Understanding Quasi-Periodic Fieldlines and Their Topology in Toroidal Magnetic Fields View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2012

AUTHORS

Allen Sanderson , Guoning Chen , Xavier Tricoche , Elaine Cohen

ABSTRACT

In the study of a magnetic confinement fusion device such as a tokamak, physicists need to understand the topology of the flux (or magnetic) surfaces that form within the magnetic field. Among the two distinct topological structures, we are particularly interested in the magnetic island chains which correspond to the break up of the ideal rational surfaces. Different from our previous method [13], in this work we resort to the periodicity analysis of two distinct functions to identify and characterize flux surfaces and island chains. These two functions are derived from the computation of the fieldlines and puncture points on a Poincaré section, respectively. They are the distance measure plot and the ridgeline plot. We show that the periods of these two functions are directly related to the topology of the surface via a resonance detection (i.e., period estimation and the common denominators computation). In addition, we show that for an island chain the two functions possess resonance components which do not occur for a flux surface. Furthermore, by combining the periodicity analysis of these two functions, we are able to devise a heuristic yet robust and reliable approach for classifying and characterizing different magnetic surfaces in the toroidal magnetic fields. More... »

PAGES

125-140

References to SciGraph publications

  • 2009. Flow Topology Beyond Skeletons: Visualization of Features in Recirculating Flow in TOPOLOGY-BASED METHODS IN VISUALIZATION II
  • 1998. Visualizing Poincaré Maps together with the Underlying Flow in MATHEMATICAL VISUALIZATION
  • 2007. Topology-Based Flow Visualization, The State of the Art in TOPOLOGY-BASED METHODS IN VISUALIZATION
  • 1991. Dynamics and Bifurcations in NONE
  • Book

    TITLE

    Topological Methods in Data Analysis and Visualization II

    ISBN

    978-3-642-23174-2
    978-3-642-23175-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-23175-9_9

    DOI

    http://dx.doi.org/10.1007/978-3-642-23175-9_9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1032372175


