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| [[File:Halbach array field.jpg|thumb|250px|The flux diagram of a Halbach array]]
| | enjoying a brand upcoming clash of clans crack tool, see the take advantage of book. Most quests possess a book you can buy individually. You might want to think about doing doing this and studying it a person begin play, or even you will need to playing. In this fact manner, you can complete out of your gameplay.<br><br>Guys may possibly play applications to rest following an incredibly long working day at your workplace. Some as if socializing by tinkering by [http://www.Wired.com/search?query=friends friends] and family. If you have all of the inquiries about where we have to use Clash relating to Clans Cheat, you will contact with us at just our web site. Other individuals perform associated with when they're jobless with require something for having their brains away as well as her scenario. No subject matter reasons why you enjoy, this information will give you some help to engage in usual way which is more effectively.<br><br>Lots of people which play clash of clans crave ways of getting free gems. Here's more information about how to hack clash of clans - [http://circuspartypanama.com just click the following website] - have a look at our own web-site. The gemstone are very important they give the player functions and the power increase their gaming experience. As opposed to other equivalent games in transportable websites, especially those where individuals use various crevices in buy to get these practical information in relation to free, the nature among farmville and its page architecture does not enable nearly any varieties of hacks that anyone can put to the mission. Everyone is always looking for ways teaching how to get free gems in clash of clans risk most important thing to perform is to employ a great venue to earn these people for free, save each of them suitably and use ashamed where necessary.<br><br>Daily check several distinct boutiques before purchasing a gaming. Be sure to assist you to look both online and therefore in genuine brick yet mortar stores in your amazing region. The costs of a video game may differ widely, particularly if a game must be not brand new. By performing a hardly any additional leg work, understand it is possible to have clash of clans.<br><br>Investigation your child's xbox play enjoying. Video video games are now rated primarily like films and the fact that can help. This specific enables you to keep an eye on specific information your kids is exposed to. Conditional upon your child's age, continue to keep my man clear of video online games that happen to be a little more meant for people who are more fully developed than him.<br><br>So that you can access it into excel, copy-paste this continued menu into corpuscle B1. If you again gain an majority of second in abnormal in corpuscle A1, the bulk all through treasures will arise while in B1.<br><br>Numerous our options are considered and approved from the best possible virus recognition software not to mention anti-virus in the target ensure a security-level the size of you can, in argument you fear for protection of your computer or maybe your cellular device, no hardships. In case you nevertheless have any doubts, take a evaluate the movie and you'll take note of it operates and it is 100% secure! It takes merely a few moments of your respective! |
| [[File:Halbach2.svg|thumb|250px|A Halbach array, showing the orientation of each piece's magnetic field. This array would give a strong field underneath, while the field above would cancel.]]
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| A '''Halbach array''' is a special arrangement of permanent [[magnet]]s that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side.<ref name="Halbach1980"/> This is achieved by having a spatially rotating pattern of magnetisation.
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| The rotating pattern of permanent magnets (on the front face; on the left, up, right, down) can be continued indefinitely and have the same effect. The effect of this arrangement is roughly similar to many horseshoe magnets placed adjacent to each other, with similar poles touching.
