Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation
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.
KeywordsMadison Symmetric Torus (MST) Magnetohydrodyamic (MHD) Sine-Gordon toroidal Dynamic modeling Reversed-field pinch (RFP)
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 was provided by Public Authority of Applied Education and Training (Grant No. TS16-11).
- 4.Yagi, Y., Koguchi, H., Nilsson, J.-A.B., Bolzonella, T., Zanca, P., Sekine, S., Osakabe, K., Sakakita, H.: Phase and wall-locked modes found in a large reversed-field pinch machine. Jpn. J. Appl. Phys. 38, L780 (19990)Google Scholar
- 5.Hansen, A.K.: Kinematics of nonlinearly interacting MHD instabilities in a plasma. Ph.D. Thesis, University of Wisconsin -Madison (2000)Google Scholar
- 13.Almagri, A. F.: The effects of magnetic field errors on reversed-field pinch plasmas, Ph.D. thesis, University of Wisconsin-Madison (1990)Google Scholar
- 14.White, R., Fitzpatrick, R.: Effect of rotation and velocity shear on tearing layer stability in tokamak plasmas. Phys. Plasmas 22, (2015)Google Scholar
- 15.Fitzpatrick, R.: Phase locking of multi-helicity neoclassical tearing modes in Tokomak plasmas. Phys. Plasmas 22 (2015)Google Scholar
- 16.Xu Tao, Hu, Xi-Wei, Qi-Ming, Hu, Qing-Quan, Yu.: Locking of tearing modes by the error field. Chin. Phys. Lett. 22, 9 (2011)Google Scholar
- 17.Ivanov, N.V., Kakurin, A.M.: Locking of Small Magnetic Islands by Error Field in T-10 Tokamak. In: 38th EPS Conference on Plasma Physics (2011)Google Scholar
- 18.Fitzpatrick, R.: Linear and nonlinear response of a rotating tokomak plasma to a resonant error-field. Phys. Plasmas 21, (2014)Google Scholar
- 19.Scott, A.C.: Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press, Oxford (2006)Google Scholar