Title: Специализация: 510403 Физика магнитосферы и солнечно-земных связей
Author: ego
Last saved by: d.k.
Company: magnetosphere

Specialization: 010700/07 Physics of Earth and planets
Syllabus: 03 Physics of the Sun-Earth’s relations
Programme director: prof. V.S Semenov 
Earth’s Physics Department
Superwiser: prof. V.S Semenov 
Reviewer: prof. V.A. Sergeev

Kink and sausage modes of flapping oscillations in the Earth’s magnetotail.
D.I. Kubyshkina 

Flapping oscillations observed in the current sheet of the Earth’s magnetotail, represent rather slow waves propagating from the center to the flanks with a typical speed ~20-60 km/s, amplitude ~1-2R_e and quasiperiod ~2-10 minutes. The relevant model is based on double gradient of magnetic field: gradient of tangential (B_x) component along the normal (z) direction and normal component (B_z) along the x-direction [1]. Calculations were made for two different variants of initial disturbance to exclude its influence on the results.
By numerical calculations we get theoretical parameters (double gradient frequency, phase and groupe velocities, components of  the plasma speed and magnetic field vectors) which good correlate with experimental values.
In the framework of this model the rotation of the vector of magnetic field in the plane Z-Y as well as vector of plasma velocity is investigated to find differences between kink and sausage modes of the flapping oscillations. Were observed that rotation of the vectors does not depend on type of initial disturbance and  it is also shown that the speed of the rotation of the vector (v or B) gives the fundamental parameters of the model including double gradient frequency.
The theoretical results are compared to the flapping oscillations observed by space mission Themis on 03.05.2008 in the morning sector of the magnetotail. The rotation of the velocity vector simultaneously observed  on two spacecrafts of Themis mission corresponds to the kink mode of the flapping oscillations.
Obtained mechanism of the modes separating were analized on ability to withstand noise. It was shown that behavior of the speed vector is more invariable then magnetic field’s. By this fact we can explain why theoretical prediction of magnetic field vector rotation  was not found out in the experimental data.
Also we analized behavior of the speed vector in case of combined modes.
The results obtained show that data on rotation of v and B vectors can give important information about modes and characteristics of the flapping waves.

References
[1] Erkaev N.V.,. Semenov V.S, and Biernat H.K., Magnetic double-gradient instability and flapping waves in a current sheet, Phys. Rev. Lett., 99, 235003, doi:10.1103/PhysRevLett.99.235003, 2007;

The list of the publications 
1. Д.И. Кубышкина. Моды флэппинг-колебаний токового слоя в хвосте магнитосферы // Абстракты конференции Геофизика-2009
2. D.I. Kubyshkina, D.A. Sormakov, V.A. Sergeev, V.S. Semenov, N.V. Erkaev. Comparison of flapping oscillations observed by Themis with the double gradient model // Problems of Gepcosmos 8^th International Conference Book of abstracts, St. Petersburg, 2010, p.59-60
3. D.I. Kubyshkina, D.A. Sormakov. Kink and sausage modes of flapping oscillations in the current sheet of the magnetotail // Conference abstracts International Student Conference “Science and Progress” – SPb.: SOLO, 2010-204pp, ISBN 978-5-98340-243-0, p.47
4. D.I. Kubyshkina, D.A. Sormakov, V.S. Semenov, V.A. Sergeev. Kink and sausage modes of the flapping oscillations in the  magnetotail current sheet // Physics of Auroral Phenomena, 35th Apatity Seminar Book of abstracts, Apatity, 2012