Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

J. S. Sarff; S. Assadi; A. F. Almagri; M. Cekic; D. J. Den Hartog; G. Fiksel; S. A. Hokin; H. Ji; S. C. Prager; W. Shen; K. L. Sidikman; M. R. Stoneking

doi:10.1063/1.860741

Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

J. S. Sarff, S. Assadi, A. F. Almagri, M. Cekic, D. J. Den Hartog, G. Fiksel, S. A. Hokin, H. Ji, S. C. Prager, W. Shen, K. L. Sidikman, M. R. Stoneking

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Abstract

Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in "k-space." The strength of nonlinear three-wave interactions satisfying the sum rules m₁+m₂=m₃ and n ₁+n₂=n₃ is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the "crash" phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.

Original language	English (US)
Pages (from-to)	2540-2545
Number of pages	6
Journal	Physics of Fluids B
Volume	5
Issue number	7
DOIs	https://doi.org/10.1063/1.860741
State	Published - 1993

All Science Journal Classification (ASJC) codes

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
General Physics and Astronomy
Fluid Flow and Transfer Processes

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10.1063/1.860741

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@article{da2e44b4dd374eeabd69777c723e21a4,

title = "Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus",

abstract = "Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in {"}k-space.{"} The strength of nonlinear three-wave interactions satisfying the sum rules m1+m2=m3 and n 1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the {"}crash{"} phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.",

author = "Sarff, {J. S.} and S. Assadi and Almagri, {A. F.} and M. Cekic and {Den Hartog}, {D. J.} and G. Fiksel and Hokin, {S. A.} and H. Ji and Prager, {S. C.} and W. Shen and Sidikman, {K. L.} and Stoneking, {M. R.}",

year = "1993",

doi = "10.1063/1.860741",

language = "English (US)",

volume = "5",

pages = "2540--2545",

journal = "Physics of Fluids B",

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publisher = "American Institute of Physics Publising LLC",

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TY - JOUR

T1 - Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

AU - Sarff, J. S.

AU - Assadi, S.

AU - Almagri, A. F.

AU - Cekic, M.

AU - Den Hartog, D. J.

AU - Fiksel, G.

AU - Hokin, S. A.

AU - Ji, H.

AU - Prager, S. C.

AU - Shen, W.

AU - Sidikman, K. L.

AU - Stoneking, M. R.

PY - 1993

Y1 - 1993

N2 - Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in "k-space." The strength of nonlinear three-wave interactions satisfying the sum rules m1+m2=m3 and n 1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the "crash" phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.

AB - Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in "k-space." The strength of nonlinear three-wave interactions satisfying the sum rules m1+m2=m3 and n 1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the "crash" phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.

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JO - Physics of Fluids B

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Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

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