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Utah", 
              "id": "https://www.grid.ac/institutes/grid.223827.e", 
              "name": [
                "SCI Institute, University of Utah, Salt Lake City, UT\u00a084112, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sanderson", 
            "givenName": "Allen", 
            "id": "sg:person.0734426271.40", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0734426271.40"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Utah", 
              "id": "https://www.grid.ac/institutes/grid.223827.e", 
              "name": [
                "SCI Institute, University of Utah, Salt Lake City, UT\u00a084112, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chen", 
            "givenName": "Guoning", 
            "id": "sg:person.0662364174.05", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0662364174.05"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Purdue University", 
              "id": "https://www.grid.ac/institutes/grid.169077.e", 
              "name": [
                "Purdue University, West Lafayette, IN\u00a047907, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Tricoche", 
            "givenName": "Xavier", 
            "id": "sg:person.014405044562.80", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014405044562.80"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Utah", 
              "id": "https://www.grid.ac/institutes/grid.223827.e", 
              "name": [
                "University of Utah, Salt Lake City, UT\u00a084112, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Cohen", 
            "givenName": "Elaine", 
            "id": "sg:person.0604047154.70", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0604047154.70"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0021-9991(92)90137-n", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000406985"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1002021001", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-4426-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002021001", 
              "https://doi.org/10.1007/978-1-4612-4426-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-4426-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002021001", 
              "https://doi.org/10.1007/978-1-4612-4426-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-70823-0_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010785810", 
              "https://doi.org/10.1007/978-3-540-70823-0_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-70823-0_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010785810", 
              "https://doi.org/10.1007/978-3-540-70823-0_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-88606-8_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033170005", 
              "https://doi.org/10.1007/978-3-540-88606-8_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-88606-8_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033170005", 
              "https://doi.org/10.1007/978-3-540-88606-8_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1467-8659.2003.00723.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037915580"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-662-03567-2_23", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043201293", 
              "https://doi.org/10.1007/978-3-662-03567-2_23"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/2945.928168", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061146363"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tvcg.2007.1021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061812750"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tvcg.2010.133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061813317"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/1.9781611972764.63", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1088800142"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2012", 
        "datePublishedReg": "2012-01-01", 
        "description": "In the study of a magnetic confinement fusion device such as a tokamak, physicists need to understand the topology of the flux (or magnetic) surfaces that form within the magnetic field. Among the two distinct topological structures, we are particularly interested in the magnetic island chains which correspond to the break up of the ideal rational surfaces. Different from our previous method [13], in this work we resort to the periodicity analysis of two distinct functions to identify and characterize flux surfaces and island chains. These two functions are derived from the computation of the fieldlines and puncture points on a Poincar\u00e9 section, respectively. They are the distance measure plot and the ridgeline plot. We show that the periods of these two functions are directly related to the topology of the surface via a resonance detection (i.e., period estimation and the common denominators computation). In addition, we show that for an island chain the two functions possess resonance components which do not occur for a flux surface. Furthermore, by combining the periodicity analysis of these two functions, we are able to devise a heuristic yet robust and reliable approach for classifying and characterizing different magnetic surfaces in the toroidal magnetic fields.", 
        "editor": [
          {
            "familyName": "Peikert", 
            "givenName": "Ronald", 
            "type": "Person"
          }, 
          {
            "familyName": "Hauser", 
            "givenName": "Helwig", 
            "type": "Person"
          }, 
          {
            "familyName": "Carr", 
            "givenName": "Hamish", 
            "type": "Person"
          }, 
          {
            "familyName": "Fuchs", 
            "givenName": "Raphael", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-642-23175-9_9", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-3-642-23174-2", 
            "978-3-642-23175-9"
          ], 
          "name": "Topological Methods in Data Analysis and Visualization II", 
          "type": "Book"
        }, 
        "name": "Understanding Quasi-Periodic Fieldlines and Their Topology in Toroidal Magnetic Fields", 
        "pagination": "125-140", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-642-23175-9_9"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "9a3775b03b73cd6e65249324c4d86ad3bbd6d93a780fc31da9b9630ad316f0cb"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1032372175"
            ]
          }
        ], 
        "publisher": {
          "location": "Berlin, Heidelberg", 
          "name": "Springer Berlin Heidelberg", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-642-23175-9_9", 
          "https://app.dimensions.ai/details/publication/pub.1032372175"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T21:03", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8690_00000263.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-642-23175-9_9"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-23175-9_9'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-23175-9_9'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-23175-9_9'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-23175-9_9'


     

    This table displays all metadata directly associated to this object as RDF triples.

