Nonlinear model for coherent electric field structures in the magnetosphere

A new pseudo-three-dimensional electron hole in a magnetized plasma is possible when the low-frequency ion dynamics is taken into account. The newly found nonlinear Bernstein-Greene-Kruskal stationary solution, whose parallel phase velocity ranges between almost zero and the electron thermal speed, has the form of a cylinder that is tilted relative to the magnetic field. These structures are interpreted as three-dimensional electron holes coupled with hydrodynamic vortices, and provide a possible theoretical explanation for the POLAR and FAST satellite observations of coherent structures characterized by bipolar spikes of the parallel electric field and large perpendicular ion kinetic energies.