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Nonlinear Dynamics

, Volume 93, Issue 4, pp 1989–2001 | Cite as

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

  • Hameed K. Ebraheem
  • Nizar J. Alkhateeb
  • Ebraheem K. Sultan
Original Paper

Abstract

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.

Keywords

Madison Symmetric Torus (MST) Magnetohydrodyamic (MHD) Sine-Gordon toroidal Dynamic modeling Reversed-field pinch (RFP) 

Notes

Acknowledgements

The authors would like to thank S. C. Prager, and A. F. Almagri from the MST scientific research group at University of Wisconsin-Madison for providing the experimental data taken at MST.

Funding

Funding was provided by Public Authority of Applied Education and Training (Grant No. TS16-11).

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electronic Engineering Technology, College of Technological Studies (CTS)The Public Authority of Applied Education and Training (PAAET)ShuwiekhKuwait

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