Hayashi, Takaya; Sato, Tetsuya Spheromak global instabilities and stabilization by nearby conductors. (English) Zbl 0587.76073 Phys. Fluids 28, 3654-3666 (1985). By means of a three-dimensional magnetohydrodynamic simulation, the stabilization effects of conducting walls on the tilting instability of spheromaks created by the Princeton induction method are extensively studied. The nonlinear development and deformation of the spheromak resulting from global instabilities with toroidal modes \(n=1\) (tilting), 2, and 3 are also studied in detail. Simulation results have shown that while the induction effect of the wall current is insufficient, the line tying effect is much more powerful for the suppression of the strong tilting instability. For a perfect line-tying stabilization, a certain amount of surface magnetic flux around the spheromak should be tied to the conducting wall. The influence of the shape of the cylindrical vacuum vessel on the stabilization is studied. It is found that the created spheromak assumes a similar figure irrespective of the vessel shape; thus we conclude that controlling the spheromak shape by changing the vacuum vessel is ineffective. Also investigated is the tilting behavior when the magnetic index is changed. The result is not conclusive in the sense that a well-developed oblate spheromak could not be created when the magnetic index was close to 1. Simulation runs in which \(n=2\) and \(n=3\) perturbations are applied in addition to the tilt mode \((n=1)\), have shown that the spheromak with a large aspect ratio is unstable to all of these modes. Interestingly, it is found that as the \(n=2\) mode develops sufficiently, the spheromak torus is severely folded and twisted; consequently, the folded arms undergo reconnection internally. MSC: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76M99 Basic methods in fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Keywords:wall stabilization; cylindrical belt; magnetic index controlling; nearly equilibrium spheromak; slow induction scheme; three-dimensional magnetohydrodynamic simulation; stabilization effects of conducting walls; tilting instability of spheromaks; Princeton induction method; deformation of the spheromak; global instabilities; perfect line-tying stabilization; oblate spheromak Software:ERATO PDFBibTeX XMLCite \textit{T. Hayashi} and \textit{T. Sato}, Phys. Fluids 28, 3654--3666 (1985; Zbl 0587.76073) Full Text: DOI References: [1] Rosenbluth, Nucl. Fusion 19 pp 489– (1979) · doi:10.1088/0029-5515/19/4/007 [2] Finn, Phys. Fluids 24 pp 1336– (1981) [3] Jardin, Nucl. Fusion 21 pp 1203– (1981) · doi:10.1088/0029-5515/21/9/004 [4] M. Yamada, R. Ellis, Jr., H. P. Furth, R. Hulse, A. Janos, S. C. Jardin, D. McNeill, C. Munson, M. Okabayashi, S. Paul, D. Post, J. Sinnis, C. Skinner, Y. C. Sun, F. Wysocki, C. Chin-Fatt, A. W. DeSilva, G. C. Goldenbaum, G. W. Hart, R. Hess, R. S. Shaw, C. W. Barnes, I. Hennins, H. W. Hoida, T. R. Jarboe, S. O. Knox, R. K. Linford, J. Lipson, J. Marshall, D. A. Platts, A. R. Sherwood, and B. L. Wright, inPlasma Physics and Controlled Nuclear Fusion Research 1982(IAEA, Vienna, 1983), Vol. 2, p. 265. [5] Sato, Phys. Rev. Lett. 50 pp 38– (1983) [6] Janos, Bull. Am. Phys. Soc. 29 pp 1201– (1984) [7] Hayashi, Phys. Fluids 27 pp 778– (1984) [8] T. Hayashi, T. Sato, F. Wysocki, D. D. Meyerhofer, and M. Yamada, submitted to J. Phys. Soc. Jpn. [9] Sato, Phys. Fluids 26 pp 775– (1983) [10] Oda, J. Phys. Soc. Jpn. 54 pp 958– (1985) [11] Sato, Phys. Fluids 22 pp 1189– (1979) [12] Brackbill, J. Comp. Phys. 35 pp 426– (1980) [13] Dibiase, J. Comp. Phys. 24 pp 158– (1977) [14] Schnack, J. Comp. Phys. 35 pp 110– (1980) [15] A. A. Mirin, N. J. O’Neill, and A. G. Sgro, inProceedings of the US-Japan Workshop on 3D MHD Studies(Oak Ridge National Laboratory, Oak Ridge, TN, 1984), p. 88. [16] K. Watanabe and T. Uyama (private communication). [17] Pfersich, Nucl. Fusion 23 pp 1127– (1983) · doi:10.1088/0029-5515/23/9/002 [18] Gruber, Comput. Phys. Commun. 21 pp 323– (1981) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.