Halbach Array

A Halbach array is an arrangement of permanent magnets that causes an one-sided flux, i.e. the magnetic field is maximized on one side, while minimized on the other.

Although this effect was first described by John Mallinson in 1973 while working at Ampex (Redwood City, CA), he described the “one-sided flux” structures as a “curiosity,” and saw their primary application in improving magnetic tape recording.Refrigerator magnets (typically a dispersion of barium ferrite particles in a rubber matrix) are the most common example of an one-sided magnetic flux.

  • John C. Mallinson, “One-Sided Fluxes — A Magnetic Curiosity?” IEEE Transactions on Magnetics, Volume 9 (1973) pp. 678-682, doi:10.1109/TMAG.1973.1067714 (Reformatted and color illustrations added, June 2009)

Klaus Halbach, a physicist at Lawrence Berkeley Laboratory, invented the Halbach array for use in accelerator particle beams. Unlike electromagnets, Halbach’s permanent magnets were smaller and used no power; facilitating their use in the tight confines of particle accelerators and electron storage rings. His three most commonly cited papers are:

  • Klaus Halbach, “Design of Permanent Multipole Magnets with Oriented Rare Earth Cobalt Materials,” Nuclear Instruments and Methods, 169 (1980) pp. 1-10, doi:10.1016/0029-554X(80)90094-4 (Reformatted and color illustrations added, June 2009)
  • Klaus Halbach, “Physical and Optical Properties of Rare Earth Cobalt Magnets,” Nuclear Instruments and Methods 187 (1981) pp. 109-117, doi:10.1016/0029-554X(81)90477-8 (Reformatted and color illustrations added, June 2009)
  • Klaus Halbach, “Perturbation Effects in Segmented Rare Earth Cobalt Multipole Magnets,” Nuclear Instruments and Methods 198 (1982), pp. 213-215, doi:10.1016/0167-5087(82)90258-7 (Reformatted and color illustrations added, June 2009)

Subsequently, he wrote several papers examining specific implementations of permanent magnets:

  • Klaus Halbach, “Conceptual Design of a Permanent Quadrupole Magnet with Adjustable Strength,” Nuclear Instruments and Methods 206 (1983), pp. 353-354 (Reformatted and color illustrations added, July 2009)
  • Klaus Halbach, “Permanent Multipole Magnets with Adjustable Strength,” IEEE Transactions on Nuclear Science, Volume 30, Number 4, August 1983, pp. 3323-3325, doi:10.1109/TNS.1983.4336645 (Reformatted and color illustrations added, July 2009)
  • Klaus Halbach, “Specialty Magnets,” AIP 1985 Conference Proceedings, U.S. Summer School on High Energy Particle Accelerators (Reformatted and color illustrations added, July 2009)
  • Klaus Halbach, “Magnet Innovations for Linacs,” Proceedings of the 1986 Linac Conference, SLAC-R-303, LINAC86-105, TH2-1 (Reformatted and color illustrations added, July 2009)

Two parallel Halbach arrays are used to implement wiggler and undulator magnets that cause relativistic electrons to emit synchrotron radiation. Wiggler magnets provides an extended spectral range and overall enhancement of the radiation brightness, whereas undulators have interference effects that result in peaks at one or more wavelengths.

  • Klaus Halbach, “Applications of Permanent Magnets in Accelerators and Electron Storage Rings,” Journal of Applied Physics, Volume 57, Number 1, April 1985, pp. 3605-3608, doi:10.1063/1.335021 (Reformatted and color illustrations added, June 2009)
  • Klaus Halbach, “Permanent Magnets for Production and Use of High Energy Particle Beams,” 8th International Workshop on Rare Earth Magnets and Their Applications, May 1985, Paper No. 11-2 (Reformatted and color illustrations added, June 2009)
  • George Brown, Klaus Halback, John Harris, and Herman Winick; “Wiggler and Undulator Magnets — A Review,” Nuclear Instruments and Methods, Volume 208, 1983, pp. 65-77, doi: 10.1016/0167-5087(83)91105-5 (Reformatted and color illustrations added, October 2009)
  • Herman Winick, George Brown, Klaus Halbach and John Harris, “Wiggler and Undulator Magnets,” Physics Today, May 1981, Volume 34, issue 5, pp. 50-63, doi: 10.1063/1.2914568 (Reformatted and color illustrations added, November 2009)

Herbert Leupold and Ernest Potenziani showed how the Hallbach array could be extended to a hollow spherical flux source; now referred to as a “Halbach sphere.”

  • Herbert Leupold and Ernest Potenziani, “Novel High-Field Permanent Magnet Flux Sources,” IEEE Transactions on Magnetics, Volume 23, Number 5, September 1987, pp. 3628-3629, doi:10.1109/TMAG.1987.1065195 (Reformatted and color illustrations added, June 2009)

Subsequently, with Douglas Basarab, they showed how the self-shielding properties of a Halbach array could be used in constructing a permanent magnet rotor assembly that eliminated the need for additional ferromagnetic material for flux shaping or shielding.

  • Ernest Potenziani, Herbert Leupold, and Douglas Basarab; “A Novel Self-Shielding Permanent Magnet Rotor Assembly,” Journal of Applied Physics, Volume 64, Issue 10, pp. 5986-5987, November 1988,doi:10.1063/1.342171 (Reformatted and color illustrations added, July 2009)

Richard Post proposed the construction of an electric motor/generator using a Halbach array to generate a uniform dipole field in 1990. These motors could be constructed without any magnetic materials other than permanent magnets — reducing both weight and losses due to eddy currents in the laminations or back iron. The uniform magnetic field also allows a larger airgap, minimizing “whirl” instability.

  • Bernard T. Merritt, Robert F. Post, Gary R. Dreifuerst, and Donald A. Bender; “Halbach Array Motor/Generators — A Novel Generalized Electric Machine,” October 28, 1994, Lawrence Livermore National Laboratory, UCRL-JC-119050; Halbach Festschrift Symposium, Berkeley, CA; February 3, 1995. (Reformatted and color illustrations added, July 2009)

Halbach magnetic bearings have been studied by several investigators. The following paper provides an excellent example showing how actual performance compares to calculated design.

  • Dennis Eichenberg, Christoper Gallo, and William Thompson; “Development and Testing of an Axial Halbach Magnetic Bearing,” NASA/TM-2006-214357, July 2006.

Subsequently, in the mid-1990s, Richard Post was studying the use of Halbach arrays for passive magnetic bearings in high-speed flywheels. This led to developing a new type of magnetic levitation system, where Halbach arrays are mounted on a moving object, and travel over a track of shorted electrical circuits.

  • Richard Post, “The Inductrack: A Simpler Approach to Magnetic Levitation,” IEEE Transactions on Applied Superconductivity, March 2000, Volume 10, Number 1, pp. 901-904, doi:10.1109/77.828377 (Reformatted and color illustrations added, June 2009)

Klaus Halbach died May 19, 2000. On August 1, 2009, Ruth Halbach, executor of the Klaus Halbach estate, provided permission to republish the papers on this site. The following article summarizes Klaus Halbach’s many accomplishments.

  • Lynn Yarris, “Klaus Halbach (1925-2000) — Revered Magnet and Accelerator Design Expert,” Lawrence Berkeley Laboratory