Physicists Prof. Dr. Ingo Rehberg from the University of Bayreuth and Dr. Peter Blümler from Johannes Gutenberg University Mainz have developed and experimentally validated an innovative approach for generating homogeneous magnetic fields using permanent magnets.

Their method outperforms the classical Halbach arrangement—which is optimal only for infinitely long and therefore unrealizable magnets—by producing higher field strengths and improved homogeneity in compact, finite-sized configurations.

The study was published in Physical Review Applied, which shows significant advances in the applied sciences at the intersection of physics with engineering, materials science, chemistry, biology, and medicine.

A new approach to magnetic field homogenization

Homogeneous magnetic fields can be generated over relatively large spatial regions through the targeted arrangement of permanent magnets.

A well-known example of an effective design is the so-called Halbach array. However, this approach is based on the idealized assumption that very long—ideally infinitely long—magnets (line dipoles) can be arranged in a circle in such a way that the individual contributions superimpose to produce a homogeneous magnetic field in the center region.

In practical applications, using magnets of finite length, the resulting field deviates significantly from this ideal: the field strength inside the circle varies considerably depending on the position.

The classical Halbach geometry is therefore clearly suboptimal for compact, practically implementable magnet arrangements when the aim is to achieve the strongest and/or most uniform magnetic field possible.

In their work, Peter Blümler and Ingo Rehberg present optimal three-dimensional arrangements of very compact magnets, idealized by point dipoles. With a view to possible applications, they investigated, among other things, the optimal orientation of the magnets for two geometries relevant to practical use: a single ring and a stacked double ring.

A so-called “focused” design additionally allows the generation of homogeneous fields outside the magnet plane, for example in an object positioned above the magnets.

For these new arrangements, Rehberg and Blümler developed analytical formulas, which they subsequently validated experimentally. To this end, they constructed magnet arrays from 16 FeNdB cuboids mounted on 3D-printed supports. The resulting magnetic fields were measured and compared with theoretical predictions, revealing excellent agreement.

In terms of both magnetic field strength and homogeneity, the new configurations clearly outperform the classical Halbach arrangement as well as its modifications described in the literature.

Potential for numerous applications

The new design concepts offer great potential for applications in which strong and homogeneous magnetic fields are required. In conventional magnetic resonance imaging (MRI), for example, powerful superconducting magnets are used to polarize hydrogen nuclei in tissue.

These nuclei are then excited by radio waves, generating measurable voltages in detectors surrounding the body. Algorithms use these signals to calculate detailed cross-sectional images that allow physicians to distinguish tissue types based on properties such as density, water or fat content and diffusion.

However, superconducting magnets are technically complex and extremely costly, making this technology hardly available in many parts of the world.

For such cases, intensive research is underway to develop alternative methods for generating homogeneous magnetic fields using permanent magnets—a field to which the present study makes a promising contribution. Further potential areas of application include particle accelerators and magnetic levitation systems.