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| The effect was discovered by John C. Mallinson in 1973, and these "one-sided flux" structures were initially described by him as a "curiosity", although he recognised at the time the potential for significant improvements in [[magnetic tape]] technology.<ref>J.C. Mallinson, [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=22922&arnumber=1067714&type=ref "One-Sided Fluxes — A Magnetic Curiosity?"], ''IEEE Transactions on Magnetics'', '''9''', 678-682, 1973, {{doi|10.1109/TMAG.1973.1067714}}</ref>
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| In the 1980s, [[Lawrence Berkeley National Laboratory]] physicist Klaus Halbach, independently invented the Halbach array to focus accelerator particle beams.<ref>[http://www.eurekalert.org/features/doe/2004-11/ddoe-mlt111104.php "Magnetically levitated train takes flight"]</ref>
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| ==Flat Halbach arrays==
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| ===Magnetization===
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| [[File:HalbachArray1.png|thumb|upright=1.5|Cancellation of magnetic components resulting in a one-sided flux]]
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| Although this magnetic flux distribution seems somewhat counter-intuitive to those familiar with, for example, bar magnets or [[solenoids]], the reason for this flux distribution can be intuitively visualised using Mallinson's original diagram (note this uses the negative y-component, unlike the diagram in Mallinson's paper). The diagram shows the field from a strip of [[ferromagnetic]] material with alternating magnetization in the y direction (top left) and in the x direction (top right). Note that the field above the plane is in the ''same'' direction for both structures, but the field below the plane is in ''opposite'' directions. The effect of superimposing both of these structures is shown in the figure:
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| The crucial point is that the flux will ''cancel below the plane and reinforce itself above the plane''. In fact, any magnetization pattern where the components of magnetization are <math>\scriptstyle\frac{\pi}{2}</math> out of phase with each other will result in a one-sided flux. The mathematical transform which shifts the phase of all components of some function by <math>\scriptstyle\frac{\pi}{2}</math> is called a [[Hilbert transform]]; the components of the magnetization vector can therefore be any Hilbert transform pair (the simplest of which is simply <math>\scriptstyle\sin(x)\cos(y)</math>, as shown in the diagram above).
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| [[File:InfiniteHalbachArray.JPG|thumb|The magnetic field around an infinite halbach array of cube magnets. The field doesn't perfectly cancel due to the discrete magnets used.]]
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| The field on the non-cancelling side of the ideal, continuously varying, infinite array is of the form:<ref>[http://www.uta.edu/physics/main/resources/ug_seminars/papers/HalbachArrays.doc]</ref>
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| <math>F(x,y) = F_0 e^{ikx} e^{-ky}</math>
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| Where:
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| :<math>\scriptstyle F(x,y)</math> is the field in the form <math>\scriptstyle F_x + i F_y</math>
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| :<math>\scriptstyle F_0</math> is the magnitude of the field at the surface of the array
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| :<math>\scriptstyle k</math> is the spatial [[wavenumber]], (i.e., the spatial frequency) <math>\scriptstyle\frac{2 \pi}{\lambda}</math>
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| ===Applications===
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| The advantages of one sided flux distributions are twofold:
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| *The field is twice as large on the side on which the flux is confined (in the idealised case).
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| *No [[stray field]] is produced (in the ideal case) on the opposite side. This helps with field confinement, usually a problem in the design of magnetic structures.
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| Although one-sided flux distributions may seem somewhat abstract, they have a surprising number of applications ranging from the [[refrigerator magnet]] through industrial applications such as the brushless AC motor and magnetic coupling, to high-tech applications such as [[wiggler (synchrotron)|wiggler]] magnets used in [[particle accelerator]]s and [[free electron laser]]s. This device is also a key component of the [[Inductrack]] [[Maglev train]] system wherein the Halbach arrays repel loops of wire that form the track after the train has been accelerated to speed, lifting the train.
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| [[File:Fridge Magnet Halbach.svg|thumb|upright=1.5|Fridge magnet flux distribution]]
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| The simplest example of a one sided flux magnet is a refrigerator magnet. These are usually composed of powdered ferrite in a binder such as plastic or rubber. The extruded magnet is exposed to a rotating field giving the ferrite particles in the magnetic compound a magnetization resulting in a one-sided flux distribution. This distribution increases the holding force of the magnet when placed on a permeable surface, compared to the holding force from, say, a uniform magnetization of the magnetic compound. | |
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| [[File:HalbachArrayFEL2.png|thumb|upright=1.5|Schematic diagram of a free electron laser]]
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| Scaling up this design and adding a top sheet gives a wiggler magnet, used in synchrotrons 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.
