Comparison of different configurations of NbTi magnetic lenses
Identifieur interne : 001624 ( Istex/Corpus ); précédent : 001623; suivant : 001625Comparison of different configurations of NbTi magnetic lenses
Auteurs : Z Y Zhang ; S. Matsumoto ; S. Choi ; R. Teranishi ; T. KiyoshiSource :
- Superconductor Science and Technology [ 0953-2048 ] ; 2011.
Abstract
Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetismof superconductors. Magnetic lenses of two types made from NbTi sheets wereconstructed; measurements were made on them and they were systematicallystudied. TypeA was constructed by stacking NbTi rings that had identical outerdiameters and increasing inner diameters to form a hollow cone. Each ring had a slitto suppress the circumference current. Three construction methods for typeAwere tested: the rings were stacked with their slits aligned but with no insulationbetween the rings (A-1), with their slits aligned and with insulation betweenthe rings (A-2), and with their slits in different positions and with insulationbetween the rings (A-3). For typeB, sheets were rolled into hollow cones. Threeidentical cones were stacked to form a lens (B-1) and a single cone was used as areference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat witha NbTi magnet. The quenching behavior, concentration ratio, hysteresis, anddecay behavior were measured. Because of its larger dimensions, typeB had alarger concentration ratio (2.49 for B-1) than typeA (1.87 for A-1). Both lenses(typesA and B-1) were quenched when the concentrated flux density reached about0.64T. The results suggest that quenching was caused by the NbTi sheet itself.
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DOI: 10.1088/0953-2048/24/10/105012
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Matsumoto</name><affiliation><mods:affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</mods:affiliation></affiliation></author><author><name sortKey="Choi, S" sort="Choi, S" uniqKey="Choi S" first="S" last="Choi">S. Choi</name><affiliation><mods:affiliation>Busan Center, Korea Basic Science Institute, Geumjeong, Busan 609-735, Korea</mods:affiliation></affiliation></author><author><name sortKey="Teranishi, R" sort="Teranishi, R" uniqKey="Teranishi R" first="R" last="Teranishi">R. Teranishi</name><affiliation><mods:affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</mods:affiliation></affiliation></author><author><name sortKey="Kiyoshi, T" sort="Kiyoshi, T" uniqKey="Kiyoshi T" first="T" last="Kiyoshi">T. Kiyoshi</name><affiliation><mods:affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:1272CE4EDE03E70D7F3B0557844EDD952033A233</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1088/0953-2048/24/10/105012</idno><idno type="url">https://api.istex.fr/document/1272CE4EDE03E70D7F3B0557844EDD952033A233/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001624</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Comparison of different configurations of NbTi magnetic lenses</title><author><name sortKey="Zhang, Z Y" sort="Zhang, Z Y" uniqKey="Zhang Z" first="Z Y" last="Zhang">Z Y Zhang</name><affiliation><mods:affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail:ZHANG.Zhiyu@nims.go.jp</mods:affiliation></affiliation></author><author><name sortKey="Matsumoto, S" sort="Matsumoto, S" uniqKey="Matsumoto S" first="S" last="Matsumoto">S. Matsumoto</name><affiliation><mods:affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</mods:affiliation></affiliation></author><author><name sortKey="Choi, S" sort="Choi, S" uniqKey="Choi S" first="S" last="Choi">S. Choi</name><affiliation><mods:affiliation>Busan Center, Korea Basic Science Institute, Geumjeong, Busan 609-735, Korea</mods:affiliation></affiliation></author><author><name sortKey="Teranishi, R" sort="Teranishi, R" uniqKey="Teranishi R" first="R" last="Teranishi">R. Teranishi</name><affiliation><mods:affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</mods:affiliation></affiliation></author><author><name sortKey="Kiyoshi, T" sort="Kiyoshi, T" uniqKey="Kiyoshi T" first="T" last="Kiyoshi">T. Kiyoshi</name><affiliation><mods:affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Superconductor Science and Technology</title><title level="j" type="abbrev">Supercond. Sci. Technol.</title><idno type="ISSN">0953-2048</idno><idno type="eISSN">1361-6668</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2011">2011</date><biblScope unit="volume">24</biblScope><biblScope unit="issue">10</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="7">7</biblScope><biblScope unit="production">Printed in the UK & the USA</biblScope></imprint><idno type="ISSN">0953-2048</idno></series><idno type="istex">1272CE4EDE03E70D7F3B0557844EDD952033A233</idno><idno type="DOI">10.1088/0953-2048/24/10/105012</idno><idno type="PII">S0953-2048(11)99444-5</idno><idno type="articleID">399444</idno><idno type="articleNumber">105012</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0953-2048</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetismof superconductors. Magnetic lenses of two types made from NbTi sheets wereconstructed; measurements were made on them and they were systematicallystudied. TypeA was constructed by stacking NbTi rings that had identical outerdiameters and increasing inner diameters to form a hollow cone. Each ring had a slitto suppress the circumference current. Three construction methods for typeAwere tested: the rings were stacked with their slits aligned but with no insulationbetween the rings (A-1), with their slits aligned and with insulation betweenthe rings (A-2), and with their slits in different positions and with insulationbetween the rings (A-3). For typeB, sheets were rolled into hollow cones. Threeidentical cones were stacked to form a lens (B-1) and a single cone was used as areference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat witha NbTi magnet. The quenching behavior, concentration ratio, hysteresis, anddecay behavior were measured. Because of its larger dimensions, typeB had alarger concentration ratio (2.49 for B-1) than typeA (1.87 for A-1). Both lenses(typesA and B-1) were quenched when the concentrated flux density reached about0.64T. The results suggest that quenching was caused by the NbTi sheet itself.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>Z Y Zhang</name><affiliations><json:string>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</json:string><json:string>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</json:string><json:string>E-mail:ZHANG.Zhiyu@nims.go.jp</json:string></affiliations></json:item><json:item><name>S Matsumoto</name><affiliations><json:string>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</json:string></affiliations></json:item><json:item><name>S Choi</name><affiliations><json:string>Busan Center, Korea Basic Science Institute, Geumjeong, Busan 609-735, Korea</json:string></affiliations></json:item><json:item><name>R Teranishi</name><affiliations><json:string>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</json:string></affiliations></json:item><json:item><name>T Kiyoshi</name><affiliations><json:string>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</json:string><json:string>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetismof superconductors. Magnetic lenses of two types made from NbTi sheets wereconstructed; measurements were made on them and they were systematicallystudied. TypeA was constructed by stacking NbTi rings that had identical outerdiameters and increasing inner diameters to form a hollow cone. Each ring had a slitto suppress the circumference current. Three construction methods for typeAwere tested: the rings were stacked with their slits aligned but with no insulationbetween the rings (A-1), with their slits aligned and with insulation betweenthe rings (A-2), and with their slits in different positions and with insulationbetween the rings (A-3). For typeB, sheets were rolled into hollow cones. Threeidentical cones were stacked to form a lens (B-1) and a single cone was used as areference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat witha NbTi magnet. The quenching behavior, concentration ratio, hysteresis, anddecay behavior were measured. Because of its larger dimensions, typeB had alarger concentration ratio (2.49 for B-1) than typeA (1.87 for A-1). Both lenses(typesA and B-1) were quenched when the concentrated flux density reached about0.64T. The results suggest that quenching was caused by the NbTi sheet itself.