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In the past few years, the concept of an electromagnetic invisibility cloak has received much attention. Based on the pioneering theoretical work, invisibility cloaks have been greatly developed. Inspired by those theoretical researches, varieties of electromagnetic cloaks, acoustic cloaks, matter wave cloaks, mass diffusion cloaks, heat cloaks, magnetic cloaks, dc magnetic cloaks and electrostatic cloaks have been designed theoretically and demonstrated experimentally. The first experimentally demonstrated invisible cloak is made of metamaterial with simplified material parameters. The simplified cloak inherits some properties of the ideal cloak, but finite scattering exists. It is difficult to develop a perfectly invisible electromagnetic cloak having homogeneous and anisotropic components by using the natural materials. In this work, a bi-layer magnetic cloak made of neodymium iron boron (NdFeB) permanent magnetic material is designed. When the direction of the intrinsic magnetization intensity of the material is opposite to that of the applied magnetic field, the magnetic field lines will be repelled. When the direction of the intrinsic magnetization intensity is the same as the direction of applied magnetic field, the magnetic field lines will be attracted. With those properties, the two magnetic rings are designed, one is made of NdFeB, and the other is made of neodymium iron chromium boron (NdFeCrB). The direction of the intrinsic magnetization intensity is opposite or parallel to the applied magnetic field. The two magnetic rings nest a bi-layer magnetic ring. When a uniform magnetic field is applied, by using the formulas of the magnetic scalar potential in a cylindrical coordinate system and the constitute relations of magnetic rings, the distribution of magnetic field and scalar potential within the bi-layer concentric cylindrical permanent magnetic material are deduced. Based on theory as demonstrated, the bi-layer permanent magnetic material cylinder can cloak a magneto-static field. Under the conditions of the magnetic cloak with the specific relative permeability and the intrinsic magnetization intensity, the relation between the radius ratio and the applied magnetic field is obtained. The calculation results show that when the radius ratio and the applied magnetic field satisfy this relationship, the bi-layer permanent magnetic material cylinder can cloak the magneto-static field. The magnetic field distributions of both the magnetic non-cloak and magnetic cloak are simulated to show the effectiveness of the proposed theory.In summary, the results show that the cloak performance is influenced not only by the size parameters of the permanent magnetic material cylinder but also the relative permeability, the intrinsic magnetization intensity, and the applied magnetic field. The NdFeB permanent magnetic material used in the magnetic cloak is very common and can be easily obtained, which gives more convenience for the design and application of the magnetic cloak.
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Keywords:
- magneto-static shielding /
- cloak /
- permanent magnetic material
[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Leonhardt U 2006 Science 312 1777
[3] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D 2006 Science 314 977
[4] Ma Y, Liu Y, Lan L, Wu T, Jiang W, Ong C K, He S 2013 Sci. Rep 3 2182
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[6] Zigoneanu L, Popa B I, Cummer S A 2014 Nat. Mater. 13 352
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[9] Zeng L, Song R 2013 Sci. Rep 3 3359
[10] Kohn R V, Shen H, Vogelius M S, Weinstein M 2008 Inverse Probl. 24 015016
[11] Zeng L, Zhao Y, Zhao Z, Li H 2015 Physica B Condens. Matter. 462 70
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[13] Zhu J, Jiang W, Liu Y, Yin G, Yuan J, He S, Ma Y 2015 Nat. Commun. 6 8931
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[15] Narayana S, Sato Y 2012 Adv. Mater. 24 71
[16] Yao P, Liang Z, Jiang X 2008 App Phys. Lett. 92 31111
[17] Yang F, Mei Z L, Jin T Y, Cui T J 2012 Phys. Rev. Lett. 109 053902
[18] Alitalo P, Tretyakov S A 2009 Mater. Today 12 22
[19] Zhang B L, Wu B I 2009 Phys. Rev. Lett. 103 243901
[20] Wang Z, Luo X Y, Liu J Y, Dong J F 2013 Acta Phys. Sin. 62 024101 (in Chinese)[王战, 罗孝阳, 刘锦景, 董建峰2013物理学报62 024101]
[21] Wang Z, Dong J F, Liu J Y, Luo X Y 2012 Acta Phys. Sin. 61 204101 (in Chinese)[王战, 董建峰, 刘锦景, 罗孝阳2012物理学报61 204101]
[22] Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303 (in Chinese)[沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森2012物理学报61 134303]
[23] Prat-Camps J, Sanchez A, Navau C 2013 Supercond. Sci Tech. 26 74001
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Leonhardt U 2006 Science 312 1777
[3] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D 2006 Science 314 977
[4] Ma Y, Liu Y, Lan L, Wu T, Jiang W, Ong C K, He S 2013 Sci. Rep 3 2182
[5] Chen H, Chan C T 2010 J. Phys. D 43 113001
[6] Zigoneanu L, Popa B I, Cummer S A 2014 Nat. Mater. 13 352
[7] Lin D, Luan P 2012 Phys. Lett. A 376 675
[8] Zeng L, Tang Z, Li H, Zhao Y, Dai C, Song R 2014 Mod. Phys. Lett. B 28 1450098
[9] Zeng L, Song R 2013 Sci. Rep 3 3359
[10] Kohn R V, Shen H, Vogelius M S, Weinstein M 2008 Inverse Probl. 24 015016
[11] Zeng L, Zhao Y, Zhao Z, Li H 2015 Physica B Condens. Matter. 462 70
[12] Souc J, Solovyov M, Gomory F, Prat-Camps J, Navau C, Sanchez A 2013 New J. Phys. 15 053019
[13] Zhu J, Jiang W, Liu Y, Yin G, Yuan J, He S, Ma Y 2015 Nat. Commun. 6 8931
[14] Gömöry F, Solovyov M,Šouc J, Navau C, Prat-Camps J, Sanchez A 2012 Science 335 1466
[15] Narayana S, Sato Y 2012 Adv. Mater. 24 71
[16] Yao P, Liang Z, Jiang X 2008 App Phys. Lett. 92 31111
[17] Yang F, Mei Z L, Jin T Y, Cui T J 2012 Phys. Rev. Lett. 109 053902
[18] Alitalo P, Tretyakov S A 2009 Mater. Today 12 22
[19] Zhang B L, Wu B I 2009 Phys. Rev. Lett. 103 243901
[20] Wang Z, Luo X Y, Liu J Y, Dong J F 2013 Acta Phys. Sin. 62 024101 (in Chinese)[王战, 罗孝阳, 刘锦景, 董建峰2013物理学报62 024101]
[21] Wang Z, Dong J F, Liu J Y, Luo X Y 2012 Acta Phys. Sin. 61 204101 (in Chinese)[王战, 董建峰, 刘锦景, 罗孝阳2012物理学报61 204101]
[22] Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303 (in Chinese)[沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森2012物理学报61 134303]
[23] Prat-Camps J, Sanchez A, Navau C 2013 Supercond. Sci Tech. 26 74001
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