  Nonlinear interaction of a low density electron beam with a uniform plasma is
studied using two-dimensional particle-in-cell (PIC) simulations. We focus on
formation of coherent phase space structures in the case, when a wide
two-dimensional wave spectrum is driven unstable, and we also study how
nonlinear evolution of these structures is affected by the external magnetic
field. In the case of isotropic plasma, nonlinear buildup of filamentation
modes due to the combined effects of two-stream and oblique instabilities is
found to exist and growth mechanisms of secondary instabilities destroying the
BGK--type nonlinear wave are identified. In the weak magnetic field, the energy
of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction
goes predominantly to the short-wavelength upper-hybrid waves propagating
parallel to the magnetic field, whereas in the strong magnetic field the
spectral energy is transferred to the electrostatic whistlers with oblique
propagation.