</abstract><qualityIndicators><score>6.566</score><pdfVersion>1.4</pdfVersion><pdfPageSize>595 x 842 pts (A4)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1343</abstractCharCount><pdfWordCount>3702</pdfWordCount><pdfCharCount>20939</pdfCharCount><pdfPageCount>7</pdfPageCount><abstractWordCount>197</abstractWordCount></qualityIndicators><title>Comparison of different configurations of NbTi magnetic lenses</title><pii><json:string>S0953-2048(11)99444-5</json:string></pii><genre><json:string>article</json:string></genre><host><volume>24</volume><pages><total>7</total><last>7</last><first>1</first></pages><issn><json:string>0953-2048</json:string></issn><issue>10</issue><genre></genre><language><json:string>unknown</json:string></language><eissn><json:string>1361-6668</json:string></eissn><title>Superconductor Science and Technology</title></host><publicationDate>2011</publicationDate><copyrightDate>2011</copyrightDate><doi><json:string>10.1088/0953-2048/24/10/105012</json:string></doi><id>1272CE4EDE03E70D7F3B0557844EDD952033A233</id><fulltext><json:item><original>true</original><mimetype>application/pdf</mimetype><extension>pdf</extension><uri>https://api.istex.fr/document/1272CE4EDE03E70D7F3B0557844EDD952033A233/fulltext/pdf</uri></json:item><json:item><original>false</original><mimetype>application/zip</mimetype><extension>zip</extension><uri>https://api.istex.fr/document/1272CE4EDE03E70D7F3B0557844EDD952033A233/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/1272CE4EDE03E70D7F3B0557844EDD952033A233/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Comparison of different configurations of NbTi magnetic lenses</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>IOP Publishing</publisher><availability><p>IOP</p></availability><date>2011</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Comparison of different configurations of NbTi magnetic lenses</title><author><persName><forename type="first">Z Y</forename><surname>Zhang</surname></persName><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation><affiliation>E-mail:ZHANG.Zhiyu@nims.go.jp</affiliation></author><author><persName><forename type="first">S</forename><surname>Matsumoto</surname></persName><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation></author><author><persName><forename type="first">S</forename><surname>Choi</surname></persName><affiliation>Busan Center, Korea Basic Science Institute, Geumjeong, Busan 609-735, Korea</affiliation></author><author><persName><forename type="first">R</forename><surname>Teranishi</surname></persName><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation></author><author><persName><forename type="first">T</forename><surname>Kiyoshi</surname></persName><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation></author></analytic><monogr><title level="j">Superconductor Science and Technology</title><title level="j" type="abbrev">Supercond. Sci. Technol.</title><idno type="pISSN">0953-2048</idno><idno type="eISSN">1361-6668</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2011"></date><biblScope unit="volume">24</biblScope><biblScope unit="issue">10</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="7">7</biblScope><biblScope unit="production">Printed in the UK & the USA</biblScope></imprint></monogr><idno type="istex">1272CE4EDE03E70D7F3B0557844EDD952033A233</idno><idno type="DOI">10.1088/0953-2048/24/10/105012</idno><idno type="PII">S0953-2048(11)99444-5</idno><idno type="articleID">399444</idno><idno type="articleNumber">105012</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2011</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetismof superconductors. Magnetic lenses of two types made from NbTi sheets wereconstructed; measurements were made on them and they were systematicallystudied. TypeA was constructed by stacking NbTi rings that had identical outerdiameters and increasing inner diameters to form a hollow cone. Each ring had a slitto suppress the circumference current. Three construction methods for typeAwere tested: the rings were stacked with their slits aligned but with no insulationbetween the rings (A-1), with their slits aligned and with insulation betweenthe rings (A-2), and with their slits in different positions and with insulationbetween the rings (A-3). For typeB, sheets were rolled into hollow cones. Threeidentical cones were stacked to form a lens (B-1) and a single cone was used as areference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat witha NbTi magnet. The quenching behavior, concentration ratio, hysteresis, anddecay behavior were measured. Because of its larger dimensions, typeB had alarger concentration ratio (2.49 for B-1) than typeA (1.87 for A-1). Both lenses(typesA and B-1) were quenched when the concentrated flux density reached about0.64T. The results suggest that quenching was caused by the NbTi sheet itself.</p></abstract><textClass><classCode scheme="">74.25.Ha</classCode><classCode scheme="">74.25.N-</classCode></textClass></profileDesc><revisionDesc><change when="2011">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/1272CE4EDE03E70D7F3B0557844EDD952033A233/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1" </istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_2.dtd" name="istex:docType"></istex:docType><istex:document><article artid="sust399444"><article-metadata><jnl-data jnlid="sust"><jnl-fullname>Superconductor Science and Technology</jnl-fullname><jnl-abbreviation>Supercond. Sci. Technol.</jnl-abbreviation><jnl-shortname>SUST</jnl-shortname><jnl-issn>0953-2048</jnl-issn><jnl-coden>SUSTEF</jnl-coden><jnl-imprint>IOP Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/SUST</jnl-web-address></jnl-data><volume-data><year-publication>2011</year-publication><volume-number>24</volume-number></volume-data><issue-data><issue-number>10</issue-number><coverdate>October 2011</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper" numbering="article" artnum="105012"></type-number><article-number>399444</article-number><first-page>1</first-page><last-page>7</last-page><length>7</length><pii>S0953-2048(11)99444-5</pii><doi>10.1088/0953-2048/24/10/105012</doi><copyright>IOP Publishing Ltd</copyright><ccc>0953-2048/11/105012 + 7$33.00</ccc><printed>Printed in the UK & the USA</printed><features colour="global"></features></article-data></article-metadata><header><title-group><title>Comparison of different configurations of NbTi magnetic lenses</title><short-title>Comparison of different configurations of NbTi magnetic lenses
</short-title><ej-title>Comparison of different configurations of NbTi magnetic lenses
</ej-title></title-group><author-group><author address="sust399444ad1 sust399444ad2" email="sust399444ea1"><first-names>Z Y</first-names><second-name>Zhang</second-name></author><author address="sust399444ad2"><first-names>S</first-names><second-name>Matsumoto</second-name></author><author address="sust399444ad3"><first-names>S</first-names><second-name>Choi</second-name></author><author address="sust399444ad1"><first-names>R</first-names><second-name>Teranishi</second-name></author><author address="sust399444ad1 sust399444ad2"><first-names>T</first-names><second-name>Kiyoshi</second-name></author><short-author-list>Z Y Zhang <italic>et al</italic> </short-author-list></author-group><address-group><address id="sust399444ad1"><orgname>Department of Materials Science and Engineering, Kyushu University</orgname>, Nishi Ku, Fukuoka
819-0395,
<country>Japan</country></address><address id="sust399444ad2"><orgname>National Institute for Materials Science, Superconducting Wire Unit</orgname>, Tsukuba, Ibaraki
305-0003,
<country>Japan</country></address><address id="sust399444ad3"><orgname>Busan Center, Korea Basic Science Institute</orgname>, Geumjeong, Busan 609-735,
<country>Korea</country></address><e-address id="sust399444ea1"><email mailto="ZHANG.Zhiyu@nims.go.jp">ZHANG.Zhiyu@nims.go.jp</email></e-address></address-group><history received="6 July 2011" finalform="12 August 2011" online="2 September 2011"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetism
of superconductors. Magnetic lenses of two types made from NbTi sheets were
constructed; measurements were made on them and they were systematically
studied. Type A was constructed by stacking NbTi rings that had identical outer
diameters and increasing inner diameters to form a hollow cone. Each ring had a slit
to suppress the circumference current. Three construction methods for type A
were tested: the rings were stacked with their slits aligned but with no insulation
between the rings (A-1), with their slits aligned and with insulation between
the rings (A-2), and with their slits in different positions and with insulation
between the rings (A-3). For type B, sheets were rolled into hollow cones. Three
identical cones were stacked to form a lens (B-1) and a single cone was used as a
reference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat with
a NbTi magnet. The quenching behavior, concentration ratio, hysteresis, and
decay behavior were measured. Because of its larger dimensions, type B had a
larger concentration ratio (2.49 for B-1) than type A (1.87 for A-1). Both lenses