    141 TRIPLES      23 PREDICATES      38 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-642-23175-9_9 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N60e9d19b369c410fb95b1e7cbdb912c1
    4 schema:citation sg:pub.10.1007/978-1-4612-4426-4
    5 sg:pub.10.1007/978-3-540-70823-0_1
    6 sg:pub.10.1007/978-3-540-88606-8_11
    7 sg:pub.10.1007/978-3-662-03567-2_23
    8 https://app.dimensions.ai/details/publication/pub.1002021001
    9 https://doi.org/10.1016/0021-9991(92)90137-n
    10 https://doi.org/10.1109/2945.928168
    11 https://doi.org/10.1109/tvcg.2007.1021
    12 https://doi.org/10.1109/tvcg.2010.133
    13 https://doi.org/10.1111/j.1467-8659.2003.00723.x
    14 https://doi.org/10.1137/1.9781611972764.63
    15 schema:datePublished 2012
    16 schema:datePublishedReg 2012-01-01
    17 schema:description In the study of a magnetic confinement fusion device such as a tokamak, physicists need to understand the topology of the flux (or magnetic) surfaces that form within the magnetic field. Among the two distinct topological structures, we are particularly interested in the magnetic island chains which correspond to the break up of the ideal rational surfaces. Different from our previous method [13], in this work we resort to the periodicity analysis of two distinct functions to identify and characterize flux surfaces and island chains. These two functions are derived from the computation of the fieldlines and puncture points on a Poincaré section, respectively. They are the distance measure plot and the ridgeline plot. We show that the periods of these two functions are directly related to the topology of the surface via a resonance detection (i.e., period estimation and the common denominators computation). In addition, we show that for an island chain the two functions possess resonance components which do not occur for a flux surface. Furthermore, by combining the periodicity analysis of these two functions, we are able to devise a heuristic yet robust and reliable approach for classifying and characterizing different magnetic surfaces in the toroidal magnetic fields.
    18 schema:editor Nb10c5f79173d450aa068e55cdfb23cc8
    19 schema:genre chapter
    20 schema:inLanguage en
    21 schema:isAccessibleForFree false
    22 schema:isPartOf N263a13a7ad694dc9908616d46ab673f1
    23 schema:name Understanding Quasi-Periodic Fieldlines and Their Topology in Toroidal Magnetic Fields
    24 schema:pagination 125-140
    25 schema:productId N699af6f2360342ae9a0fc9411ed5b052
    26 N87bd0f46149a428bb3e0d69ccb9e6120
    27 N8f0779a51a8b4442954e0400711aa9d5
    28 schema:publisher Nbfc1b31201c04d5fabee94d5fead8117
    29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032372175
    30 https://doi.org/10.1007/978-3-642-23175-9_9
    31 schema:sdDatePublished 2019-04-15T21:03
    32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    33 schema:sdPublisher N628e79b975f54a9f932a7d08d85b6674
    34 schema:url http://link.springer.com/10.1007/978-3-642-23175-9_9
    35 sgo:license sg:explorer/license/
    36 sgo:sdDataset chapters
    37 rdf:type schema:Chapter
    38 N0386e3c8bffb47dcab87c93147172816 schema:familyName Fuchs
    39 schema:givenName Raphael
    40 rdf:type schema:Person
    41 N263a13a7ad694dc9908616d46ab673f1 schema:isbn 978-3-642-23174-2
    42 978-3-642-23175-9
    43 schema:name Topological Methods in Data Analysis and Visualization II
    44 rdf:type schema:Book
    45 N26968d3e826943b1a10155b2bb91fce1 schema:familyName Hauser
    46 schema:givenName Helwig
    47 rdf:type schema:Person
    48 N365990b56bac44d290e52acd01e16c8e rdf:first N26968d3e826943b1a10155b2bb91fce1
    49 rdf:rest N5ba402d2d10f41918557687553f8152b
    50 N5ba402d2d10f41918557687553f8152b rdf:first Nd7e07db4038943a18e4b7ff7af5f3f2b
    51 rdf:rest Ne903945b391d4b9e995c494a17ca5dd9
    52 N60e9d19b369c410fb95b1e7cbdb912c1 rdf:first sg:person.0734426271.40
    53 rdf:rest Nc362ec1e20524e55ae44ce8e80737376
    54 N628e79b975f54a9f932a7d08d85b6674 schema:name Springer Nature - SN SciGraph project
    55 rdf:type schema:Organization
    56 N699af6f2360342ae9a0fc9411ed5b052 schema:name doi
    57 schema:value 10.1007/978-3-642-23175-9_9
    58 rdf:type schema:PropertyValue
    59 N7c590dd0a759491aafad891ca80cd6bf schema:familyName Peikert
    60 schema:givenName Ronald
    61 rdf:type schema:Person
    62 N87bd0f46149a428bb3e0d69ccb9e6120 schema:name readcube_id
    63 schema:value 9a3775b03b73cd6e65249324c4d86ad3bbd6d93a780fc31da9b9630ad316f0cb
    64 rdf:type schema:PropertyValue
