Hall MHD model of the flapping oscillations of the magnetotail current sheet

Erkaev N.V.1, Semenov V.S.2, Biernat H.K.3, Rabetskaya O.I.4, Mezentsev A.V.4
  1. Institute of Computational Modelling , Krasnoyarsk, Russia
  2. S.-Petersburg State University, S.-Petersburg, Russia
  3. Space Research Institute, Graz, Austria
  4. Siberian Federal University, Krasnoyarsk, Russia

The Hall MHD model is applied to describe the flapping oscillation of the magnetotail current sheet with a
normal magnetic field component varying along the sheet. The initial undisturbed current sheet is considered
to have a one-dimensional structure, characterized by a Harris-like profile of the tangential magnetic field com-
ponent. The normal magnetic field component is assumed to have a weak linear increase towards Earth. Linear
current sheet oscillations are considered, and the corresponding eigenfrequencies are calculated as functions of
the wave number for the "kink" and "sausage" flapping wave modes. The obtained dispersion equation was
used to calculate the flapping wave disturbances induced by a moving source localized to the center of the
current sheet. In a framework of the Hall MHD model, the flapping eigenfrequency is enhanced for the waves
propagating along the electric current vector (towards dusk), and it is diminished for the opposite wave propa-
gation with respect to the current vector (towards dawn), in comparison to that in the ideal MHD model. The
dawn-dusk asymmetry of the flapping wave propagation appears due to the Hall MHD effects. This asymmetry
is pronounced stronger for thinner current sheets. This is related to the Doppler effect caused by the proton
current velocity.