Patrick Robert

Bio: Patrick Robert is an academic researcher from École Polytechnique. The author has contributed to research in topics: Magnetosphere & Magnetopause. The author has an hindex of 19, co-authored 42 publications receiving 3023 citations. Previous affiliations of Patrick Robert include Centre national de la recherche scientifique.

Evidence of a Cascade and Dissipation of Solar-Wind Turbulence at the Electron Gyroscale

Abstract: We report the first direct determination of the dissipation range of magnetofluid turbulence in the solar wind at the electron scales. Combining high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectrum of turbulence and found two distinct breakpoints in the magnetic spectrum at 0.4 and 35 Hz, which correspond, respectively, to the Doppler-shifted proton and electron gyroscales, ${f}_{{\ensuremath{\rho}}_{p}}$ and ${f}_{{\ensuremath{\rho}}_{e}}$. Below ${f}_{{\ensuremath{\rho}}_{p}}$, the spectrum follows a Kolmogorov scaling ${f}^{\ensuremath{-}1.62}$, typical of spectra observed at 1 AU. Above ${f}_{{\ensuremath{\rho}}_{p}}$, a second inertial range is formed with a scaling ${f}^{\ensuremath{-}2.3}$ down to ${f}_{{\ensuremath{\rho}}_{e}}$. Above ${f}_{{\ensuremath{\rho}}_{e}}$, the spectrum has a steeper power law $\ensuremath{\sim}{f}^{\ensuremath{-}4.1}$ down to the noise level of the instrument. We interpret this as the dissipation range and show a remarkable agreement with theoretical predictions of a quasi-two-dimensional cascade into Kinetic Alfv\'en Waves (KAW).

Universality of Solar-Wind Turbulent Spectrum from MHD to Electron Scales

Abstract: To investigate the universality of magnetic turbulence in space plasmas, we analyze seven time periods in the free solar wind under different plasma conditions. Three instruments on Cluster spacecraft operating in different frequency ranges give us the possibility to resolve spectra up to 300 Hz. We show that the spectra form a quasiuniversal spectrum following the Kolmogorov's law $\ensuremath{\sim}{k}^{\ensuremath{-}5/3}$ at MHD scales, a $\ensuremath{\sim}{k}^{\ensuremath{-}2.8}$ power law at ion scales, and an exponential $\ensuremath{\sim}\mathrm{exp} [\ensuremath{-}\sqrt{k{\ensuremath{\rho}}_{e}}]$ at scales $k{\ensuremath{\rho}}_{e}\ensuremath{\sim}[0.1,1]$, where ${\ensuremath{\rho}}_{e}$ is the electron gyroradius. This is the first observation of an exponential magnetic spectrum in space plasmas that may indicate the onset of dissipation. We distinguish for the first time between the role of different spatial kinetic plasma scales and show that the electron Larmor radius plays the role of a dissipation scale in space plasma turbulence.

Plasma sheet instability related to the westward traveling surge

Abstract: The detailed analysis of an isolated dispersionless substorm is performed on the basis of field and particle data collected in situ by the geostationary satellite GEOS 2 and of data from ground-based instruments installed close to the GEOS 2 magnetic footprint. These data give evidence for (1) quasi-periodic variations of the magnetic field configuration, which is alternatively taillike and dipolelike, (2) in-phase oscillations of the flux of energetic electrons, which is high when the configuration is dipolelike and vice versa, (3) a gradient in the flux of energetic ions, which is, on the average, earthward but undergoes large fluctuations around this average direction, and (4) large transient fluctuations of the quasi-dc electric field, which reverses its direction from eastward to westward. It is shown that these results are consistent with the development of an instability which leads to a westward propagating “wave”. The source of the instability is the differential drift of energetic electrons and ions in a highly stressed magnetic field configuration (in a high β plasma). Evidence is given for a system of localized field-aligned currents flowing alternately earthward and equatorward at the leading and trailing edges of the westward propagating wave. This current system resulting from the temporal development of the instability produces the so-called Pi 2 pulsations, at the ionospheric level. The closure of this current system in the equatorial region leads to a current antiparallel to the tail current, and therefore to its reduction or cancellation. This reduction/cancellation of the tail current restores the dipole magnetic field (dipolarization) and generates a large westward directed induced electric field (injection). Hence, dipolarization and injection are the consequences of the instability. Finally, it is suggested that the westward traveling surge observed simultaneously by all-sky cameras, close to the magnetic field of GEOS 2, is the image of the instability in the equatorial region transmitted to the upper atmosphere by precipitating electrons.

