Cluster observations in the magnetosheath – Part 2: Intensity of the turbulence at electron scales

Abstract. The Cluster STAFF Spectral Analyser measures the magnetic and electric power spectral densities (PSD) δB² and δE² in the magnetosheath between 8 Hz and 4 kHz, i.e. between about the lower hybrid frequency and 10 times the proton plasma frequency. We study about 23 h of data on four different days. We do not consider the whistler waves and the electrostatic pulses (which are not always observed) but the underlying permanent fluctuations. Paper 1 (Mangeney et al., 2006) shows why the permanent PSD at a given frequency f depends strongly on the angle Θ_BV between the magnetic field B and the flow velocity V: this is observed for the electromagnetic (e.m.) fluctuations, δB² and δE_em², below the electron cyclotron frequency f_ce, and for the electrostatic (e.s.) fluctuations δE_es² at and above f_ce. This dependence is due to the Doppler shift of fluctuations which have a highly anisotropic distribution of the intensity of the wave vector k spectrum, and have a power law intensity ∝k^−ν with ν≃3 to 4. In the present paper, we look for parameters, other than Θ_BV, which control the intensity of the fluctuations. At f≃10 Hz, δB² and δE²_em increase when the solar wind dynamic pressure P_DYN^SW increases. When P_DYN^SW increases, the magnetosheath P_DYN^MS∝N V² also increases, so that the local Doppler shift (k.V) increases for a given k. If V increases, a given frequency f will be reached by fluctuations with a smaller k, which are more intense: the variations of δB² (10 Hz) with P_DYN^SW are only due to the Doppler shift in the spacecraft frame. We show that the e.m. spectrum in the plasma frame has an invariant shape I_1D∝A_em (kc/ω_pe)^−ν related to the electron inertial length c/ω_pe: the intensity A_em does not depend on P_DYN, nor on the electron to proton temperature ratio T_e/T_p, nor on the upstream bow shock angle θ_BN. Then, we show results of 3-D MHD numerical simulations of the magnetosheath plasma, which map the regions where the angle Θ_BV is ≃90°. The e.m. fluctuations are more intense in these magnetosheath regions, in the spacecraft frame where they are observed in the "whistler" range; and the e.s. fluctuations are less intense in these same regions, in the spacecraft frame where they are observed in the "ion acoustic" range. We conclude that the intensity of the permanent fluctuations in the e.m. range only depends on the Doppler shift, so that from day to day and from place to place in the magnetosheath, the k spectrum in the plasma frame has an invariant shape and a constant intensity. This is observed on scales ranging from kc/ω_pe≃0.3 (50 km) to kc/ω_pe≃30 (500 m), i.e. at electron scales smaller than the Cluster separation.