Generation of electrostatic nonlinear wave structures

The development of the electron sound instability driven by warm ion beams propogating along the magnetic field lines in the Earths magnetotail is examined in the weak nonlinear approximation. It is shown that the instability evolution can be described with the Korteveg-de Vris equation involving a weak wave growth and dumping due to resonance wave particle interactions. Analytical estimates and numerical calculations show the existence of quasi-stationary solutions in the form of solitary and nonlinear periodic waves with amplitudes of the order of experimentally observed ≈10−3 ÷ 10−4V/m.