| ABSTRACT
It is well known that a Bernstein-Greene-Kruskal
(BGK) mode can be easily constructed as an exact nonlinear solution of the
one dimensional Vlasov-Poisson equation for a plasma. BGK modes have been used
to explain electrostatic structures observed in space. However, some three
dimensional (3D) features were also observed in these structures. For a long
time, there has not been much effort in trying to construct exact 3D or 2D
BGK modes. A solution for an infinitely strong magnetic field case has been
constructed under the guiding center approximation, but there have been questions
about the existence of solutions in a 3D unmagnetized plasma. We showed recently
for such case that a spherically symmetric solution can indeed be constructed
if it depends on energy as well as angular momentum. We have also constructed
2D BGK modes with cylindrical symmetry for the case with a finite magnetic
guide field. Some comparisons with observations will be shown.
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