    65 N8f0779a51a8b4442954e0400711aa9d5 schema:name dimensions_id
    66 schema:value pub.1032372175
    67 rdf:type schema:PropertyValue
    68 Na6f5f9af3c6f4308960e594b2a5f6c97 rdf:first sg:person.0604047154.70
    69 rdf:rest rdf:nil
    70 Nb10c5f79173d450aa068e55cdfb23cc8 rdf:first N7c590dd0a759491aafad891ca80cd6bf
    71 rdf:rest N365990b56bac44d290e52acd01e16c8e
    72 Nb2d1e505f79240ce867d6a25cffc7f0b rdf:first sg:person.014405044562.80
    73 rdf:rest Na6f5f9af3c6f4308960e594b2a5f6c97
    74 Nbfc1b31201c04d5fabee94d5fead8117 schema:location Berlin, Heidelberg
    75 schema:name Springer Berlin Heidelberg
    76 rdf:type schema:Organisation
    77 Nc362ec1e20524e55ae44ce8e80737376 rdf:first sg:person.0662364174.05
    78 rdf:rest Nb2d1e505f79240ce867d6a25cffc7f0b
    79 Nd7e07db4038943a18e4b7ff7af5f3f2b schema:familyName Carr
    80 schema:givenName Hamish
    81 rdf:type schema:Person
    82 Ne903945b391d4b9e995c494a17ca5dd9 rdf:first N0386e3c8bffb47dcab87c93147172816
    83 rdf:rest rdf:nil
    84 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    85 schema:name Mathematical Sciences
    86 rdf:type schema:DefinedTerm
    87 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    88 schema:name Pure Mathematics
    89 rdf:type schema:DefinedTerm
    90 sg:person.014405044562.80 schema:affiliation https://www.grid.ac/institutes/grid.169077.e
    91 schema:familyName Tricoche
    92 schema:givenName Xavier
    93 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014405044562.80
    94 rdf:type schema:Person
    95 sg:person.0604047154.70 schema:affiliation https://www.grid.ac/institutes/grid.223827.e
    96 schema:familyName Cohen
    97 schema:givenName Elaine
    98 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0604047154.70
    99 rdf:type schema:Person
    100 sg:person.0662364174.05 schema:affiliation https://www.grid.ac/institutes/grid.223827.e
    101 schema:familyName Chen
    102 schema:givenName Guoning
    103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0662364174.05
    104 rdf:type schema:Person
    105 sg:person.0734426271.40 schema:affiliation https://www.grid.ac/institutes/grid.223827.e
    106 schema:familyName Sanderson
    107 schema:givenName Allen
    108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0734426271.40
    109 rdf:type schema:Person
    110 sg:pub.10.1007/978-1-4612-4426-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002021001
    111 https://doi.org/10.1007/978-1-4612-4426-4
    112 rdf:type schema:CreativeWork
    113 sg:pub.10.1007/978-3-540-70823-0_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010785810
    114 https://doi.org/10.1007/978-3-540-70823-0_1
    115 rdf:type schema:CreativeWork
    116 sg:pub.10.1007/978-3-540-88606-8_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033170005
    117 https://doi.org/10.1007/978-3-540-88606-8_11
    118 rdf:type schema:CreativeWork
    119 sg:pub.10.1007/978-3-662-03567-2_23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043201293
    120 https://doi.org/10.1007/978-3-662-03567-2_23
    121 rdf:type schema:CreativeWork
    122 https://app.dimensions.ai/details/publication/pub.1002021001 schema:CreativeWork
    123 https://doi.org/10.1016/0021-9991(92)90137-n schema:sameAs https://app.dimensions.ai/details/publication/pub.1000406985
    124 rdf:type schema:CreativeWork
    125 https://doi.org/10.1109/2945.928168 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061146363
    126 rdf:type schema:CreativeWork
    127 https://doi.org/10.1109/tvcg.2007.1021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061812750
    128 rdf:type schema:CreativeWork
    129 https://doi.org/10.1109/tvcg.2010.133 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061813317
    130 rdf:type schema:CreativeWork
    131 https://doi.org/10.1111/j.1467-8659.2003.00723.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1037915580
    132 rdf:type schema:CreativeWork
    133 https://doi.org/10.1137/1.9781611972764.63 schema:sameAs https://app.dimensions.ai/details/publication/pub.1088800142
    134 rdf:type schema:CreativeWork
    135 https://www.grid.ac/institutes/grid.169077.e schema:alternateName Purdue University
    136 schema:name Purdue University, West Lafayette, IN 47907, USA
    137 rdf:type schema:Organization
    138 https://www.grid.ac/institutes/grid.223827.e schema:alternateName University of Utah
    139 schema:name SCI Institute, University of Utah, Salt Lake City, UT 84112, USA
    140 University of Utah, Salt Lake City, UT 84112, USA
    141 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...