(types A and B-1) were quenched when the concentrated flux density reached about
0.64 T. The results suggest that quenching was caused by the NbTi sheet itself.
</p></abstract></abstract-group><classifications><class-codes scheme="pacs"><code>74.25.Ha</code><code>74.25.N-</code></class-codes></classifications></header><body refstyle="numeric"><sec-level1 id="sust399444s1" label="1"><heading>Introduction</heading><p indent="no">High field magnets using low temperature superconductors are now commercially available
and applied in various research fields, such as NMR spectrometers. However, the major
increase of magnet size with magnetic fields has often limited the installation locations
and the market. A compact high field system is an important trend in magnet
development.</p><p>Kim <italic>et al</italic> [<cite linkend="sust399444bib1">1</cite>] and Brechna <italic>et al</italic> [<cite linkend="sust399444bib2">2</cite>] designed the original concepts of
field concentrators for a pulsed field in 1959 and 1965, respectively. The concentrator,
constructed with copper disks, induced current flow along the periphery of the disks to
exclude the magnetic flux.</p><p>Magnetic field concentration using the diamagnetism of superconductors is the
main concept of a magnetic lens. Kiyoshi <italic>et al</italic> [<cite linkend="sust399444bib3">3</cite>] tapered and cut a
GdBCO hollow cylinder to form a truncated cone. The magnetic field inside the
cylinder was more than doubled due to concentration of the magnetic flux. Choi
<italic>et al</italic> [<cite linkend="sust399444bib4">4</cite>] demonstrated that the GdBCO magnetic lens generated
14.76 T on increasing the external field from 12 to 13 T. The results confirmed the
idea of developing a compact high field system (above 10 T) with a magnetic
lens.</p><p>Since magnetic lenses employ the diamagnetism of superconductors, other superconductors
could also be utilized to fabricate them. NbTi, which has been widely used in many
applications, is a promising material for magnetic lenses.</p><p>Unlike GdBCO superconductors, NbTi bulk superconductors are difficult to fabricate,
although a NbTi/Nb/Cu multilayer superconducting sheet has been commercialized.
Because of the excellent mechanical properties of NbTi and its ability to form sheets with
large areas, we fabricated NbTi magnetic lenses of two types, which we refer to as types A
and B, in the present study. Some of the magnetic properties of NbTi lenses have been
reported [<cite linkend="sust399444bib5">5</cite>]. The most important characteristic of a magnetic lens is its tapered
inner diameter. Type A was constructed by stacking NbTi rings that had identical outer
diameters and increasing inner diameters to form a hollow cone. Each ring had a slit
to suppress the circumference current. Three construction methods for type A
were tested: the rings were stacked with their slits aligned but with no insulation
between the rings (A-1), with the slits aligned and with insulation between the
rings (A-2), and with their slits not aligned and with insulation between the
rings (A-3). For type B, sheets were rolled into hollow cones. Three identical cones
were stacked to form a lens (B-1) and a single cone was used as a reference lens
(B-2).</p><p>The shape of the structure was optimized using finite element method software
(OPERA-3D). The magnetic lenses were placed in a small superconducting magnet to
measure their magnetic properties and the magnetic lenses were then systemically
investigated.</p><p>The results for type A revealed the influence of the slit position. The properties of types A
and B (mainly B-1) were compared. A single-cone lens (B-2) was used to explain some
abnormal results obtained for B-1. The numerical and experimental results were compared
and analyzed.</p></sec-level1><sec-level1 id="sust399444s2" label="2"><heading>Fabrication</heading><p indent="no">NbTi/Nb/Cu superconducting multilayer sheets with a thickness of 1 mm were produced by
Nippon Steel. The details of these sheets have been described by Otsuka <italic>et al</italic>
[<cite linkend="sust399444bib6">6</cite>]. Figure <figref linkend="sust399444fig1">1</figref> shows the type A magnetic lens. It was constructed from 26 rings cut from
the sheets with a lathe. These rings had identical outer diameters of 94 mm, while their
inner diameters increased gradually from 22 to 72 mm. The magnetic lens was
constructed by gradually stacking the rings to form a hollow cone. Each ring
had a slit to suppress the shielding current induced by external magnetic fields.
Three construction methods were tested for type A. For lens A-1, the slits were
aligned to form a leakage path and no insulation was placed between the rings.
For lens A-2, the slits were aligned to form a leakage path and polyimide film (Kapton<sup>®</sup>)
12.5 µm
thick was placed between the rings for electrical insulation. For lens A-3,
insulation was placed between the rings and each ring was rotated by
90°
so that the slits were not aligned. Grease (Apiezon-N) was applied between
the rings and the polyimide films to improve the thermal conductivity.
Finally, all the lenses were completely wrapped in polyimide tape (Kapton<sup>®</sup>). Table <tabref linkend="sust399444tab1">1</tabref> lists the dimensions and the arrangements of the NbTi lenses.
<figure id="sust399444fig1" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944401.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944401.jpg"></graphic-file></graphic><caption id="sust399444fc1" type="figure" label="Figure 1"><p indent="no">Photograph and schematic illustration of a type A lens.</p></caption></figure></p><table id="sust399444tab1" width="42pc"><caption id="tc1" label="Table 1"><p indent="no">Dimensions and specifications of various arrangements of NbTi lenses.</p></caption><tgroup cols="6"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><colspec colnum="6" colname="col6" align="left"></colspec><thead><row><entry></entry><entry></entry><entry>Height (mm)</entry><entry>Inner diameter (mm)</entry><entry>Outer diameter (mm)</entry><entry>Specifications</entry></row></thead><tbody><row><entry>A</entry><entry>1</entry><entry>27.7</entry><entry>22–72</entry><entry>94</entry><entry>Slits aligned; no insulation between rings</entry></row><row><entry></entry><entry>2</entry><entry>28.5</entry><entry>22–72</entry><entry>94</entry><entry>Slits aligned; insulation between rings</entry></row><row><entry></entry><entry>3</entry><entry>28.4</entry><entry>22–72</entry><entry>94</entry><entry>Each slit rotated by 90°; insulation between rings</entry></row><row><entry>B</entry><entry>1</entry><entry>76</entry><entry>22.2</entry><entry>172.5</entry><entry>Three cones stacked</entry></row><row><entry></entry><entry>2</entry><entry>71</entry><entry>22.2</entry><entry>172.5</entry><entry>One NbTi cone sandwiched between two copper cones</entry></row></tbody></tgroup></table><p>To fabricate type B lenses, NbTi sheets were rolled into hollow cones, as shown in
figure <figref linkend="sust399444fig2">2</figref>. The cone had an outer diameter of 172.5 mm, an inner diameter of
22.2 mm, and a height of 71 mm. The whole cone was completely insulated, especially
between the overlapping parts, to suppress the shielding current. Lens B-1 was
formed by stacking three identical cones and rotating them to prevent the parts
overlapping.
