The description of the turbulent spectrum of magnetic fluctuations in the solar wind in the kinetic range of scales is not yet completely established. Here, we perform a statistical study of 100 spectra measured by the STAFF instrument on the Cluster mission, which allows us to resolve turbulent fluctuations from ion scales down to a fraction of electron scales, i.e., from ~102?km to ~300?m. We show that for k ⊥ρ e [0.03, 3] (which corresponds approximately to the frequency in the spacecraft frame f [3, 300]?Hz), all the observed spectra can be described by a general law E(k ⊥)∝k –8/3 ⊥exp (– k ⊥ρ e ), where k ⊥ is the wavevector component normal to the background magnetic field and ρ e the electron Larmor radius. This exponential tail found in the solar wind seems compatible with the Landau damping of magnetic fluctuations onto electrons.
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