Explosive Instabilities in Magnetized Plasmas: Implications for the Substorm Expansive Phase

Details Explosive Instabilities in Magnetized Plasmas: Implications for the Substorm Expansive Phase Explosive Instabilities in Magnetized Plasmas: Implications for the Substorm Expansive Phase

Dec 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufmsm51a0786d&link_type=abstract

American Geophysical Union, Fall Meeting 2001, abstract #SM51A-0786

Physics

2407 Auroral Ionosphere (2704), 2752 Mhd Waves And Instabilities, 2788 Storms And Substorms

Scientific paper

A number of plasma instabilities near the Earthward edge of the plasmasheet can be treated using a magnetohydrodynamic (MHD) description. In this work, we start with the Lagrangian of ideal MHD, which we expand up to third order in the plasma displacement. Treating perturbations as a change of coordinates proves to be very effective in this case. A second order perturbation yields the linear-MHD wave equation. Solutions of this equation provide us with the class of allowed plasma displacements. The second (W(2)) and the third order potential energy (W(3)) are then calculated to investigate stability of the plasma. In analogy with mechanics, where Lagrangian with zero second order and non-zero third order potential energy L=˙ {x}2+x^3 corresponds to explosive equation ⋰ {x}=x2, the case with the second order potential energy close to zero and the third order energy W(3)}>>W{(2) corresponds to an explosively unstable configuration. Several configurations are investigated, both analytically and numerically. However, our model only tries to answer the question of whether explosive instability is possible (probable). We do not try to describe the dynamics of the instability, since dynamical processes are likely beyond the scope of validity of MHD. The model is derived in general (curvilinear) coordinates and is therefore suitable for any smooth ambient magnetic field configuration where coordinates are defined x1 along field lines, x2 in the radial direction and x3 as x1 x x2. Cartesians coordinates can be treated as special case of curvilinear coordinates with metrics g= {diag}(1,1,1). This provides us with the way of studying stability of the Plasma Sheet without the need of detailed understanding of the nonlinear dynamics of the plasma.

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