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Of particular interest for radio and hard X‐ray diagnostics of accelerated electrons during solar flares is the understanding of the basic nonlinear mechanisms regulating the relaxation of electron beams propagating in turbulent plasmas. In this work, it is shown that in addition to scattering of beam electrons, scattering of the beam‐generated Langmuir waves via for instance mode coupling can also result in broadening of the wave‐particle resonance. We obtain a resonance‐broadened version of weak turbulence theory with mode coupling to ion sound modes. Resonance broadening is presented here as a unified framework which can quantitatively account for the reduction and possible suppression of the beam instability due to background scattering of the beam electrons themselves or due to scattering of the beam‐generated Langmuir waves in fluctuating plasmas. Resonance broadening being essentially equivalent to smoothing of the electron phase space distribution is used to construct an intuitive physical picture for the stability of inverted populations of fast electrons that are commonly observed in situ to propagate in the solar wind.

Resonance broadening due to particle scattering and mode coupling in the quasi‐linear relaxation of electron beams