MHD Modeling of the Kink "Double-gradient" Branch of the Ballooning Instability in the Magnetotail

• We present a numerical investigation of the double-gradient mode, which is believed to be responsible for the magnetotail flapping oscillations the fast vertical oscillations of the Earth's magnetotail plasma sheet (quasiperiod similar to 100 - 200 s). It is known that this mode has an unstable solution in the region of the tailward-growing normal magnetic field component. The kink branch of the mode is the focus of our study. The instability is studied using the magnetotail near-equilibrium configuration, fixed by the approximate solution of the Grad-Shafranov equation. The linear three-dimensional numerical analysis is complemented with full 3-D MUD simulations. The results of our linearized MHD code agree with the theory, and the growth rate is found to be close to the peak value provided by an analytical estimate. Also, the eigenfunctions, calculated analytically, are very similar to the perturbations obtained numerically. The full 3D MHD simulations are initialized with the numerically relaxed magnetotail equilibrium, similar to the linear code initial condition. The calculations show that the double-gradient mode is excited in a region of small radii of the magnetic field lines curvature, which is in accordance with the analytical predictions. In contrast to the linearized MHD simulations, non-local interactions are involved; hence, the overall growth rate turns out to be close to the theoretical estimate averaged over the computational domain.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

NATURVETENSKAP  -- Fysik -- Astronomi, astrofysik och kosmologi (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Astronomy, Astrophysics and Cosmology (hsv//eng)

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