Multi-spacecraft measurement of anisotropic power levels and scaling in solar wind turbulence

Measurements by the four Cluster spacecraft in the solar wind are used to determine quantitatively the field-aligned anisotropy of magnetohydrodynamic inertial range turbulence power levels and spectral indexes. We find, using time-lagged second order structure functions, that the spectral index is near 2 around the field-parallel direction, which is consistent with a "critical balance" turbulent cascade. Solar wind fluctuations are found to be anisotropic with power mainly in wavevectors perpendicular to the mean field, where the spectral index is around 5/3

Ion kinetic energy conservation and magnetic field strength constancy in multi-fluid solar wind Alfv\'enic turbulence

We investigate properties of the plasma fluid motion in the large amplitude low frequency fluctuations of highly Alfv\'enic fast solar wind. We show that protons locally conserve total kinetic energy when observed from an effective frame of reference comoving with the fluctuations. For typical properties of the fast wind, this frame can be reasonably identified by alpha particles, which, owing to their drift with respect to protons at about the Alfv\'en speed along the magnetic field, do not partake in the fluid low frequency fluctuations. Using their velocity to transform proton velocity into the frame of Alfv\'enic turbulence, we demonstrate that the resulting plasma motion is characterized by a constant absolute value of the velocity, zero electric fields, and aligned velocity and magnetic field vectors as expected for unidirectional Alfv\'enic fluctuations in equilibrium. We propose that this constraint, via the correlation between velocity and magnetic field in Alfv\'enic turbulence, is at the origin of the observed constancy of the magnetic field: while the constant velocity corresponding to constant energy can be only observed in the frame of the fluctuations, the correspondingly constant total magnetic field, invariant for Galilean transformations, remains the observational signature, in the spacecraft frame, of the constant total energy in the Alfv\'en turbulence frame.Comment: 6 pages, 6 figures, Accepted for publication in The Astrophysical Journa

Magnetic Field Rotations in the Solar Wind at Kinetic Scales

The solar wind magnetic field contains rotations at a broad range of scales, which have been extensively studied in the MHD range. Here we present an extension of this analysis to the range between ion and electron kinetic scales. The distribution of rotation angles was found to be approximately log-normal, shifting to smaller angles at smaller scales almost self-similarly, but with small, statistically significant changes of shape. The fraction of energy in fluctuations with angles larger than $\alpha$ was found to drop approximately exponentially with $\alpha$, with e-folding angle $9.8^\circ$ at ion scales and $0.66^\circ$ at electron scales, showing that large angles ($\alpha > 30^\circ$) do not contain a significant amount of energy at kinetic scales. Implications for kinetic turbulence theory and the dissipation of solar wind turbulence are discussed

Solar Wind Electric Fields in the Ion Cyclotron Frequency Range

Measurements of fluctuations of electric fields in the frequency range from a fraction of one Hz to 12.5 Hz are presented, and corrected for the Lorentz transformation of magnetic fluctuations to give the electric fields in the plasma frame. The electric fields are large enough to provide the dominant force on the ions of the solar wind in the region near the ion cyclotron frequency of protons, larger than the force due to magnetic fluctuations. They provide sufficient velocity space diffusion or heating to counteract conservation of magnetic moment in the expanding solar wind to maintain nearly isotropic velocity distributions

Anisotropy of Imbalanced Alfvenic Turbulence in Fast Solar Wind

We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The sub-dominant mode is anisotropic throughout, but in a scale-independent way (at higher frequencies). There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfven ratio and shallow scaling of the sub-dominant Elsasser mode suggest an interpretation of the observed discrepancy between the velocity and magnetic field scalings. The total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.Comment: 5 pages, 2 figure

Scaling anisotropy of the power in parallel and perpendicular components of the solar wind magnetic field