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| 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
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| : <math>H_y \approx \cos(kx)</math>
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| 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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| {{clear}}
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| ===Variable flat arrays===
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| [[File:HalbachArraySchematic1.png|thumb|upright=1.5|Schematic of a Halbach array consisting of a series magnetized rods.]]
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| [[File:HalbachArraySchematic2.png|thumb|upright=1.5|Equal gearing arrangement for a variable Halbach array.]]
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| A series of magnetic rods, magnetized perpendicular to their axes, can be arranged into a Halbach array. If each rod is then rotated alternately through 90° the resultant field moves from one side of plane of the rods to the other, as shown schematically in the figure.
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| This arrangement allows the field to effectively be turned on and off above or below the plane of the rods, depending on the rotation of the rods. Such a device makes an efficient mechanical magnetic latch requiring no power. A detailed study of this arrangement has shown that each rod is subject to a strong torque from its neighbouring rods, and therefore requires mechanical stabilization.<ref name="Hilton2012"/> However, a simple and efficient solution, providing both stabilization and the ability to rotate each rod alternately, is simply to provide an equal gearing arrangement on each rod, as shown in the figure.
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| {{clear}}
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| ==Halbach cylinder==
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| [[File:Halbach cylinder.png|thumb|upright=1.5|A ferromagnetic cylinder showing various magnetization patterns and magnetic field.]]
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| [[File:Halbach cylinder2.png|thumb|right|Cylinder magnetization.]]
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| A '''Halbach cylinder''' is a magnetized cylinder composed of [[ferromagnetic]] material producing (in the idealised case) an intense magnetic field confined entirely within the cylinder with zero field outside. The cylinders can also be magnetized such that the magnetic field is entirely outside the cylinder, with zero field inside. Several magnetization distributions are shown:
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| The direction of magnetization within the ferromagnetic material, in plane perpendicular to the axis of the cylinder, is given by
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| <center><math>M = M_r\left[\sin(k\phi)\hat{\rho}-\cos(k\phi)\hat{\phi}\right]</math></center> | |
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| where ''M<sub>r</sub>'' is the ferromagnetic [[remanence]] (A/m). A choice of +''k'' gives an internal magnetic field and -''k'' gives an external magnetic field.
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| Ideally, these structures would be created from an infinite length cylinder of magnetic material with the direction of magnetization continuously varying. The magnetic flux produced by this ideal design would be perfectly uniform and be entirely confined to the bore of the cylinder. Of course, the ideal case of infinite length is not realisable and in practice the finite length of the cylinders produces ''end effects'' which introduce non-uniformities in the field within the bore. The difficulty of manufacturing a cylinder with a continuously varying magnetization also usually leads to the design being broken into segments.
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| ===Applications===
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| 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:
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| * Brushless motors typically use cylindrical designs in which all the flux is confined to the centre of the bore (such as ''k = 4'' above, a six pole rotor) with the AC coils also contained within the bore. Such self-shielding motors designs are more efficient and produce higher torque than conventional motor designs.
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| * Magnetic coupling devices transmit torque through magnetically transparent barriers (that is, the barrier is non-magnetic or is magnetic but is 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 -''k'' magnetization patterns produce fields entirely external to the cylinder. 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.
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| ===Uniform fields===
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| [[File:Halbach array by Zureks.png|thumb|Uniform field inside Halbach cylinder]]
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| For the special case of ''k = 2'', the field inside the bore is uniform, and is given by:
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| <center><math>H = M_r\ln\left(\frac{R_o}{R_i}\right)\hat{y}</math></center> | |
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| where the inner and outer cylinder radii are ''R''<sub>i</sub> and ''R''<sub>o</sub>, respectively. ''H'' is in the ''y'' direction. This is the simplest form of the Halbach cylinder, and it can be seen that if the ratio of outer to inner radii is greater than ''[[e (mathematical constant)|e]]'' the flux inside the bore actually exceeds the [[remanence]] of the magnetic material used to create the cylinder.