<figure id="sust399444fig2" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944402.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944402.jpg"></graphic-file></graphic><caption id="sust399444fc2" type="figure" label="Figure 2"><p indent="no">Schematic illustration and photograph of type B lens.</p></caption></figure></p><p>For comparison, a single-cone lens was tested (B-2). One NbTi cone was sandwiched
between two copper cones with similar dimensions.</p></sec-level1><sec-level1 id="sust399444s3" label="3"><heading>The experiment</heading><p indent="no">In this study, the basic performance parameters of the NbTi magnetic lenses, including the
concentration ratio, the quench field, and the field sweep rate, as well as the decay
behavior, were measured.</p><p>Magnetic measurements were performed under zero-field-cooled conditions. The
magnetic lens was placed in a NbTi superconducting coil that had an inner
diameter of 174.4 mm, an outer diameter of 192.3 mm, a height of 38 mm, and a
total number of turns of 1309.9. It was excited by a power supply up to 100 A,
which corresponds to an applied magnetic flux density at the center of the coil (<italic>B</italic><sub>app</sub>) of 0.878 T.</p><p>The magnetic lens was fixed on the second stage of a Gifford–McMahon cryocooler. Two
temperature sensors were mounted on the lens and the coil. The lens performance was measured
at a temperature a little below 4 K. The magnetic flux density at the tip of the magnetic lens,
<italic>B</italic><sub>con</sub>, was obtained from the voltage of a Hall generator. The background field (<italic>B</italic><sub>back</sub>) at the center of the coil was calculated from the current.</p><p>Although type A and B lenses were examined using the same magnet system, they were
fixed using different holders. Figures <figref linkend="sust399444fig3">3</figref>(a) and (b) show schematic diagrams of the experimental setups used for
types A and B, respectively.
<figure id="sust399444fig3" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944403.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944403.jpg"></graphic-file></graphic><caption id="sust399444fc3" type="figure" label="Figure 3"><p indent="no">Schematic cross-sections of the experimental systems for types (a) A and (b) B.</p></caption></figure></p></sec-level1><sec-level1 id="sust399444s4" label="4"><heading>Results</heading><sec-level2 id="sust399444s4.1" label="4.1"><heading>Lens A-1</heading><p indent="no">Figure <figref linkend="sust399444fig4">4</figref> shows a plot of the concentrated field (<italic>B</italic><sub>con</sub>) as a function of the
background field (<italic>B</italic><sub>back</sub>) for lens A-1. <italic>B</italic><sub>cal</sub>
is the calculated field at the position of the Hall generator without a magnetic lens
(non-concentrated field). The coil was further excited until the lens was quenched again and
<italic>B</italic><sub>back</sub>
was then reduced to zero. During the charging process, the lens was quenched at fields
<italic>B</italic><sub>con</sub> of 0.65 and 1 T; the
concentration ratios (Δ<italic>B</italic><sub>con</sub>/Δ<italic>B</italic><sub>cal</sub>) at these quench points were 1.87 and 1.82, respectively. The maximum magnetic flux in
the axial direction was moved from the center of the coil to the top hole of the lens. Other
magnetic properties of lens A-1 have been reported previously [<cite linkend="sust399444bib5">5</cite>].
<italic>B</italic><sub>con</sub> decreased
below <italic>B</italic><sub>cal</sub>
once when the lens was quenched due to mutual coupling between the lens and the NbTi
coil.
<figure id="sust399444fig4" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944404.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944404.jpg"></graphic-file></graphic><caption id="sust399444fc4" type="figure" label="Figure 4"><p indent="no"><italic>B</italic><sub>con</sub> as a
function of <italic>B</italic><sub>back</sub>
for lens A-1.</p></caption></figure></p></sec-level2><sec-level2 id="sust399444s4.2" label="4.2"><heading>Lens A-2</heading><p indent="no">Lens A-2 has a similar concentration performance to lens A-1; the lens was quenched at fields
<italic>B</italic><sub>con</sub>
of 0.63 T and 0.95 T in the charging process; the concentration ratios at these quench points
were 1.76 and 1.74, respectively.</p><p>Figure <figref linkend="sust399444fig5">5</figref> shows the decay behavior of
<italic>B</italic><sub>con</sub>
before quenching. The background field was held at 0.34 T.
<italic>B</italic><sub>con</sub>
rapidly decreased by 0.1% and then remained almost constant
for more than 5 h. The inset shows a plot of the field decay of
<italic>B</italic><sub>con</sub> for
<italic>B</italic><sub>back</sub> = 0.34 T against the logarithm of time. The time at which
<italic>B</italic><sub>back</sub> = 0.34 T is
defined as <italic>t</italic> = 0.
<figure id="sust399444fig5" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944405.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944405.jpg"></graphic-file></graphic><caption id="sust399444fc5" type="figure" label="Figure 5"><p indent="no">Field decay of <italic>B</italic><sub>con</sub>
with time for lens A-2.</p></caption></figure></p><p>Figure <figref linkend="sust399444fig6">6</figref> shows the relationship between
<italic>B</italic><sub>con</sub> and
<italic>B</italic><sub>back</sub> before the quench.
Some data points for Δ<italic>B</italic><sub>con</sub>/Δ<italic>B</italic><sub>cal</sub>
near <italic>B</italic><sub>back</sub> = 0 T were omitted because they had large deviations. This plot exhibits hysteresis. The large
change in the ratio around 0 T may have been due to the relation between the magnet
current and the magnetic field deviating from linearity at low fields. The concentration
ratio gradually decreased during charging and discharging.
<figure id="sust399444fig6" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944406.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944406.jpg"></graphic-file></graphic><caption id="sust399444fc6" type="figure" label="Figure 6"><p indent="no"><italic>B</italic><sub>con</sub> and concentration
ratio as functions of <italic>B</italic><sub>back</sub>
for lens A-2.</p></caption></figure></p></sec-level2><sec-level2 id="sust399444s4.3" label="4.3"><heading>Lens A-3</heading><p indent="no">Lens A-3 also has a similar concentration performance to lens
A-1. In the charging process, the lens was quenched at fields
<italic>B</italic><sub>con</sub>
of 0.64 and 0.96 T; the concentration ratios at the quench points were 1.84 and 1.82,
respectively.</p><p>Experiments were performed to investigate the influence of the field sweep rate.
