ALBERT

Description: We present a numerical study of the generation and evolution of a mixed layer in a stably stratified layer of Boussinesq fluid. We use an external forcing in the equation of motion to model the experimental situation where the mechanical energy input is due to an oscillating grid. The results of 2D and 3D numerical simulations indicate that the basic mechanism for the entrainment is the advection of the temperature field. This advection tends to produce horizontally thin regions of small temperature vertical gradients (jets) where the hydrodynamics forces are nearly zero. At the bottom of these structures, the buoyancy brakes the vertical motions. The jets are also characterized by the presence of very short horizontal scales where the thermal diffusion time turn out to be comparable with the dynamics time. As a result, the temperature field is well mixed in a few dynamics times. This process stops when the mechanical energy injected becomes comparable with the energy dissipated by viscosity.

Description: High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD). The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.

Description: The time domain sampler (TDS) experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency fpi and smaller than or of the order of the electron plasma frequency fpe, TDS observed three kinds of electrostatic (e.s.) waves: coherent wave packets of Langmuir waves with frequencies f ~ fpe, coherent wave packets with frequencies in the ion acoustic range fpi 〈 f 〈 fpe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF) ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λD. The electric field in the isolated electrostatic structures (IES) and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ~ 25λD, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations). The type (wave packet or IES) of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.Key words. Interplanetary physics (plasma waves and turbulence; solar wind plasma). Space plasma physics (electrostatic structures).

Description: We analyse the power spectral density δB2 and δE2 of the magnetic and electric fluctuations measured by Cluster 1 (Rumba) in the magnetosheath during 23 h, on four different days. The frequency range of the STAFF Spectral Analyser (f=8 Hz to 4 kHz) extends from about the lower hybrid frequency, i.e. the electromagnetic (e.m.) range, up to about 10 times the proton plasma frequency, i.e. the electrostatic (e.s.) range. In the e.m. range, we do not consider the whistler waves, which are not always observed, but rather the underlying, more permanent fluctuations. In this e.m. range, δB2 (at 10 Hz) increases strongly while the local angle ΘBV between the magnetic field B and the flow velocity V increases from 0° to 90°. This behaviour, also observed in the solar wind at lower frequencies, is due to the Doppler effect. It can be modelled if we assume that, for the scales ranging from kc/ωpe≃0.3 to 30 (c/ωpe is the electron inertial length), the intensity of the e.m. fluctuations for a wave number k (i) varies like k−ν with ν〉≃3, (ii) peaks for wave vectors k perpendicular to B like |sinθkB|µ with µ〉≃100. The shape of the observed variations of δB2 with f and with ΘBV implies that the permanent fluctuations, at these scales, statistically do not obey the dispersion relation for fast/whistler waves or for kinetic Alfvén waves: the fluctuations have a vanishing frequency in the plasma frame, i.e. their phase velocity is negligible with respect to V (Taylor hypothesis). The electrostatic waves around 1 kHz behave differently: δE2 is minimum for ΘBV〉≃90°. This can be modelled, still with the Doppler effect, if we assume that, for the scales ranging from k λDe〉≃0.1 to 1 (λDe is the Debye length), the intensity of the e.s. fluctuations (i) varies like k−ν with ν〉≃4, (ii) peaks for k parallel to B like |cosθkB|µ with µ〉≃100. These e.s. fluctuations may have a vanishing frequency in the plasma frame, or may be ion acoustic waves. Our observations imply that the e.m. frequencies observed in the magnetosheath result from the Doppler shift of a spatial turbulence frozen in the plasma, and that the intensity of the turbulent k spectrum is strongly anisotropic, for both e.m. and e.s. fluctuations. We conclude that the turbulence has strongly anisotropic k distributions, on scales ranging from kc/ωpe≃0.3 (50 km) to kλDe≃1 (30 m), i.e. at electron scales, smaller than the Cluster separation.

Description: Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earth's magnetosheath, the ISEE 1-2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2fp) ≃ 0.5 – 4 × 10–9 rad2/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to1RE) just downstream of the shock ramp, and close to the magnetopause.

Description: 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 ΘBV between the magnetic field B and the flow velocity V: this is observed for the electromagnetic (e.m.) fluctuations, δB2 and δEem2, below the electron cyclotron frequency fce, and for the electrostatic (e.s.) fluctuations δEes2 at and above fce. 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 ΘBV, which control the intensity of the fluctuations. At f≃10 Hz, δB2 and δE2em increase when the solar wind dynamic pressure PDYNSW increases. When PDYNSW increases, the magnetosheath PDYNMS∝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 PDYNSW 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 I1D∝Aem (kc/ωpe)−ν related to the electron inertial length c/ωpe: the intensity Aem does not depend on PDYN, nor on the electron to proton temperature ratio Te/Tp, nor on the upstream bow shock angle θBN. Then, we show results of 3-D MHD numerical simulations of the magnetosheath plasma, which map the regions where the angle ΘBV 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/ωpe≃0.3 (50 km) to kc/ωpe≃30 (500 m), i.e. at electron scales smaller than the Cluster separation.