Power spectra of the components of the magnetic field parallel (Pzz) and perpendicular (Pzz+Pyy) to the local mean magnetic field direction were determined by wavelet methods from Ulysses’ MAG instrument data during eighteen 10-day segments of its first North Polar pass at high latitude at solar minimum in 1995. The power depends on frequency f and the angle θ between the solar wind direction and the local mean field, and with distance from the Sun. This data includes the solar wind whose total power (Pxx + Pyy + Pzz) in magnetic fluctuations we previously reported depends on f and the angle θ nearly as predicted by the GS95 critical balance model of strong incompressible MHD turbulence. Results at much wider range of frequencies during six evenly-spaced 10-day periods are presented here to illustrate the variability and evolution with distance from the Sun. Here we investigate the aniso tropic scaling of Pzz(f,θ) in particular because it is a reduced form of the Poloidal (pseudo-Alfvenic) component of the (incompressible) fluctuations. We also report the much larger Pxx(f,θ)+Pyy(f,θ) which is (mostly) reduced from the Toroidal (Alfvenic, i.e., perpendicular to both B and k) fluctuations, and comprises most of the total power. These different components of the total power evolve and scale differently in the inertial range. We compare these elements of the magnetic power spectral tensor with “critical balance” model predictions

Anisotropy of Alfv\'enic Turbulence in the Solar Wind and Numerical Simulations

We investigate the anisotropy of Alfv\'enic turbulence in the inertial range of slow solar wind and in both driven and decaying reduced magnetohydrodynamic simulations. A direct comparison is made by measuring the anisotropic second-order structure functions in both data sets. In the solar wind, the perpendicular spectral index of the magnetic field is close to -5/3. In the forced simulation, it is close to -5/3 for the velocity and -3/2 for the magnetic field. In the decaying simulation, it is -5/3 for both fields. The spectral index becomes steeper at small angles to the local magnetic field direction in all cases. We also show that when using the global rather than local mean field, the anisotropic scaling of the simulations cannot always be properly measured.Comment: 9 pages, 8 figure

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wavenumber ranges in a $\beta \gtrsim 1$ plasma. The $k^{-5/3}$ inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfv\'en speed. At smaller wavelengths $k \rho_i \geq 1$ the electric spectrum is softer and is consistent with the expected dispersion relation of short-wavelength kinetic Alfv\'en waves. Kinetic Alfv\'en waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluid-like nature of the solar wind.Comment: submitted; 4 pages + 3 figure

Multiscaling of galactic cosmic ray flux

Multiscaling analysis of differential flux dissipation rate of galactic cosmic rays (Carbon nuclei) is performed in the energy ranges: 56.3-73.4 Mev/nucleon and 183.1-198.7 MeV/nucleon, using the data collected by ACE/CRIS spacecraft instrument for 2000 year. The analysis reveals strong (turbulence-like) intermittency of the flux dissipation rate for the short-term intervals: 1-30 hours. It is also found that type of the intermittency can be different in different energy ranges

Power and spectral index anisotropy of the entire inertial range of turbulence in the fast solar wind

We measure the power and spectral index anisotropy of high speed solar wind turbulence from scales larger than the outer scale down to the ion gyroscale, thus covering the entire inertial range. We show that the power and spectral indices at the outer scale of turbulence are approximately isotropic. The turbulent cascade causes the power anisotropy at smaller scales manifested by anisotropic scalings of the spectrum: close to k^{-5/3} across and k^{-2} along the local magnetic field, consistent with a critically balanced Alfvenic turbulence. By using data at different radial distances from the Sun, we show that the width of the inertial range does not change with heliocentric distance and explain this by calculating the radial dependence of the ratio of the outer scale to the ion gyroscale. At the smallest scales of the inertial range, close to the ion gyroscale, we find an enhancement of power parallel to the magnetic field direction coincident with a decrease in the perpendicular power. This is most likely related to energy injection by ion kinetic modes such as the firehose instability and also marks the beginning of the dissipation range of solar wind turbulence.Comment: 5 pages, 4 figures, 1 table, submitted to MNRAS letter