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As a result of the magnetic materials permanent development, the realm of PM based magnetic field sources application becomes steady broader. Taking into account that in some special magnetic sources it is possible to obtain the field value much greater than residual induction Br of magnetic system material, permanent magnet based systems are now a powerful instrument for production of magnetic field with highest characteristics of intensity and homogeneity. At the moment PM based sources are widely adopted for beam lines, resonance spectroscopy, STM systems, magneto-optic, magneto-caloric and other studies.
For different purposes a large amount of system types are used, sometimes rather complicated. However typical is the situation when a source has a cylindrical shape with a bore inside it for putting a sample into working field area.
A good example of such magnetic field source is so called Halbach-cylinder [1,2]. A principle of this system is shown in fig.1, which represents a cross-section of a cylinder. The amount and shape of single magnets may be different, general rule is in turning magnetization direction while going from one single magnet to its neighbor. The more smoothly turns the magnetization direction along the ring (the more sectors is the ring divided to), the more closely is the field pattern to ideal one.
In case of very long cylinder according to a simple theory the flux density in the source interior is given by:
where Br is residual magnetic induction of magnets material and Rout and Rin are outer and inner radii of the cylinder, respectively. The direction of resulting magnetic field lies in the cross-section plane, as shown in the picture. According to this formula the field value can grow unlimitedly, but in practice, due to very slow logarithmic dependence on system size, for reasonable Rout, field values up to several Tesla can be reached. At the moment the world record PM based field source is a Halbach-cylinder with B = 5T, which was built in 2002 for European Synchrotron Radiation Facility [3,4].
Some authors proposed variants of Halbach like systems, using additional ferrous inserts and varying system geometry to enlarge field value and its uniformity [5].
There exist also constructions of magnetic field sources, which use a principle of Halbach-cylinder, but permit to change field value, including polarity reversal. One approach is in building two concentric Halbach-cylinders, which can be independently rotated (see fig.2), another one – in synchronous rotation of single magnetic rods, as shown in fig.3.
In case, the object needs the field direction to be axial, other technical solutions may be proposed. The most intensive axial flux density can be reached in systems based on Halbach-sphere concept. For an ideal Halbach-sphere (see fig.4) the flux density in the cavity is given by
According to this relation, analogously to Halbach-cylinder mentioned above, flux density up to 4-6T can be obtained. As obvious disadvantage of this system its complexity in production must be mentioned. For this reason in many practical applications more simple configurations are used for designing axial field sources. An example of possible geometry (section along the axis) is shown in fig.5. Optimizing geometrical and magnetic parameters of magnetic rings it is possible to achieve quite high flux density in sufficiently large volume. As an example of such calculations of magnetic system is given fig.6, drawn for system analogous to fig. 5.
References:
K.Halbach, Nucl.Instr.Methods, vol.169, p.1, 1980
K.Halbach, Nucl.Instr.Methods, vol.187, p.109, 1981
F.Bloch, O.Gugat, JC.Toussaint and G.Meunier, IEEE Trans.Magn., vol.34, p.2465, 1998
CERN Courier, vol.43, No3, p.7, 2002
S.J.Lee and D.C.Jiles, IEEE Trans.Magn., vol.36, No5, p.3105, 2000
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