{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T09:24:08Z","timestamp":1740129848677,"version":"3.37.3"},"reference-count":43,"publisher":"IOP Publishing","issue":"12","license":[{"start":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T00:00:00Z","timestamp":1351814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/page\/copyright"},{"start":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T00:00:00Z","timestamp":1351814400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nucl. Fusion"],"published-print":{"date-parts":[[2012,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A database of toroidal momentum transport on five tokamaks, Alcator C-Mod, DIII-D, JET, NSTX and JT-60U, has been constructed under a wide range of conditions in order to understand the characteristics of toroidal momentum transport coefficients, namely the toroidal momentum diffusivity (<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>) and the pinch velocity (<jats:italic>V<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>). Through an inter-machine comparison, the similarities and differences in the properties of <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> and <jats:italic>V<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub> among the machines have been clarified. Parametric dependences of these momentum transport coefficients have been investigated over a wide range of plasma parameters taking advantage of the different operation regimes in machines. The approach offers insights into the parametric dependences as follows. The toroidal momentum diffusivity (<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>) generally increases with increasing heat diffusivity (<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>i<\/jats:sub>). The correlation is observed over a wide range of <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>, covering roughly two orders of magnitude, and within each of the machines over the whole radius. Through the inter-machine comparison, it is found that <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> becomes larger in the outer region of the plasma. Also observed is a general trend for <jats:italic>V<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub> in tokamaks; the inward pinch velocity (\u2212<jats:italic>V<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>) increases with increasing <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>. The results that are commonly observed in machines will support a toroidal rotation prediction in future devices. On the other hand, differences among machines have been observed. The toroidal momentum diffusivity, <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>, is larger than or equal to <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>i<\/jats:sub> in JET and JT-60U; on the other hand, <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> is smaller than or equal to <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>i<\/jats:sub> in NSTX, DIII-D and Alcator C-Mod. In DIII-D, the ratio \u2212<jats:italic>RV<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> at <jats:italic>r<\/jats:italic>\/<jats:italic>a<\/jats:italic>\u00a0=\u00a00.5\u20130.6 is about 2, which is small compared with that in other tokamaks (\u2212<jats:italic>RV<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>\u00a0\u2248\u00a05). Based on these different observations, parametric dependences of <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>i<\/jats:sub>, <jats:italic>RV<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> and <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> have been investigated in H-mode plasmas. Across the dataset from all machines, the ratio <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>i<\/jats:sub> tends to be larger in low \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn001.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> at fixed <jats:italic>T<\/jats:italic>\n                  <jats:sub>e<\/jats:sub>\/<jats:italic>T<\/jats:italic>\n                  <jats:sub>i<\/jats:sub> and \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn002.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>. An increase in <jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub> is observed with decreasing <jats:italic>n<\/jats:italic>\n                  <jats:sub>e<\/jats:sub> and\/or increasing <jats:italic>T<\/jats:italic>\n                  <jats:sub>e<\/jats:sub>. The pinch number (\u2212<jats:italic>RV<\/jats:italic>\n                  <jats:sub>pinch<\/jats:sub>\/<jats:italic>\u03c7<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>\u03c6<\/jats:italic>\n                  <\/jats:sub>) is observed to increase with increasing \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn003.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> at both <jats:italic>q<\/jats:italic>\n                  <jats:sub>95<\/jats:sub>\u00a0=\u00a05.5\u20137.2 and <jats:italic>q<\/jats:italic>\n                  <jats:sub>95<\/jats:sub>\u00a0=\u00a03.7\u20134.5. Here \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn001.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>, \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn002.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>, <jats:italic>T<\/jats:italic>\n                  <jats:sub>e<\/jats:sub>, <jats:italic>T<\/jats:italic>\n                  <jats:sub>i<\/jats:sub>, \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn003.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> and <jats:italic>q<\/jats:italic>\n                  <jats:sub>95<\/jats:sub> are, respectively, the normalized effective electron collision frequency, the normalized ion poloidal Larmor radius, the electron and ion temperatures, the inverse ratio of density scale length, \n<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"nf439128ieqn004.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>, to the major radius, <jats:italic>R<\/jats:italic>, and the safety factor at the 95% flux surface.<\/jats:p>","DOI":"10.1088\/0029-5515\/52\/12\/123005","type":"journal-article","created":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T13:13:13Z","timestamp":1351861993000},"page":"123005","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":16,"title":["Momentum transport studies from multi-machine comparisons"],"prefix":"10.1088","volume":"52","author":[{"given":"M.","family":"Yoshida","sequence":"first","affiliation":[]},{"given":"S.","family":"Kaye","sequence":"additional","affiliation":[]},{"given":"J.","family":"Rice","sequence":"additional","affiliation":[]},{"given":"W.","family":"Solomon","sequence":"additional","affiliation":[]},{"given":"T.","family":"Tala","sequence":"additional","affiliation":[]},{"given":"R.E.","family":"Bell","sequence":"additional","affiliation":[]},{"given":"K.H.","family":"Burrell","sequence":"additional","affiliation":[]},{"given":"J.","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"Y.","family":"Kamada","sequence":"additional","affiliation":[]},{"given":"D.","family":"McDonald","sequence":"additional","affiliation":[]},{"given":"P.","family":"Mantica","sequence":"additional","affiliation":[]},{"given":"Y.","family":"Podpaly","sequence":"additional","affiliation":[]},{"given":"M.L.","family":"Reinke","sequence":"additional","affiliation":[]},{"given":"Y.","family":"Sakamoto","sequence":"additional","affiliation":[]},{"given":"A.","family":"Salmi","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2012,11,2]]},"reference":[{"key":"nf439128bib01","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1063\/1.872367","volume":"4","author":"Burrell","year":"1997","journal-title":"Phys. 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