Figure <figref linkend="sust399444fig7">7</figref> shows the quench fields and concentration ratios at different field sweep
rates. The concentration ratio was measured at the quench points. The sweep rate had
little effect on the concentration ratio. The quench field increased with decreasing field
sweep rate due to more heat being removed by thermal conduction at lower field sweep
rates.
<figure id="sust399444fig7" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944407.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944407.jpg"></graphic-file></graphic><caption id="sust399444fc7" type="figure" label="Figure 7"><p indent="no">Quench fields and concentration ratios at different sweep rates for lens A-3.</p></caption></figure></p></sec-level2><sec-level2 id="sust399444s4.4" label="4.4"><heading>Lens B-1</heading><p indent="no">Figure <figref linkend="sust399444fig8">8</figref> shows the relationship between
<italic>B</italic><sub>con</sub> and
<italic>B</italic><sub>back</sub>
for lens B-1. The lens was quenched at fields
<italic>B</italic><sub>con</sub>
of 0.65 and 0.9 T; the concentration ratios at these quench point were 2.49 and 2.46,
respectively. Unlike the other lenses, lens B-1 was quenched again in the discharging
process.
<figure id="sust399444fig8" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944408.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944408.jpg"></graphic-file></graphic><caption id="sust399444fc8" type="figure" label="Figure 8"><p indent="no">Relationship between <italic>B</italic><sub>con</sub>
and <italic>B</italic><sub>back</sub>
for lens B-1.</p></caption></figure></p><p>Figure <figref linkend="sust399444fig9">9</figref> shows a plot of the decay of
<italic>B</italic><sub>con</sub>. The
background field was maintained at 0.22 T. Lens B-1 exhibited a similar trend to the type A lenses.
<italic>B</italic><sub>con</sub>
initially decreased by only 0.1% and then remained almost constant
for more than 10 h. The inset shows a plot of the field decay of
<italic>B</italic><sub>con</sub> at
<italic>B</italic><sub>back</sub> = 0.22 T against the logarithm of time. The time at which
<italic>B</italic><sub>back</sub> = 0.22 T is
defined as <italic>t</italic> = 0.
<figure id="sust399444fig9" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944409.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944409.jpg"></graphic-file></graphic><caption id="sust399444fc9" type="figure" label="Figure 9"><p indent="no">Field decay of <italic>B</italic><sub>con</sub>
with time for lens B-1.</p></caption></figure></p><p>Figure <figref linkend="sust399444fig10">10</figref> shows the data in figure <figref linkend="sust399444fig11">11</figref> replotted to show the relationship between
<italic>B</italic><sub>con</sub> and
<italic>B</italic><sub>back</sub>. Unlike for the type A lenses, the concentration ratio gradually increased during the
charging process and the remanence was positive.
<figure id="sust399444fig10" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944410.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944410.jpg"></graphic-file></graphic><caption id="sust399444fc10" type="figure" label="Figure 10"><p indent="no"><italic>B</italic><sub>con</sub> and concentration
ratio as functions of <italic>B</italic><sub>back</sub>
for lens B-1.</p></caption></figure><figure id="sust399444fig11" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944411.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944411.jpg"></graphic-file></graphic><caption id="sust399444fc11" type="figure" label="Figure 11"><p indent="no">Quench fields and concentration ratios at different sweep rates for lens B-1.</p></caption></figure></p><p>Experiments were performed to investigate the influence of the field sweep rate.
Figure <figref linkend="sust399444fig11">11</figref> shows the quench fields and concentration ratios for different field sweep
rates. The concentration ratio was measured at the quench points. For the lens B-1, the
sweep rate had little effect on the concentration ratio, whereas the quench field increased
with decreasing field sweep rate.
</p></sec-level2><sec-level2 id="sust399444s4.5" label="4.5"><heading>Lens B-2</heading><p indent="no">Figure <figref linkend="sust399444fig12">12</figref> shows the quench fields for lens B-2. The lens was quenched at fields
<italic>B</italic><sub>con</sub> of
0.42 and 0.57 T; the concentration ratios at these quench points were 2.3 and 2.25, respectively. The
<italic>B</italic><sub>con</sub>
curve of lens B-2 showed a significant non-linearity property because it was made of only
one NbTi sheet. Matsumoto <italic>et al</italic> [<cite linkend="sust399444bib7">7</cite>] reported that the shielding performance of
the magnetic fields depended on the number of REBCO (RE is a rare earth element, such
as Gd) coated conductors.
<figure id="sust399444fig12" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944412.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944412.jpg"></graphic-file></graphic><caption id="sust399444fc12" type="figure" label="Figure 12"><p indent="no"><italic>B</italic><sub>con</sub> as a
function of <italic>B</italic><sub>back</sub>
for the single-cone lens (lens B-2).</p></caption></figure></p><p>Figure <figref linkend="sust399444fig13">13</figref> shows <italic>B</italic><sub>con</sub>
and the concentration ratio as functions of
<italic>B</italic><sub>back</sub>. In contrast to the three-cone lens (B-1), the single-cone lens exhibited a similar variation
to the type A lenses. However, the magnetic properties of the single-cone lens were unstable
and its remanence was very large.
<figure id="sust399444fig13" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944413.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944413.jpg"></graphic-file></graphic><caption id="sust399444fc13" type="figure" label="Figure 13"><p indent="no"><italic>B</italic><sub>con</sub> and concentration
ratio as functions of <italic>B</italic><sub>back</sub>
for lens B-2.</p></caption></figure></p></sec-level2></sec-level1><sec-level1 id="sust399444s5" label="5"><heading>Numerical results and discussion</heading><p indent="no">Many experiments were performed for type A and B lenses. For a magnetic lens, the quench field at
<italic>B</italic><sub>con</sub>
is an important factor that limits the range of applications. Another important factor is the
concentration ratio; it is determined by the shape of the lens and the diamagnetism
of the materials. The diamagnetism is expressed by the relative permeability
μ<sub>r</sub>. In the present experiments, the concentration ratio continually varied because the relative
permeability of the superconductor changed with the background field. The shape was
optimized using finite element method software (OPERA-3D). The simulation
results predict that the concentration ratio will be strongly influenced by the
outer diameter, the inner diameter, and the height. The type B lenses had higher
concentration ratios because they had a larger outer diameter and height than the type A
lenses.
