Numerical simulations of turbulent trapping in the weak beam–plasma instability

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Abstract
Numerical simulations of the weak beam–plasma instability were done in the turbulent regime where small‐scale trapping is a dominant feature of the instability, a regime with behavior not predicted by quasilinear theory. It occurs when the trapping frequency ν=(k2D)1/3 is larger than the growth rate γk of the instability. The results of the simulations were compared with those of a specific model of the turbulence, the so‐called ‘‘turbulent trapping’’ model, which gives precise formulas for the particle correlation functions, and predicts a growth rate well enhanced over the quasilinear value. It was found that the model gives accurate predictions for the correlation functions, and thus provides a good description of the turbulent structure of phase space. On the other hand, while growth rates were enhanced over the quasilinear values, the enhancements observed are smaller than expected from the quantitative predictions of the model.