3D stability of magnetotail Bz hump configurations

<p>Using three-dimensional MHD simulations, we explore the stability of magnetotail configurations that include a local enhancement of B_z (a ``B_z hump"), focusing on configurations that were found previously to be unstable in 2-D, neglecting cross-tail (y) variations as well as a cross-tail magnetic field component B_y. Not surprisingly, the 2-D unstable configurations were also found unstable in 3-D, developing 3-D structure after an initial rise as in 2-D. This is consistent with the fact that the selected B_z hump configurations are characterized also by a local tailward decrease of field line entropy, which has been found to govern ballooning/interchange (B/I) instability(Schindler and Birn, 2004). The evolution of the maximum electric field of the unstable 3-D modes showed an early exponential growth, whish was only modestly faster than the 2-D mode. This might suggest that the unstable ballooning regime extends from k_y \to \infty (proper ballooning modes) over finite k_y even to k_y = 0, at least for some equilibria. When the 3-D modes had evolved they grew significantly faster than the 2-D modes, associated with evolving into several narrow beams.&nbsp;The 3-D modes did not approach stable final configurations.</p> <p>The final 2-D configurations approached from the unstable ones were found to be unstable in 3-D. These findings are again consistent with the fact that the 2-D evolution, governed by ideal MHD, did not alter the characteristics of the entropy function.</p> <p>&nbsp;</p>