Simultaneous excitation of parametric decay cascades and of the oscillating two‐stream instability in one‐dimensional numerical simulations based on Zakharov's equations

Abstract

The excitation of a parametric decay cascade and of the oscillating two‐stream instability (OTSI) have been predicted earlier by one‐dimensional and two‐dimensional weak turbulence approximations for observations with the 430‐MHz radar for ionospheric modification experiments at Arecibo, for heights 1–2 km below the reflection height of the pump wave. For the same height range the present numerical simulations, using a version of the one‐dimensional driven and damped Zakharov system of equations, are shown to lead over a limited range of pump powers to the simultaneous excitation of a weak turbulence decay cascade and of the OTSI or modulational instability. The linearized form of the Zakharov equations is used to derive the functional dependence of the transfer of power from one Langmuir wave to another on the parameters of the two waves. Comparison of that function with the more correct version derived from kinetic theory was then used to guide the choice of the damping coefficient of ion acoustic waves. With that choice the simulations show that for a pump power that exceeds the threshold for excitation of the parametric decay instability by a factor less than about 3, the OTSI is not excited in the steady state which only shows the excitation of the parametric decay cascade. For pump powers that exceed the threshold power by a factor greater than about 3 but are not great enough to lead to a Langmuir condensate and ultimately to strong cavitational Langmuir turbulence, the simulations show the simultaneous excitation of a weak turbulence cascade and of the OTSI. These conclusions agree qualitatively with the conclusions reached on the basis of earlier weak turbulence approximations.