m=1 ideal internal kink modes in a line-tied screw pinch
- Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, and Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)
It is well known that the radial displacement of the m=1 internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where k{center_dot}B=0 [Rosenbluth, Dagazian, and Rutherford, Phys. Fluids 16, 1894 (1973)]. In a line-tied system, relevant to solar and astrophysical plasmas, the resonant surface is no longer a valid concept. It is then of interest to see how line-tying alters the aforementioned result for a periodic system. If the line-tied kink also produces a steep gradient, corresponding to a thin current layer, it may lead to strong resistive effects even with weak dissipation. Numerical solution of the eigenmode equations shows that the fastest growing kink mode in a line-tied system still possesses a jump in the radial displacement at the location coincident with the resonant surface of the fastest growing mode in the periodic counterpart. However, line-tying thickens the inner layer and slows down the growth rate. As the system length L approaches infinity, both the inner layer thickness and the growth rate approach the periodic values. In the limit of small {epsilon}{approx}B{sub {phi}}/B{sub z}, the critical length for instability L{sub c}{approx}{epsilon}{sup -3}. The relative increase in the inner layer thickness due to line-tying scales as {epsilon}{sup -1}(L{sub c}/L){sup 2.5}.
- OSTI ID:
- 20860217
- Journal Information:
- Physics of Plasmas, Vol. 13, Issue 9; Other Information: DOI: 10.1063/1.2336506; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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