Editing Halbach array (section)

===Applications===
These cylindrical structures are used in devices such as brushless AC motors, magnetic couplings and high-field cylinders. Both brushless motors and coupling devices use multipole field arrangements:
* Brushless motors or alternators typically use cylindrical designs in which all the flux is confined to the centre of the bore (such as ''k''&nbsp;=&nbsp;4 above, a 6-pole rotor) with the AC coils also contained within the bore. Such self-shielding motor or alternator designs are more efficient and produce higher torque or output than conventional motor or alternator designs.
* Magnetic-coupling devices transmit torque through magnetically transparent barriers (that is, the barrier is non-magnetic or is magnetic but not affected by an applied magnetic field), for instance, between sealed containers or pressurised vessels. The optimal torque couplings consists of a pair of coaxially nested cylinders with opposite +''k'' and −''k'' flux magnetization patterns, as this configuration is the only system for infinitely long cylinders that produces a torque.<ref name="Bjoerk2010"/> In the lowest-energy state, the outer flux of the inner cylinder exactly matches the internal flux of the outer cylinder. Rotating one cylinder relative to the other from this state results in a restoring torque.
*Cylindrical Halbach Arrays are used in Portable [[MRI]] Scanners.<ref>{{cite web |url=https://www.stanfordmagnets.com/halbach-magnets-history-types-and-uses.html |title=Halbach Magnets: History, Types, and Uses |last=Marchio |first=Cathy |date=May 23, 2024 |website=Stanford Magnets |access-date=July 31, 2024}}</ref> They offer the potential for a relatively lightweight, low to mid-field system with no [[cryogenics]], a small fringe field, and no electrical power requirements or heat dissipation needs.<ref>{{cite journal |last1=Cooley |first1=C. Z. |last2=Haskell |first2=M. W. |year=2018 |title=Design of Sparse Halbach Magnet Arrays for Portable MRI Using a Genetic Algorithm |journal=IEEE Transactions on Magnetics |volume=54 |issue=1 |pages=1-12 |doi=10.1109/TMAG.2017.2751001|pmc=5937527 }}</ref> The reduced stray fields also enhance safety and minimize interference with surrounding electronic devices.<ref>{{cite journal |last1=Sarwar |first1=A. |last2=Nemirovski |first2=A. |year=2012 |title=Optimal Halbach permanent magnet designs for maximally pulling and pushing nanoparticles |journal=Journal of Magnetism and Magnetic Materials |volume=234 |issue=5 |pages=742-754 |doi=10.1016/j.jmmm.2011.09.008|pmc=3547684 }}</ref>