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| [[File:Halbach cylinder3.png|thumb|Three designs producing uniform magnetic fields within their central air gap]]
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| This cylindrical design is only one class of design which produces a uniform field inside a cavity within an array of permanent magnets. Other classes of design include wedge designs, proposed by Abele and Jensen in which wedges of magnetized material are arranged to provide uniform field within cavities inside the design as shown.
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| The direction of magnetization of the wedges in (A) can be calculated using a set of rules given by Abele, and allows for great freedom in the shape of the cavity. Another class of design is the magnetic mangle (B), proposed by Coey and Cugat,<ref name="Coey2003"/><ref name="Cugat1998"/> in which uniformly magnetized rods are arranged such that their magnetization matches that of a Halbach cylinder, as shown for a six rod design. This design greatly increases access to the region of uniform field, at the expense of the volume of uniform field being smaller than in the cylindrical designs (although this area can be made larger by increasing the number of component rods). Rotating the rods relative to each other results in many possibilities including a dynamically variable field and various dipolar configurations. It can be seen that the designs shown in A and B are closely related to the ''k = 2'' Halbach cylinder. Other very simple designs for a uniform field include separated magnets with soft iron return paths, as shown in figure (C).
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| In the last years, these Halbach dipoles have been used to conduct low-field [[NMR]] experiments.<ref>Raich, H., Blümler, P., ''Design and construction of a dipolar Halbach array with a homogeneous field from identical bar magnets: NMR Mandhalas'' in ''Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering'' 01/2004; 23B:16-25</ref> Compared to commercially available ([[Bruker]] Minispec) standard plate geometries (C) of permanent magnets, they, as explained above, offer a huge bore diameter, while still having a reasonably homogeneous field.
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| ===Varying the field===
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| Halbach cylinders give a static field. However cylinders can be nested, and by rotating one cylinder relative to the other, cancellation of the field and adjustment of the direction can be achieved.<ref>[http://www.tipmagazine.com/tip/INPHFA/vol-4/iss-3/p34.pdf Tip Magazine: Magnets, Markets, and Magic Cylinders The Industrial Physicist by Michael Coey and Denis Weaire]</ref> As the outside field of a cylinder is quite low, the relative rotation does not require strong forces.
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| ==Halbach spheres==
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| If the two dimensional magnetic distribution patterns of the Halbach cylinder are extended to three dimensions, the result is the Halbach sphere. These designs have an extremely uniform field within the interior of the design, as they are not affected by the 'end effects' prevalent in the finite length cylinder design. The magnitude of the uniform field for a sphere also increases to 4/3 the amount for the ideal cylindrical design with the same inner and outer radii. However, being spherical, access to the region of uniform field is usually restricted to a narrow hole at the top and bottom of the design. | |
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| The equation for the field in a Halbach sphere is:<ref>[http://www.magnetocaloric.com/Code/pub01.htm Permanent magnet based sources of magnetic field]</ref>
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| <math>B = \frac{4}{3} B_0 \ln\left(\frac {R_o} {R_i}\right)</math> | |
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| Higher fields are possible by optimising the spherical design to take account of the fact that it is composed of point dipoles (and not line dipoles). This results in the stretching of the sphere to an elliptical shape and having a non-uniform distribution of magnetization over the component parts of the sphere. Using this method, as well as soft pole pieces within the design, 4.5 T in a working volume of 20 mm<sup>3</sup> was achieved by Bloch ''et al.'' in 1998<ref name="Bloch1998"/> and this was increased further to 5 T in 2000,{{Citation needed|date=December 2010}} although over a smaller working volume of 0.05 mm<sup>3</sup>. As hard materials are temperature dependent, refrigeration of the entire magnet array can increase the field within the working area further as shown by Kumada ''et al.'' This group also reported development of a 5.16 T Halbach dipole cylinder in 2003.<ref name="Kumada2004"/>
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| ==See also==
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| *[[Supermagnet]]
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| *[[Permanent magnet]]
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| *[[Strong focusing]]
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| *[[Inductrack]] uses Halbach arrays to generate strong fields for [[Maglev (transport)|maglev]]
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| *[[Helmholtz coil]] can give very even magnetic fields
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| == References ==
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| {{reflist|refs=
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| <ref name="Bloch1998">{{cite journal
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| | author = Bloch, F. and Cugat, O. and Meunier, G. and Toussaint, J.C.
