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 n onlinear processes, including the closely related processes of scattering o ff thermal ions (STI) and a decay process in which the ion response is orga nized into a product ion acoustic wave. Calculations of the nonlinear growt h rates predict that the decay process should always dominate STI, creating two paradoxes. The first is that three independent computer simulation stu dies show STI proceeding, with no evidence for the decay at all. The second is that observations in space of type III solar radio bursts and Earth's f oreshock, which the simulations were intended to model, show evidence for t he decay proceeding but no evidence for STI. Resolutions to these paradoxes follow from the realization that a nonlinear process cannot proceed when i ts growth rate exceeds the minimum frequency of the participating waves, si nce the required collective response cannot be maintained and the waves can not respond appropriately, and that a significant number of e-foldings and wave periods must be contained in the time available. It is shown that appl ication of these ''collective'' and ''time scale'' constraints to the simul ations explains why the decay does not proceed in them, as well as why STI proceeds in specific simulations. This appears to be the first demonstratio n that collective constraints are important in understanding nonlinear phen omena. Furthermore, applying these constraints to space observations, it is predicted that the decay should proceed (and dominate STI) in type III sou rces and the high beam speed regions of Earth's foreshock for a specific ra nge of wave levels, with a possible role for STI alone at slightly higher w ave levels. Deeper in the foreshock, for slower beams and weaker wave level s, the decay and STI are predicted to become ineffective. Suggestions are g iven for future testing of the collective constraint and an explanation for why waves in space are usually much weaker than in the simulations. (C) 20 00 American Institute of Physics. [S1070-664X(00)02512-X].