Halbach and Stelter Arrays

Klaus Halbach, a professor with the University of California’s Lawrence Berkeley Labs, was an innovator in the application of permanent magnets to accelerator and synchrotron light projects around the world. The principle behind his innovative work is superposition. The superposition theorem states that the components of force at a point in space contributed by several independent objects will add algebraically.

Applying the theorem to permanent magnets is possible only when using materials with coercivity nearly equal to residual induction. While ferrite magnets have this characteristic, it was not practical to use the material this way because simple Alnico magnets provided more intense fields at a lower cost. The advent of high residual induction "rare earth" magnets such as Sm-Co and Nd-Fe-B made the use of superposition practical and affordable. These materials allow developing intense magnetic fields in small volumes without the energy requirements of electromagnets. The disadvantage for electromagnets is the space occupied by electrical windings, and the need to dissipate the heat generated by the coils.

While Dr. Halbach pursued "high end" applications of superposition, Dexter’s Dick Stelter used the theorem in commercial applications. Halbach taught the use of "magic ring" dipoles to develop intense fields in a circular aperture. In this device trapezoidal magnets are assembled to form a ring. The orientation of each trapezoidal magnet is such that there is a continuous rotation of the magnetic vector in each half of the ring, and for an infinitely long ring, field strength in the aperture is proportional to the natural log of the ratio of OD to ID.

Stelter Arrays use the minimum number of rectangular magnet shapes to reach the desired results in a rectangular aperture. For a "Stelter Array", the relationships are similar, and the internal field is proportional to the natural log of the outer periphery to inner periphery ratio. Using rectangular shapes also permits "flux bottling" to shape the internal field. Highly uniform magnetic fields of over 2-3T can be routinely generated in a range of air gaps, and Dexter applications based on the patented Stelter Array include dipoles for NMR/MRI, "open" NMR, mass spectrometers, sputtering magnetrons, hard disk erasers, miniature rotary actuators, bulk erase tools and many more.

For further inquiries, please e-mail us at info@dextermag.com -or- call us at:  800-345-4082 (In North America) or +44 (0) 1189 602430 (In Europe).