniformity in a large cylindrical volume , 2008 .

[11]  Sijiong Zhang,et al.  An improved Helmholtz coil and analysis of its magnetic field homogeneity , 2002 .

[12]  T. Holst,et al.  Optimization of field homogeneity of Helmholtz-like coils for measuring the balance of planar gradiometers , 1999 .

[13]  L. Paulsson,et al.  Influence of field inhomogeneity in magnetic calibration coils , 1996 .

[14]  E. L. Bronaugh,et al.  Helmholtz coils for calibration of probes and sensors: limits of magnetic field accuracy and uniformity , 1995, Proceedings of International Symposium on Electromagnetic Compatibility.

[15]  R S Caprari,et al.  Optimal current loop systems for producing uniform magnetic fields , 1995 .

[16]  E. Boridy Magnetic fields generated by axially symmetric systems , 1989 .

[17]  K. Kaminishi,et al.  Practical method of improving the uniformity of magnetic fields generated by single and double Helmholtz coils , 1981 .

[18]  J. R. Craig,et al.  Magnetic Field Uniformity around Near‐Helmholtz Coil Configurations , 1969 .

[19]  J. R. Craig,et al.  Optimum Spacing of Square and Circular Coil Pairs , 1968 .

[20]  F. Crownfield Optimum Spacing of Coil Pairs , 1964 .

[21]  W. Franzen,et al.  Generation of Uniform Magnetic Fields by Means of Air-Core Coils , 1962 .

[22]  J. Kirschvink,et al.  Uniform magnetic fields and double-wrapped coil systems: improved techniques for the design of bioelectromagnetic experiments. , 1992, Bioelectromagnetics.