MHD modeling of the double‐gradient (kink) magnetic instability

Abstract

[1] The paper presents the detailed numerical investigation of the "double-gradient mode," which is believed to be responsible for the magnetotail flapping oscillations-the fast vertical (normal to the layer) oscillations of the Earth's magnetotail plasma sheet with a quasiperiod 100-200 s. The instability is studied using the magnetotail near-equilibrium configuration. For the first time, linear three-dimensional numerical analysis is complemented with full 3-D MHD simulations. It is known that the "double-gradient mode" has unstable solutions in the region of the tailward growth of the magnetic field component, normal to the current sheet. The unstable kink branch of the mode is the focus of our study. Linear MHD code results agree with the theory, and the growth rate is found to be close to the peak value, provided by the analytical estimates. Full 3-D simulations are initialized with the numerically relaxed magnetotail equilibrium, similar to the linear code initial condition. The calculations show that current layer with tailward gradient of the normal component of the magnetic field is unstable to wavelengths longer than the curvature radius of the field line. The segment of the current sheet with the earthward gradient of the normal component makes some stabilizing effect (the same effect is registered in the linearized MHD simulations) due to the minimum of the total pressure localized in the center of the sheet. The overall growth rate is close to the theoretical double-gradient estimate averaged over the computational domain.

Numerical linearized MHD model of flapping oscillations

“…11, broaden gradually. This is in accordance with our previous findings, 34 stating that the magnetic field line curvature radius is a lower limit for the DG mode wavelength.…”

“…34,35 It is found out that numerical growth rates are close to the analytical prediction with x f ¼ max½x f ðxÞ for 2D simulations and x f ¼ hx f ðxÞi for 3D simulations, where angle brackets mean averaging. It was shown also that an instability does not evolve when curvature radius is too large (R c > L > k).…”

“…Plasmas 23, 062905 (2016) due to the interaction with the ionosphere. Threedimensional MHD simulations 34 reveal that the flapping frequency is a non-local quantity, which can be affected by changes in remote parts of the current sheet. Furthermore, in Ref.…”

“…22,23 A detailed discussion of the DG and other MHD [24][25][26] and kinetic [27][28][29][30][31][32][33] models of flapping oscillations is provided in our previous papers. 34,35 To avoid repetitions, here we just outline briefly the essential features of the DG model and its limitations.…”

“…The perturbations were found to be almost uniform on the x-coordinate, in support of the analytical assumptions. 34 Hence, the analytical limitations enumerated above are partly justified. However, several open questions remain and are addressed in the present paper: (a) Does the analytical model match the oscillating regime?…”