Four‐point Cluster application of magnetic field analysis tools: The Curlometer

Abstract: [1] For the first time, the Cluster spacecraft have collected 3-D information on magnetic field structures at small to medium scales in the Earth's dayside magnetosphere. We focus here on the first application of the Curlometer (direct estimation of the electric current density from curl(B), using measured spatial gradients of the magnetic field) analysis technique. The applicability of this multipoint technique is tested, for selected events within the data set, in the context of various mission constraints (such as position, timing, and experimental accuracy). For the Curlometer, nonconstant spatial gradients over the spacecraft volume, time dependence, and measurement errors can degrade the quality of the estimate. The estimated divergence of the magnetic field can be used to monitor (indirectly) the effect of nonconstant gradients in the case of many magnetic field structures. For others, and at highly distorted spacecraft configurations, this test may not reflect the quality of the Curlometer well. The relative scales and relative geometry between the spacecraft array and the structures present, as well as measurement errors, all are critical to the quality of the calculation. We demonstrate that even when instrumental and other errors are known to contribute to the uncertainty in the estimate of the current, a number of current signatures within the magnetosphere can be plausibly determined in direction, if not absolute size. A number of examples show consistent currents at the magnetopause, both separate from, and nearby or in the cusp region. Field-aligned currents near the polar cap boundary are also estimated reliably. We also demonstrate one example of an anomalous current arising from the effect of a highly distorted spacecraft configuration.

A systematic study of ULF Waves Above FH+ from GEOS 1 and 2 Measurements and Their Relationships with proton ring distributions

Abstract: A detailed analysis of the ULF noise observed on the GEOS magnetic antennas in the frequency range ∼0.2'12 Hz has revealed the properties of structured emissions occurring just above the proton gyrofrequency whose existence was reported by Russell et al. (1970) and Gurnett (1976). These waves are observed in the vicinity of the geomagnetic equator at all L values between ∼4 and ∼8. They propagate in a direction perpendicular to the dc magnetic field. The waves consist of harmonically related monochromatic emissions. The fundamental frequency is generally of the order of the local proton gyrofrequency. Sometimes the fundamental and first harmonics are missing. If there is more than one fundamental frequency present, nonlinear coupling often occurs between the different emissions. The amplitudes of individual events vary from some tens of milligammas to some hundreds. Their duration ranges from some tens of minutes to some hours. Within the range of sensitivity of the detectors (10−2 γ Hz−1/2 at 1 Hz, 10−3 γ Hz−1/2) at 8 Hz the average probability of emission occurrence during a given hour is 12%, this number increases to ∼30% during the afternoon and in the pre-midnight sectors. Simultaneous observations of proton fluxes, as obtained from the two GEOS particle experiments show that these waves are often associated with distribution functions peaking at some energy (5 ≲ E ≲ 30 keV) for 90° pitch angle particles. This ring-like distribution provides the energy source for the excitation of non-resonant (k∥ = 0) instabilities near nFH+ (n = running number). A theoretical model is presented that qualitatively explains the main characteristics of the observed waves.

Current disruption in the Earth's magnetosphere: Observations and models

Abstract: Observations and models of current disruption in the Earth's magnetosphere are briefly reviewed. At the approach of current disruption onset, the cross-tail current sheet shows a rapid growth in the current density, a large upsurge in the duskward ion bulk speed to nearly the ion thermal speed, an increase in the plasma pressure and its isotropy, a rise in the plasma beta, and a decrease in the current sheet thickness to a length scale comparable to the thermal ion gyroradius. During current disruption, there are (1) large changes in the local magnetic and electric fields, (2) significant magnetic and electric fluctuations over a broad frequency range, (3) magnetic field-aligned counterstreaming electron beams, (4) ion energization perpendicular to the magnetic field, and (5) reduction in the cross-tail current by an amount similar to that built up during the growth phase. Observations further indicate that regions of local reversal of the north-south magnetic field component are not necessarily sites of intense particle energization. Remote sensing of disruption activities shows that at least some current disruptions are not caused by a disturbance propagating earthward from the tail beyond 10 RE downstream. The timescale involved is comparable to or shorter than the ion gyroperiod. Current disruption thus has spatial and temporal scales outside the MHD regime. Several models for current disruption are briefly discussed. Two roles are considered for the cross-field current instability proposed for current disruption. It can provide anomalous resistivity for magnetic reconnection as advocated by the traditional viewpoint or act singly to instigate global changes of the magnetosphere during the initial substorrn expansion phase. The latter role is elaborated by showing that the instability may modify significantly the local current density and any such process will alter the force equilibrium in the current sheet and give rise to an efficient plasma and energy transport on a global scale. Furthermore, such a process can generate field-aligned current with intensity comparable to those associated with an auroral breakup arc at substorrn expansion onset. This scenario leads to a new emphasis that in addition to magnetic reconnection, rapid conversion of magnetic energy into particle energy in magnetotail systems may take place without a magnetic X line or separatrix playing the key role in energy conversion.

Potential waves for relativistic electron scattering and stochastic acceleration during magnetic storms

Abstract: The possibility of electron stochastic energization to relativisitic energies (≥ 1 MeV) via resonant wave-particle interactions during a magnetic storm is explored. The minimum electron energy Emin for cyclotron resonant interaction with various electromagnetic waves is calculated for conditions representative of storm-times. Since Emin > 1 MeV for resonance with L-mode ion cyclotron waves, intense stormtime EMIC waves could contribute to relativistic electron loss, but not acceleration. Inside the plasmapause whistler mode waves, and highly oblique magnetosonic waves near the lower hybrid frequency, can resonate with electrons over the important energy range from ∼ 100 keV to ∼ 1 MeV. In low density regions outside the plasmapause, the whistler, RX, LO and Z modes can resonate with electrons over a similar energy range. These waves have the potential to contribute to the stochastic acceleration of electrons up to relativistic energies during magnetic storms.

Universality of Solar-Wind Turbulent Spectrum from MHD to Electron Scales

Abstract: To investigate the universality of magnetic turbulence in space plasmas, we analyze seven time periods in the free solar wind under different plasma conditions. Three instruments on Cluster spacecraft operating in different frequency ranges give us the possibility to resolve spectra up to 300 Hz. We show that the spectra form a quasiuniversal spectrum following the Kolmogorov's law $\ensuremath{\sim}{k}^{\ensuremath{-}5/3}$ at MHD scales, a $\ensuremath{\sim}{k}^{\ensuremath{-}2.8}$ power law at ion scales, and an exponential $\ensuremath{\sim}\mathrm{exp} [\ensuremath{-}\sqrt{k{\ensuremath{\rho}}_{e}}]$ at scales $k{\ensuremath{\rho}}_{e}\ensuremath{\sim}[0.1,1]$, where ${\ensuremath{\rho}}_{e}$ is the electron gyroradius. This is the first observation of an exponential magnetic spectrum in space plasmas that may indicate the onset of dissipation. We distinguish for the first time between the role of different spatial kinetic plasma scales and show that the electron Larmor radius plays the role of a dissipation scale in space plasma turbulence.

Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas

Abstract: An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

A synthesis of magnetospheric substorm models

Abstract: Three decades of research in magnetospheric substorms has not led to a general consensus view of the substorm process. Several substorm models, mostly phenomenological, are presently under consideration. These competing models, each being justifiable on the basis of certain features of a substorm, have major differences as well as similarities among them. A synthesis substorm model is desirable, as first suggested by Siscoe (1986). In this paper we construct a coherent description of substorm development by extracting some important components from these existing models. The scenario of the synthesis model includes the ionospheric influence on substorm expansion onset, current disruptions leading to convection surges and tailward propagating rarefaction waves, wave-induced precipitation, local time expansion of the disturbance region via velocity-shear-related instabilities, plasma sheet heating by resonant absorption of hydromagnetic waves, and the formation of magnetic reconnection domains. This synthesis represents one possible way to integrate the different existing models coherently.