"Nonlinear theory of mirror (diamagnetic) instability near its excitation threshold"
Corresponding member of RAS - Kuznetsov E.A. ( FI RASm Moscow).
Abstract:
It is demonstrated that near threshold of mirror instability the main
contribution to the quadratic nonlinearity is connected with
perpendicular pressure. We derive the three-dimensional equation which
describes the weakly nonlinear behavior of the
system. This equation turns out to be pseudodifferential and can be
related to the gradient type. As a consequence the
corresponding free energy decreases in time providing a blow-up
appearance of magnetic holes. Near singular
time we define self-similar asymptotics of
the magnetic field fluctuations which are in qualitative agreement with
the one-dimensional numerical simulations.
Presented theory explains many observable peculiarities of magnetic
holes in the Earth magnetosheath.