</p><sec-level2 id="sust399444s5.1" label="5.1"><heading>Type A</heading><p indent="no">Table <tabref linkend="sust399444tab2">2</tabref> lists the quench results for lenses A-1, A-2, and A-3 during
the charging process. Three construction methods were used to investigate the
influence of slit alignment. All three lenses had nearly the same quench fields
Δ<italic>B</italic><sub>con</sub>
and concentration ratios for the first quench. In a previous study [<cite linkend="sust399444bib3">3</cite>],
simulations revealed that a little magnetic flux leaked from the slit. As table <tabref linkend="sust399444tab2">2</tabref> shows, the slit position had little effect on the flux leakage even though
all the slits were aligned to form a leakage path in A-1 and A-2. The presence or absence of
insulation between the rings had hardly any effect. Compared to that for the first quench,
Δ<italic>B</italic><sub>con</sub>
for the second quench decreased a little because
μ<sub>r</sub>
increased with increasing field. Consequently, the three type A lenses have similar
performances. Accordingly, type A was compared with type B.</p><table id="sust399444tab2"><caption id="tc2" label="Table 2"><p indent="no">Quench field results for type A lenses during the charging process.</p></caption><tgroup cols="5"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><thead><row><entry></entry><entry namest="col2" nameend="col3" align="center">First quench</entry><entry namest="col4" nameend="col5" align="center">Second quench</entry></row><row><entry>Type A</entry><entry>Δ<italic>B</italic><sub>back</sub>
(T)</entry><entry>Δ<italic>B</italic><sub>con</sub>
(T)</entry><entry>Δ<italic>B</italic><sub>back</sub>(<italic>B</italic><sub>back</sub>)
(T)</entry><entry>Δ<italic>B</italic><sub>con</sub>
(T)</entry></row></thead><tbody><row><entry>A-1</entry><entry>0.36</entry><entry>0.65</entry><entry>0.37 (0.73)</entry><entry>0.64</entry></row><row><entry>A-2</entry><entry>0.37</entry><entry>0.63</entry><entry>0.35 (0.72)</entry><entry>0.58</entry></row><row><entry>A-3</entry><entry>0.36</entry><entry>0.64</entry><entry>0.34 (0.7)</entry><entry>0.6</entry></row></tbody></tgroup></table></sec-level2><sec-level2 id="sust399444s5.2" label="5.2"><heading>Types A and B</heading><p indent="no">To compare the properties of types A and B (mainly B-1) lenses, in table <tabref linkend="sust399444tab3">3</tabref> we list the quench field results of lenses A-3 and B-1.
In the charging process, the two kinds of lenses had similar values of
Δ<italic>B</italic><sub>con</sub>
of about 0.64 T when they were quenched, which suggests that they were quenched
because of the NbTi sheet itself. This result demonstrates that the induced
current density inside the magnetic lens exceeded the critical current density (<italic>J</italic><sub>c</sub>) of the NbTi sheet and the field dependence of the
<italic>J</italic><sub>c</sub>
of the NbTi sheet played a significant role for the different structures of the lenses. Because
of its larger dimensions, lens B-1 had a higher concentration ratio (2.49) than lens A-3
(1.84). During the discharging process, lens A-3 was quenched only once and
Δ<italic>B</italic><sub>con</sub> was
0.742 T, which is a little larger than that in the charging process. Lens B-1 was quenched again and
the Δ<italic>B</italic><sub>con</sub>
values were approximately the same as those in the charging process.</p><table id="sust399444tab3"><caption id="tc3" label="Table 3"><p indent="no">Quench field results for lenses A-3 and B-1.</p></caption><tgroup cols="5"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><thead><row><entry></entry><entry></entry><entry>Quench</entry><entry>Δ<italic>B</italic><sub>back</sub>(<italic>B</italic><sub>back</sub>)
(T)</entry><entry>Δ<italic>B</italic><sub>con</sub>
(T)</entry></row></thead><tbody><row><entry>A-3</entry><entry>Charging</entry><entry>First</entry><entry>0.36 (0.36)</entry><entry>0.64</entry></row><row><entry></entry><entry></entry><entry>Second</entry><entry>0.34 (0.7)</entry><entry>0.6</entry></row><row><entry></entry><entry>Discharging</entry><entry>Third</entry><entry>0.42 (0.28)</entry><entry>0.74</entry></row><row><entry>B-1</entry><entry>Charging</entry><entry>First</entry><entry>0.27 (0.27)</entry><entry>0.65</entry></row><row><entry></entry><entry></entry><entry>Second</entry><entry>0.27 (0.54)</entry><entry>0.63</entry></row><row><entry></entry><entry>Discharging</entry><entry>Third</entry><entry>0.27 (0.27)</entry><entry>0.64</entry></row><row><entry></entry><entry></entry><entry>Fourth</entry><entry>0.27 (0)</entry><entry>0.64</entry></row></tbody></tgroup></table><p>Figure <figref linkend="sust399444fig14">14</figref> shows the slit models of lenses A and B-1. Although both
lenses A and B-1 consisted of stacked sheets, they were both simplified as solid
bodies in the models. Lens A had a slit (1 mm). Lens B-1 was modeled as
having a very small slit (0.2 mm). In the simulation, the NbTi lenses were
assumed to have perfect diamagnetism at low field. Static analyses (TOSKA in
OPERA-3D) were carried out by setting the relative magnetic permeability at
1 × 10<sup> − 100</sup>. The experimental and calculated concentration ratios of lenses at the quench field are
compared in table <tabref linkend="sust399444tab4">4</tabref>. It has been proved that both experimental and calculated concentration
ratios of lens B-1 are larger than those of lens A due to the larger dimensions. It is
reasonable that all the experimental concentration ratios of lenses A were smaller than the
calculated values. However, the lens B-1 had approximately similar values of both
experimental and calculated results that might have been caused by imperfect stacking,
especially for lens B-1, as the results for B-2 indicate. Furthermore, the inside of lens A
was modeled as a hollow cone for simplicity. Lens A had 26 rings, whereas the
lens B-1 was assumed to consist of four layers that partially overlapped each
other. Compared to that of lens B-1, the model of lens A is therefore much more
realistic.
<figure id="sust399444fig14" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" scale="100" filename="images/9944414.eps"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/9944414.jpg"></graphic-file></graphic><caption id="sust399444fc14" type="figure" label="Figure 14"><p indent="no">Schematic illustrations of numerical analyzing models of lens A and B-1.</p></caption></figure></p><table id="sust399444tab4"><caption id="tc4" label="Table 4"><p indent="no">The experimental and calculated concentration ratios of lenses at the quench
field.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><thead><row><entry></entry><entry namest="col2" nameend="col3" align="center">Concentration ratio = Δ<italic>B</italic><sub>con</sub>/Δ<italic>B</italic><sub>cal</sub></entry><entry></entry></row><row><entry></entry><entry>Experimental result</entry><entry>Calculated result</entry><entry>Calculated <italic>J</italic>
(A m<sup> − 2</sup>)</entry></row></thead><tbody><row><entry>A-1</entry><entry>1.87 (at 0.36 T)</entry><entry></entry><entry></entry></row><row><entry>A-2</entry><entry>1.76 (at 0.37 T)</entry><entry>2.07</entry><entry>1.48 × 10<sup>8</sup></entry></row><row><entry>A-3</entry><entry>1.84 (at 0.36 T)</entry><entry></entry><entry></entry></row><row><entry>B-1</entry><entry>2.49 (at 0.27 T)</entry><entry>2.51</entry><entry>3.96 × 10<sup>8</sup></entry></row></tbody></tgroup></table><p>According to the experimental results, the induced current densities in the lenses at the
quench field were estimated by means of transient analyses (ELEKTRA-TR in
OPERA-3D). The calculated current densities are listed in table <tabref linkend="sust399444tab4">4</tabref>; the results agreed well with the critical current density of NbTi sheet [<cite linkend="sust399444bib6">6</cite>].</p><p>The decay behaviors of lenses A-2 and B-1 are shown in figures <figref linkend="sust399444fig5">5</figref> and <figref linkend="sust399444fig9">9</figref>. The two plots show similar weak decays, with
<italic>B</italic><sub>con</sub>
initially decreasing only by 0.1% and then remaining almost constant for several hours. However,
<italic>B</italic><sub>con</sub>
for lens A-2 dropped faster than that for lens B-1. Nevertheless, the persistent fields of
both lenses fluctuated slightly, perhaps due to the influence of vibration of the refrigerator.
