Ideal m=1 internal kink mode in line-tied screw pinch

Details Ideal m=1 internal kink mode in line-tied screw pinch Ideal m=1 internal kink mode in line-tied screw pinch

Apr 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aps..apr.d1037h&link_type=abstract

American Physical Society, APS April Meeting, April 22-26, 2006, abstract #D1.037

Astronomy and Astrophysics

Astrophysics

Scientific paper

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 .B=0. 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 result for a periodic system. If the line-tied kink also produces a steep gradient, it may lead to strong heating even with weak dissipation. Numerical solution of the eigenmode equations finds 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 reduces 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 ɛ˜Bφ/Bz, the critical length for instability Lc˜1/3̂. The relative increase in the inner layer thickness due to line-tying scales as (1/ɛ)(Lc/L)^2.5. The nonlinear equilibrium after the onset of the kink instability is of greater interest. Work is in progress to solve the new equilibrium by a magnetofrictional relaxation method. To avoid reconnection due to numerical resistivity, we take a Lagrangian approach formulated in Clebsch coordinates.

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