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

The Cluster STAFF Spectral Analyser measures the magnetic and electric power spectral densities (PSD) delta B-2 and delta E-2 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 I (Mangeney et al., 2006) shows why the permanent PSD at a given frequency f depends strongly on the angle Theta(BV) between the magnetic field B and the flow velocity V: this is observed for the electromagnetic (e.m.) fluctuations, delta B-2 and delta E-em(2) below the electron cyclotron frequency f(ce), and for the electrostatic (e.s.) fluctuations delta E-es(2) 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 alpha k(-v) with v similar or equal to 3 to 4. In the present paper, we look for parameters, other than Theta(BV), which control the intensity of the fluctuations. At f similar or equal to 10Hz, delta B-2 and delta E-em(2) increase when the solar wind dynamic pressure P-DYN(SW) increases. When P-DYN(SW) increases, the magnetosheath P-DYN(MS)proportional to N V-2 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 delta B-2(10Hz) 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 proportional to)A(em)(kc/omega pe)(-v) related to the electron inertial length c/omega(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 theta(BN). Then, we show results of 3-D MHD numerical simulations of the magnetosheath plasma, which map the regions where the angle Theta(BV) is similar or equal to 90 degrees. 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/omega(pe)similar or equal to 0.3 (50km) to kc/omega(pe)similar or equal to 30 (500m), i.e. at electron scales smaller than the Cluster separation.