The results demonstrate that NbTi lenses are capable of sustaining a constant magnetic
field for a long time.</p><p>The greatest differences between type A and lens B-1 were observed in their hystereses and
variations in the concentration ratio. As shown in figures <figref linkend="sust399444fig6">6</figref> and <figref linkend="sust399444fig10">10</figref>, the ratio for lens A-2 decreased gradually during charging because the
relative permeability increased with increasing magnetic field. In contrast, the
concentration ratio of lens B-1 increased throughout the charging. Moreover, type A had a
negative remanence, whereas lens B-1 had a positive remanence.
</p></sec-level2><sec-level2 id="sust399444s5.3" label="5.3"><heading>Type B</heading><p indent="no">To explain the above-described results, measurements were made on a single-cone lens as a
B-2 lens. One NbTi cone was sandwiched between two copper cones with similar
dimensions.</p><p>Table <tabref linkend="sust399444tab5">5</tabref> lists the quench results for the type B lenses. The quench field (Δ<italic>B</italic><sub>con</sub>) of lens B-1 is larger than that of B-2. It can be suggested that the quench field
of the type B lens increased with increasing thickness and then reached the
saturation level (about 0.64 T) which is determined by the NbTi sheet itself. The
Δ<italic>B</italic><sub>con</sub>
had already reached the maximum value at the thickness of lens B-1. Furthermore, lens B-1 was
quenched again in the discharging process and the concentration ratio increased with increasing
<italic>B</italic><sub>back</sub>. In contrast, like the type A lenses, lens B-2 was only quenched once in the discharging process and
Δ<italic>B</italic><sub>con</sub>
in the discharging process was larger than that in the charging process because the critical
current density decreased with increasing magnetic field.</p><table id="sust399444tab5"><caption id="tc5" label="Table 5"><p indent="no">Quench results for B-1 and B-2 lenses.</p></caption><tgroup cols="5"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><thead><row><entry></entry><entry></entry><entry>Quench</entry><entry>Δ<italic>B</italic><sub>back</sub>(<italic>B</italic><sub>back</sub>)
(T)</entry><entry>Δ<italic>B</italic><sub>con</sub>
(T)</entry></row></thead><tbody><row><entry>Lens B-1 (three cones)</entry><entry>Charging</entry><entry>First</entry><entry>0.27 (0.27)</entry><entry>0.65</entry></row><row><entry></entry><entry></entry><entry>Second</entry><entry>0.27 (0.54)</entry><entry>0.63</entry></row><row><entry></entry><entry>Discharging</entry><entry>Third</entry><entry>0.27 (0.27)</entry><entry>0.64</entry></row><row><entry></entry><entry></entry><entry>Fourth</entry><entry>0.27 (0)</entry><entry>0.64</entry></row><row><entry>Lens B-2 (one cone)</entry><entry>Charging</entry><entry>First</entry><entry>0.19 (0.19)</entry><entry>0.42</entry></row><row><entry></entry><entry></entry><entry>Second</entry><entry>0.17 (0.36)</entry><entry>0.37</entry></row><row><entry></entry><entry>Discharging</entry><entry>Third</entry><entry>0.21 (0.15)</entry><entry>0.5</entry></row></tbody></tgroup></table><p>From the results shown in figures <figref linkend="sust399444fig10">10</figref> and <figref linkend="sust399444fig13">13</figref> we infer that the inverse variation in the hysteresis and the
concentration ratio in B-1 were caused by a mechanical problem. Lens B-1 consisted
of three cones that could not be perfectly stacked because they overlapped by
about one third; thus, there was a small gap between the cones and some flux
may have leaked. A large force presses the lens when it is placed in the magnetic
field. The gap became smaller with increasing magnetic field, so the flux leakage
decreased. This may have been a result of the concentration ratio increasing with
increasing magnetic field and lens B-1 being quenched twice in the discharging
process.
</p></sec-level2></sec-level1><sec-level1 id="sust399444s6" label="6"><heading>Conclusion</heading><p indent="no">NbTi magnetic lenses of two types were constructed; measurements were made on them
and they were systematically studied. The concentration ratio of type A was about 1.87 and
that of type B was about 2.49 (B-1). Due to its larger dimensions, type B had a larger
concentration ratio than type A. All the type A lenses and lens B-1 were quenched at a
concentrated flux density of 0.64 T, which was determined by the NbTi sheet. The quench
field increased with decreasing field sweep rate, but the field sweep rate had little
effect on the concentration ratio. For both lenses, the concentrated flux density
initially decayed by only 0.1% and then remained almost constant for a long
time.</p><p>Three construction methods were tested using type A lenses. The slit position and
insulation between each ring had little influence on their magnetic properties. For type A,
the concentration ratio decreased gradually with increasing magnetic field. In contrast, lens
B-1 exhibited an inverse variation between hysteresis and concentration ratio because the
flux leaked from the gaps between the cones. The gaps became smaller as the magnetic
field increased.</p><p>The NbTi magnetic lens seems difficult to use for high field generation if the quench fields
remain at the present performance level. However, concentration ratios of about 2 were
obtained in low fields. When a superconductor sheet that has better high field performance
is developed, the construction methods described here can be used. At least the NbTi
magnetic lens is useful for concentrating low fields over a wide area. It may be useful as a
field amplifier.</p></sec-level1><acknowledgment><heading>Acknowledgment</heading><p indent="no">This work was supported in part by Kakenhi (Grant No. 20656015).
