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International audienceIn this paper, we study relativistic electron scattering by fast magnetosonic waves. We compareresults of test particle simulations and the quasi-linear theory for different spectra of waves toinvestigate how a fine structure of the wave emission can influence electron resonant scattering.We show that for a realistically wide distribution of wave normal angles h (i.e., when the dispersiondh  0:5), relativistic electron scattering is similar for a wide wave spectrum and for a spectrumconsisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations withquasi-linear theory show that for dh > 0:5, the quasi-linear approximation describes resonantscattering correctly for a large enough plasma frequency. For a very narrow h distribution (whendh  0:05), however, the effect of a fine structure in the wave spectrum becomes important. Inthis case, quasi-linear theory clearly fails in describing accurately electron scattering by fastmagnetosonic waves. We also study the effect of high wave amplitudes on relativistic electronscattering. For typical conditions in the earth’s radiation belts, the quasi-linear approximationcannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. Wediscuss various applications of the obtained results for modeling electron dynamics in the radiationbelts and in the Earth’s magnetotai

Relativistic electron scattering by magnetosonic waves: Effects of discrete wave emission and high wave amplitudes