Editing Halbach array (section)

===Applications===
The advantages of one-sided flux distributions are twofold:
* The field is twice as large on the side on which the flux is confined (in the idealized case).
* There is no [[stray field]] produced (in the ideal case) on the opposite side. This helps with field confinement, usually a problem in the design of magnetic structures.

Thus they have a number of applications, ranging from flat [[refrigerator magnet|refrigerator magnets]] through industrial applications such as the brushless [[DC motor]], [[voice coil]]s,<ref>{{Cite web|url=https://patents.google.com/patent/US7368838B2/en|title=High efficiency voice coil motor}}</ref> magnetic drug targeting<ref name="Sarwar2012"/> to high-tech applications such as [[Wiggler (synchrotron)|wiggler]] magnets used in [[particle accelerator]]s and [[free-electron laser]]s.

The [[Inductrack]] [[maglev train]]<ref>{{cite web |author1=Richard F. Post |date=10 October 2005 |title=Toward More Efficient Transport: The Inductrack Maglev System |url=https://gcep.stanford.edu/pdfs/ChEHeXOTnf3dHH5qjYRXMA/09_Post_10_11_trans.pdf |access-date=1 December 2017 |publisher=Lawrence Livermore National Laboratory |archive-date=4 April 2023 |archive-url=https://web.archive.org/web/20230404162449/https://gcep.stanford.edu/pdfs/ChEHeXOTnf3dHH5qjYRXMA/09_Post_10_11_trans.pdf |url-status=dead }}</ref> and Inductrack rocket-launch system<ref name="Tung2001"/> utilize the Halbach array to lift the train by repelling loops of wire in the track.
[[File:Magnetic_viewing_film.jpg|thumb|[[Magnetic viewing film]] showing a flat refrigerator magnet's magnetization|220x220px]]
Flat flexible (not [[Ferrite (magnet)#Hard ferrites|hard ceramic ferrite]]) refrigerator magnets are created with a Halbach magnetization pattern for a stronger holding force when attached to a flat [[ferromagnetic]] surface (e.g. a fridge door) than the holding force from a uniform magnetization. They're made from powdered ferrite mixed in a flexible binder (e.g. plastic or rubber) that is exposed to a Halbach magnetization field pattern as it is [[Extrusion|extruded]], permanently giving the ferrite particles in the magnetic compound this one-sided flux distribution (which can be viewed with [[magnetic viewing film]]).

[[File:Fridge Magnet Halbach.svg|thumb|Flux distribution for a flat refrigerator magnet|220x220px]][[File:HalbachArrayFEL2.png|thumb|Schematic diagram of a free-electron laser|220x220px]]
Scaling up this design and adding a top sheet gives a [[wiggler magnet]], used in [[synchrotron]]s and [[free-electron laser]]s. Wiggler magnets wiggle, or oscillate, an electron beam perpendicular to the magnetic field. As the electrons are undergoing acceleration, they radiate electromagnetic energy in their flight direction, and as they interact with the light already emitted, photons along its line are emitted in phase, resulting in a "laser-like" monochromatic and coherent beam.

The design shown above is usually known as a Halbach wiggler. The magnetization vectors in the magnetized sheets rotate in the opposite senses to each other; above, the top sheet's magnetization vector rotates clockwise, and the bottom sheet's magnetization vector rotates counter-clockwise. This design is chosen so that the ''x'' components of the magnetic fields from the sheets cancel, and the ''y'' components reinforce, so that the field is given by

: <math>H_y \approx \cos(kx),</math>

where ''k'' is the [[wavenumber]] of the magnetic sheet given by the spacing between magnetic blocks with the same magnetization vector.

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