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| | title = Innovating approaches to the generation of intense magnetic fields : design and optimization of a 4 Tesla permanent magnet flux source
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| | journal = IEEE Transactions on Magnetics
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| | volume = 34
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| | issue = 5
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| | pages = 2465–2468
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| | year = 1998
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| | doi = 10.1109/20.717567
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| |bibcode = 1998ITM....34.2465B }}</ref>
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| <ref name="Kumada2004">{{cite journal
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| | author = Kumada, M. and Antokhin, E.I. and Iwashita, Y. and Aoki, M. and Sugiyama, E.
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| | title = Super strong permanent dipole magnet
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| | journal = IEEE Transactions on Applied Superconductivity
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| | volume = 14
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| | issue = 2
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| | pages = 1287–1289
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| | year = 2004
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| | doi = 10.1109/TASC.2004.830555
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| }}</ref>
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| <ref name="Halbach1980">{{cite journal
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| | author = K. Halbach
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| | title = Design of permanent multipole magnets with oriented rare earth cobalt material
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| | journal = Nuclear Instruments and Methods
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| | volume = 169
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| | number = 1
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| | pages = 1–10
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| | year = 1980
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| | issn = 0029-554X
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| | doi = 10.1016/0029-554X(80)90094-4
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| |bibcode = 1980NucIM.169....1H }}</ref>
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| <ref name="Coey2003">{{cite book
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| | author = J. M. D. Coey and T.R. Ní Mhíocháin
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| | chapter = Permanent Magnets
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| | title = High Magnetic Fields: Science and Technology
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| | editor = F. Herlach and N. Miura
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| | publisher = World Scientific Publishing
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| | volume = Volume 1
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| | pages = 25–47
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| | year = 2003
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| }}</ref>
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| <ref name="Cugat1998">{{cite journal
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| | author = O. Cugat, F. Bloch and J.C. Toussaint
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| | title = 4-Tesla Permanent Magnetic Flux Source
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| | journal = Proc. 15th International Workshop on Rare Earth Magnets and Their Applications
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| | pages = 807
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| | year = 1998
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| }}</ref>
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| <ref name="Hilton2012">{{cite journal
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| | author = J. E. Hilton and S. M. McMurry
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| | title = An adjustable linear Halbach array
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| | journal = Journal of Magnetism and Magnetic Materials
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| | volume = 324
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| | issue = 13
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| | pages = 2051–2056
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| | year = 2012
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| | doi = 10.1016/j.jmmm.2012.02.014
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| |bibcode = 2012JMMM..324.2051H }}</ref>
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| }}
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| == External links ==
| |
| * [http://www.unimodal.net/index.php?option=com_content&task=view&id=14&Itemid=36&limit=1&limitstart=4 Skytran technology]
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| * [http://web.archive.org/web/20040405022851/dmtwww.epfl.ch/~jsandtne/GPMB/project1.htm Passive levitation of a shaft]
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| * [http://goldeneye.ethz.ch/motoren/electric/inrunner/index_EN/ Electric model aircraft motor]
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| * [http://www.reeserail.com magnet levitated vehicle switching system]
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| {{Use dmy dates|date=December 2010}}
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| | |
| {{DEFAULTSORT:Halbach Array}}
| |
| [[Category:Magnetic levitation]]
| |
| [[Category:Magnetic devices]]
| |
| [[Category:Types of magnets]]
| |
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