Two-Dimensional Filamentary Magnetohydrodynamics, Current-Vortex Method

Y. Yatsuyanagi, T. Hatori1), T. Kato2) and T. Ebisuzaki3)

Graduate School of Human and Environmental Studies, Kyoto University, Sakyo, Kyoto 606-8501, Japan
1)Department of Information Science, Kanagawa University, Hiratsuka, Kanagawa 256-1293, Japan
2)Department of Applied Physics, Waseda University, Shinjuku, Tokyo 169-8555, Japan
3)RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan

A two-dimensional simulation model of the "magnetohydrodynamic (MHD)" vortex method, current-vortex method, is developed [1]. It is assumed that electric current and vorticity have discontinuous filamentary (point) distributions on the two-dimensional plane, and both the point electric current and the point vortex are confined in a filament. The spatial profiles of the electric current and the vorticity are determined by the sum of such filaments. Time development equations for a filament are obtained by integrating the two-dimensional MHD equations around the filament. Like the traditional vortex method, the current-vortex method uses the Biot-Savart integral to determine the velocity and the magnetic field from the distributions of the point electric current and the point vortex. It takes a considerable time to calculate the Biot-Savart integral in simulations. Thus a special-purpose computer, MDGRAPE-2, is used to accelerate the calculations of the Biot-Savart integral. We conclude that the current-vortex method reproduces the result obtained by the traditional MHD code.

References

[1] Y. Yatsuyanagi, T. Ebisuzaki, T. Hatori and T. Kato, Phys. Plasmas, 10 (2003) 3181.

This work was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientist.