Scaling of the Electron Dissipation Range of Solar Wind Turbulence

Abstract

Electron scale solar wind turbulence has attracted great interest in recent years. Clear evidences have been given from the Cluster data that turbulence is not fully dissipated near the proton scale but continues cascading down to the electron scales. However, the scaling of the energy spectra as well as the nature of the plasma modes involved at those small scales are still not fully determined. Here we survey 10 years of the Cluster search-coil magnetometer (SCM) waveforms measured in the solar wind and perform a statistical study of the magnetic energy spectra in the frequency range [1, 180]Hz. We show that a large fraction of the spectra exhibit clear breakpoints near the electron gyroscale ρ e , followed by steeper power-law like spectra. We show that the scaling below the electron breakpoint cannot be determined unambiguously due to instrumental limitations that will be discussed in detail. We compare our results to those reported in other studies and discuss their implication on the physical mechanisms and the theoretical modeling of energy dissipation in the SW.

Ideal MHD turbulence: the inertial range spectrum with collisionless dissipation

“…Indications for exponential spectral decays have been found in solar wind [7] and Earth's foreshock [32] as inferred from CLUSTER magnetic fields at high frequencies f f exp ≫ f 2 at f exp ∼ 10 2 Hz, roughly two orders of magnitude above f 2 . Identifying f exp ≈ f (λ e ), the inferred solar wind density N sw ∼ f 2 λ e ≈ 10 cm −3 agrees conveniently with measured average densities.…”

“…Strictly spoken, Taylor's hypothesis applies to V = V sw + v gr , with v gr the eddy group velocity. Any v gr > 0 shifts the frequency spectrum up into the dissipation range, causing modification of the spectrum to the observed power law (see Figure 1) and the foreshock spectrum [32]. For instance, the power law ∼ f −3 could result from shifting the K-range up by a turbulent flow-parallel veloc-…”

“…Additional sources of turbulence are instabilities and internal interactions in the flow, generating spectral anisotropy and modifying eddies and clusters of turbulent waves. One does not expect that observations of solar wind turbulence yield any ideal spectra of stationary homogeneous turbulence when applying the Taylor hypothesis that all the eddies in the flow are simply convected downstream (see discussion in Sahraoui et al [32]). …”

“…The IK-like range is mapped less clearly with varying slopes ranging from extremely flat ∼ k −1 up to IK as, for instance, indicated in the CLUSTER observation in Figure 1 of Alexandrova et al [7], Horbury et al [24] and more pronounced in the MESSENGER/Ulysses observations [26] where the slope found was ∼ − 5 4 . At the high frequency end the spectrum enters a dissipation range, at 0.5 Hz < f < 0.8 Hz in Figure 1, still power law though from case to case exhibiting varying slopes −3 [e.g., 26,32], sometimes even much steeper. It was found from CLUSTER [7,32] that at frequencies f > 10 Hz (corresponding to electron gyro-or inertial scales) the spectral decay becomes exponential indicating takeover of pure dissipation.…”

“…At the high frequency end the spectrum enters a dissipation range, at 0.5 Hz < f < 0.8 Hz in Figure 1, still power law though from case to case exhibiting varying slopes −3 [e.g., 26,32], sometimes even much steeper. It was found from CLUSTER [7,32] that at frequencies f > 10 Hz (corresponding to electron gyro-or inertial scales) the spectral decay becomes exponential indicating takeover of pure dissipation. Originally, dissipation was attributed to ion-cyclotron damping (e.g., in Goldstein and Roberts 23; Zhou et al 3) of magnetized ions, implying the magnetized-ion range extending in frequency substantially beyond the observed dissipation range in Figure 1.…”