</p></acknowledgment></body><back><references><heading>References</heading><reference-list type="numeric"><journal-ref id="sust399444bib1" num="1"><authors><au><second-name>Kim</second-name><first-names>Y B</first-names></au><au><second-name>Platner</second-name><first-names>E D</first-names></au></authors><year>1959</year><jnl-title>Rev. Sci. Instrum.</jnl-title><volume>30</volume><pages>524</pages>
<crossref><cr_doi>http://dx.doi.org/10.1063/1.1716674</cr_doi><cr_issn type="print">00346748</cr_issn><cr_issn type="electronic"></cr_issn></crossref></journal-ref><journal-ref id="sust399444bib2" num="2"><authors><au><second-name>Brechna</second-name><first-names>H</first-names></au><au><second-name>Hill</second-name><first-names>D A</first-names></au><au><second-name>Bailey</second-name><first-names>B M</first-names></au></authors><year>1965</year><jnl-title>Rev. Sci. Instrum.</jnl-title><volume>36</volume><pages>1529</pages>
<crossref><cr_doi>http://dx.doi.org/10.1063/1.1719384</cr_doi><cr_issn type="print">00346748</cr_issn><cr_issn type="electronic"></cr_issn></crossref></journal-ref><journal-ref id="sust399444bib3" num="3"><authors><au><second-name>Kiyoshi</second-name><first-names>T</first-names></au><au><second-name>Choi</second-name><first-names>S</first-names></au><au><second-name>Matsumoto</second-name><first-names>S</first-names></au><au><second-name>Asano</second-name><first-names>T</first-names></au><au><second-name>Uglietti</second-name><first-names>D</first-names></au></authors><year>2009</year><jnl-title>IEEE Trans. Appl. Supercond.</jnl-title><volume>19</volume><pages>2174</pages>
<crossref><cr_doi>http://dx.doi.org/10.1109/TASC.2009.2018440</cr_doi><cr_issn type="print">1051-8223</cr_issn><cr_issn type="electronic">1558-2515</cr_issn></crossref></journal-ref><journal-ref id="sust399444bib4" num="4"><authors><au><second-name>Choi</second-name><first-names>S</first-names></au><au><second-name>Kiyoshi</second-name><first-names>T</first-names></au><au><second-name>Matsumoto</second-name><first-names>S</first-names></au></authors><year>2009</year><jnl-title>J. Appl. Phys.</jnl-title><volume>105</volume><pages>07E705</pages>
<crossref><cr_doi>http://dx.doi.org/10.1063/1.3068645</cr_doi><cr_issn type="print">00218979</cr_issn><cr_issn type="electronic"></cr_issn></crossref></journal-ref><journal-ref id="sust399444bib5" num="5"><authors><au><second-name>Zhang</second-name><first-names>Z Y</first-names></au><au><second-name>Matsumoto</second-name><first-names>S</first-names></au><au><second-name>Choi</second-name><first-names>S</first-names></au><au><second-name>Teranishi</second-name><first-names>R</first-names></au><au><second-name>Kiyoshi</second-name><first-names>T</first-names></au></authors><year>2011</year><jnl-title>Physica</jnl-title><part>C</part><misc-text>at press</misc-text></journal-ref><journal-ref id="sust399444bib6" num="6"><authors><au><second-name>Otsuka</second-name><first-names>H</first-names></au><au><second-name>Sugiyama</second-name><first-names>M</first-names></au><au><second-name>Itoh</second-name><first-names>I</first-names></au><au><second-name>Sawamura</second-name><first-names>M</first-names></au></authors><year>1998</year><jnl-title>Cryogenics</jnl-title><volume>38</volume><pages>309</pages>
<crossref><cr_doi>http://dx.doi.org/10.1016/S0011-2275(97)00160-4</cr_doi><cr_issn type="print">00112275</cr_issn><cr_issn type="electronic"></cr_issn></crossref></journal-ref><journal-ref id="sust399444bib7" num="7"><authors><au><second-name>Matsumoto</second-name><first-names>S</first-names></au><au><second-name>Kiyoshi</second-name><first-names>T</first-names></au><au><second-name>Uchida</second-name><first-names>A</first-names></au></authors><year>2011</year><jnl-title>IEEE Trans. Appl. Supercond.</jnl-title><volume>21</volume><pages>2283</pages>
<crossref><cr_doi>http://dx.doi.org/10.1109/TASC.2010.2089036</cr_doi><cr_issn type="print">1051-8223</cr_issn><cr_issn type="electronic">1558-2515</cr_issn></crossref></journal-ref></reference-list></references></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Comparison of different configurations of NbTi magnetic lenses</title></titleInfo><titleInfo type="abbreviated"><title>Comparison of different configurations of NbTi magnetic lenses</title></titleInfo><titleInfo type="alternative"><title>Comparison of different configurations of NbTi magnetic lenses</title></titleInfo><name type="personal"><namePart type="given">Z Y</namePart><namePart type="family">Zhang</namePart><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation><affiliation>E-mail:ZHANG.Zhiyu@nims.go.jp</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S</namePart><namePart type="family">Matsumoto</namePart><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S</namePart><namePart type="family">Choi</namePart><affiliation>Busan Center, Korea Basic Science Institute, Geumjeong, Busan 609-735, Korea</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R</namePart><namePart type="family">Teranishi</namePart><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">T</namePart><namePart type="family">Kiyoshi</namePart><affiliation>Department of Materials Science and Engineering, Kyushu University, Nishi Ku, Fukuoka 819-0395, Japan</affiliation><affiliation>National Institute for Materials Science, Superconducting Wire Unit, Tsukuba, Ibaraki 305-0003, Japan</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper"></genre><originInfo><publisher>IOP Publishing</publisher><dateIssued encoding="w3cdtf">2011</dateIssued><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><note type="production">Printed in the UK & the USA</note></physicalDescription><abstract>Magnetic lenses are new devices that concentrate magnetic flux by using the diamagnetismof superconductors. Magnetic lenses of two types made from NbTi sheets wereconstructed; measurements were made on them and they were systematicallystudied. TypeA was constructed by stacking NbTi rings that had identical outerdiameters and increasing inner diameters to form a hollow cone. Each ring had a slitto suppress the circumference current. Three construction methods for typeAwere tested: the rings were stacked with their slits aligned but with no insulationbetween the rings (A-1), with their slits aligned and with insulation betweenthe rings (A-2), and with their slits in different positions and with insulationbetween the rings (A-3). For typeB, sheets were rolled into hollow cones. Threeidentical cones were stacked to form a lens (B-1) and a single cone was used as areference lens (B-2). The lenses were assembled in a cryocooler-cooled cryostat witha NbTi magnet. The quenching behavior, concentration ratio, hysteresis, anddecay behavior were measured. Because of its larger dimensions, typeB had alarger concentration ratio (2.49 for B-1) than typeA (1.87 for A-1). Both lenses(typesA and B-1) were quenched when the concentrated flux density reached about0.64T. The results suggest that quenching was caused by the NbTi sheet itself.</abstract><classification authority="pacs">74.25.Ha</classification><classification authority="pacs">74.25.N-</classification><relatedItem type="host"><titleInfo><title>Superconductor Science and Technology</title></titleInfo><titleInfo type="abbreviated"><title>Supercond. Sci. Technol.</title></titleInfo><genre type="Journal">journal</genre><identifier type="ISSN">0953-2048</identifier><identifier type="eISSN">1361-6668</identifier><identifier type="PublisherID">SUST</identifier><identifier type="CODEN">SUSTEF</identifier><identifier type="URL">stacks.iop.org/SUST</identifier><part><date>2011</date><detail type="volume"><caption>vol.</caption><number>24</number></detail><detail type="issue"><caption>no.</caption><number>10</number></detail><extent unit="pages"><start>1</start><end>7</end><total>7</total></extent></part></relatedItem><identifier type="istex">1272CE4EDE03E70D7F3B0557844EDD952033A233</identifier><identifier type="DOI">10.1088/0953-2048/24/10/105012</identifier><identifier type="PII">S0953-2048(11)99444-5</identifier><identifier type="articleID">399444</identifier><identifier type="articleNumber">105012</identifier><accessCondition type="use and reproduction" contentType="copyright">IOP Publishing Ltd</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>IOP Publishing Ltd</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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