Description: We investigate the spectral shape, the anisotropy of the wave vector distributions and the anisotropy of the amplitudes of the magnetic fluctuations in the Earth's magnetosheath within a broad range of frequencies [10−3, 10] Hz which corresponds to spatial scales from ~10 to 105 km. We present the first observations of a Kolmogorov-like inertial range of Alfvénic fluctuations δB2⊥}~f−5/3 in the magnetosheath flanks, below the ion cyclotron frequency fci. In the vicinity of fci, a spectral break is observed, like in solar wind turbulence. Above the break, the energy of compressive and Alfvénic fluctuations generally follows a power law with a spectral index between −3 and −2. Concerning the anisotropy of the wave vector distribution, we observe a clear change in its nature in the vicinity of ion characteristic scales: if at MHD scales there is no evidence for a dominance of a slab (kł〉〉k⊥) or 2-D (k⊥〉〉kł) turbulence, above the spectral break, (f〉fci, kc/ωpi〉1) the 2-D turbulence dominates. This 2-D turbulence is observed in six selected one-hour intervals among which the average ion β varies from 0.8 to 10. It is observed for both the transverse and compressive magnetic fluctuations, independently on the presence of linearly unstable modes at low frequencies or Alfvén vortices at the spectral break. We then analyse the anisotropy of the magnetic fluctuations in a time dependent reference frame based on the field B and the flow velocity V directions. Within the range of the 2-D turbulence, at scales [1,30]kc/ωpi, and for any β we find that the magnetic fluctuations at a given frequency in the plane perpendicular to B have more energy along the B×V direction. This non-gyrotropy of the fluctuations at a fixed frequency is consistent with gyrotropic fluctuations at a given wave vector, with k⊥〉〉kł, which suffer a different Doppler shift along and perpendicular to V in the plane perpendicular to B.

Description: The solar wind properties depend on λ, the heliomagnetic latitude with respect to the heliospheric current sheet (HCS), more than on the heliographic latitude. We analyse the wind properties observed by Wind at 1 AU during about 2.5 solar rotations in 1995, a period close to the last minimum of solar activity. To determine λ, we use a model of the HCS which we fit to the magnetic sector boundary crossings observed by Wind. We find that the solar wind properties mainly depend on the modulus |λ|. But they also depend on a local parameter, the total pressure (magnetic pressure plus electron and proton thermal pressure). Furthermore, whatever the total pressure, we observe that the plasma properties also depend on the time: the latitudinal gradients of the wind speed and of the proton temperature are not the same before and after the closest HCS crossing. This is a consequence of the dynamical stream interactions. In the low pressure wind, at low |λ|, we find a clear maximum of the density, a clear minimum of the wind speed and of the proton temperature, a weak minimum of the average magnetic field strength, a weak maximum of the average thermal pressure, and a weak maximum of the average β factor. This overdense sheet is embedded in a density halo. The latitudinal thickness is about 5° for the overdense sheet, and 20° for the density halo. The HCS is thus wrapped in an overdense sheet surrounded by a halo, even in the non-compressed solar wind. In the high-pressure wind, the plasma properties are less well ordered as functions of the latitude than in the low-pressure wind; the minimum of the average speed is seen before the HCS crossing. The latitudinal thickness of the high-pressure region is about 20°. Our observations are qualitatively consistent with the numerical model of Pizzo for the deformation of the heliospheric current sheet and plasma sheet.Key words: Interplanetary physics (solar wind plasma)

Description: The STAFF-SC observations complemented by the data from other instruments on Cluster spacecraft were used to study the main properties of magnetospheric lion roars: sporadic bursts of whistler emissions at f~0.1–0.2fe where fe is the electron gyrofrequency. Magnetospheric lion roars are shown to be similar to the emissions in the magnetosheath while the conditions for their generation are much less favorable: the growth rate of the cyclotron temperature anisotropy instability is much smaller due to a smaller number of the resonant electrons. This implies a nonlinear mechanism of generation of the observed wave emissions. It is shown that the observed whistler turbulence, in reality, consists of many nearly monochromatic wave packets. It is suggested that these structures are nonlinear Gendrin's whistler solitary waves. Properties of these waves are widely discussed. Since the group velocity of Gendrin's waves is aligned with the magnetic field, these well guided wave packets can propagate through many magnetic "bottles" associated with mirror structures, without being trapped.

Description: We analyse the fluctuations of the electron density and of the magnetic field in the Earth's magnetosheath to identify the waves observed below the proton gyrofrequency. We consider two quiet magnetosheath crossings i.e. 2 days characterized by small-amplitude waves, for which the solar wind dynamic pressure was low. On 2 August 1978 the spacecraft were in the outer magnetosheath. We compare the properties of the observed narrow-band waves with those of the unstable linear wave modes calculated for an homogeneous plasma with Maxwellian electron and bi-Maxwellian (anisotropic) proton and alpha particle distributions. The Alfvén ion cyclotron (AIC) mode appears to be dominant in the data, but there are also density fluctuations nearly in phase with the magnetic fluctuations parallel to the magnetic field. Such a phase relation can be explained neither by the presence of a proton or helium AIC mode nor by the presence of a fast mode in a bi-Maxwellian plasma. We invoke the presence of the helium cut-off mode which is marginally stable in a bi-Maxwellian plasma with α particles: the observed phase relation could be due to a hybrid mode (proton AIC+helium cut-off ) generated by a non-Maxwellian or a non-gyrotropic part of the ion distribution functions in the upstream magnetosheath. On 2 September 1981 the properties of the fluctuations observed in the middle of the magnetosheath can be explained by pure AIC waves generated by protons which have reached a bi-Maxwellian equilibrium. For a given wave mode, the phase difference between B\Vert and the density is sensitive to the shape of the ion and electron distribution functions: it can be a diagnosis tool for natural and simulated plasmas.