Role of Collective Effects in Dominance of Scattering Off Thermal Ions Over Langmuir Wave Decay: Analysis, Simulations, and Space Applications

Langmuir waves driven to high levels by beam instabilities are subject to nonlinear processes, including the closely related processes of scattering off thermal ions (STI) and a decay process in which the ion response is organized into a product ion acoustic wave. Calculations of the nonlinear growth rates predict that the decay process should always dominate STI, creating two paradoxes. The first is that three independent computer simulation studies show STI proceeding, with no evidence for the decay at all. The second is that observations in space of type 3 solar radio bursts and Earth's foreshock, which the simulations were intended to model, show evidence for the decay proceeding but no evidence for STI. Resolutions to these paradoxes follow from the realization that a nonlinear process cannot proceed when its growth rate exceeds the minimum frequency of the participating waves, since the required collective response cannot be maintained and the waves cannot respond appropriately, and that a significant number of e-foldings and wave periods must be contained in the time available. It is shown that application of these 'collective' and 'time scale' constraints to the simulations explains why the decay does not proceed in them, as well as why STI proceeds in specific simulations. This appears to be the first demonstration that collective constraints are important in understanding nonlinear phenomena. Furthermore, applying these constraints to space observations, it is predicted that the decay should proceed (and dominate STI) in type 3 sources and the high beam speed regions of Earth's foreshock for a specific range of wave levels, with a possible role for STI alone at slightly higher wave levels. Deeper in the foreshock, for slower beams and weaker wave levels, the decay and STI are predicted to become ineffective. Suggestions are given for future testing of the collective constraint and an explanation for why waves in space are usually much weaker than in the simulations.