Bernard J. Vasquez

Dependence of the Dissipation Range Spectrum of Interplanetary Magnetic Fluctuationson the Rate of Energy Cascade

We investigate the nature of turbulent magnetic dissipation in the solar wind. We employ a database describing the spectra of over 800 intervals of interplanetary magnetic field and solar wind measurements recorded by the ACE spacecraft at 1 AU. We focus on the spectral properties of the dissipation range that forms at spacecraft frequencies ≥0.3 Hz and show that while the inertial range at lower frequencies displays a tightly constrained range of spectral indexes, the dissipation range exhibits a broad range of power-law indexes. We show that the explanation for this variation lies with the dependence of the dissipation range spectrum on the rate of energy cascade through the inertial range such that steeper spectral forms result from greater cascade rates.

Simulation study of the role of ion kinetics in low-frequency wave train evolution

The evolution of uniform, parallel propagating, low-frequency (≲ion cyclotron) wave trains is followed with a one-dimensional hybrid numerical code with fluid electrons and particle ions. We show that moderate amplitude (δB/B 1 and instability exists for wavenumbers both below and above the wavenumber of an initial, left-handed wave train or pump wave. For corresponding parameters a fluid theory gives only a narrow range of instability above the pump wavenumber where decay and beat instabilities can occur. In simulations wave energy inverse cascades to smaller wavenumbers and into a greater number of forward than backward going waves. In fluids energy by decay goes mostly to backward ones of smaller wavenumber, and energy by beat goes mostly to forward ones of larger wavenumber. Neither fluid instability explains simulation results. The instability is saturated by thermalizing ions and sometimes exciting small wavenumber electrostatic or acoustic modes. In contrast, saturation in fluids first occurs by generating the harmonics of the growing linear modes. Harmonic generation is mostly absent in simulations. Simulations are carried out to long times and mostly reach a limit beyond which no further significant evolution can occur. Application to Alfvenic fluctuations in the solar wind is discussed.

A reconnection layer associated with a magnetic cloud

Abstract We examine a 3-hour long interval on December 24, 1996, containing a magnetic hole associated with an interplanetary magnetic cloud. Two sets of perturbations are observed by the Wind spacecraft at 1 AU. In the first, the field and flow rotate at constant field strength, and the plasma is accelerated to the local Alfven speed. We show this to be a rotational discontinuity. In the second, observed 25 min later, the plasma is heated and the field decreases. We show this to be a slow shock. The whole structure is in pressure balance. We interpret the observations as MHD discontinuities arriving with varying delays from a reconnection site closer to the Sun. Energetic particle observations suggest further that ejecta material is present for many hours prior to the magnetic cloud observation and separated from it by the layer. This suggests that reconnection took place between field lines of a CME of which the magnetic cloud formed a part.

Dissipation of the Perpendicular Turbulent Cascade in the Solar Wind

The core solar wind protons are observed to be heated perpendicularly to the magnetic field. This is taken to be a signature of the cyclotron damping of the turbulent fluctuations, which are thought to be responsible for the heating. At the same time, it is commonly accepted that the turbulent cascade produces mostly highly oblique (quasi-two-dimensional) fluctuations, which cannot be immediately cyclotron resonant with the ions because of their low frequencies and small parallel wavenumbers. To address this problem, we propose a new, indirect mechanism for damping the quasi-two-dimensional fluctuations. The mechanism involves a plasma instability, which excites ion cyclotron resonant waves. As the cascade proceeds to higher wavenumbers, it generates increasingly high velocity shear associated with the turbulent fluctuations. The shear eventually becomes unstable to waves near harmonics of the ion cyclotron frequency. Once the frequency of the waves is upshifted, they can heat ions perpendicularly, extracting the energy from the quasi-two-dimensional fluctuations. The dissipation rates of quasi-two-dimensional fluctuations are incorporated into a model of the energy transfer in the turbulent cascade. Our analysis of the observed spectra shows that the spectral break separating the inertial and dissipation ranges of the turbulence, where the dissipation sets in, corresponds to the same shear under a wide range of plasma conditions, in agreement with the prediction of the theory. The observed turbulence spectra often have power-law dissipation ranges with an average spectral index of -3. We demonstrate that this fact is simply a consequence of a marginal state of the instability in the dissipation range.

Statistical Analysis of the High-Frequency Spectral Break of the Solar Wind Turbulence at 1 AU

The physical mechanism responsible for the dissipation of the solar wind turbulence and the resulting plasma heating is not completely understood. To be a viable means of dissipation, any mechanism has to reproduce several observational features of the turbulence spectra. One important characteristic of the spectrum is its high-frequency break, where the spectral slope becomes considerably steeper than the Kolmogorov-like scaling law observed in the inertial range. The onset of the spectral steepening can be inferred from the observations fairly accurately, and it is a good benchmark to test various theories of the turbulence dissipation. In this paper, a large database of magnetic field spectra and plasma parameters at 1 AU measured by the ACE spacecraft is used to determine the spectral break. The statistical correlation of the data points calculated according to existing theoretical formulae for the break is analyzed, and the least-squares fits to the data are compared with the theoretically predicted scalings. It is concluded that the position of the spectral break is not determined just by a scale of the turbulent fluctuations, but by a combination of their scale and the amplitude at that scale. This suggests that the dissipation of the solar wind turbulence is an essentially nonlinear process.

THE TURBULENT CASCADE AND PROTON HEATING IN THE SOLAR WIND AT 1 AU

We examine the convergence of third-order structure function expressions derived to measure the rate of turbulent energy cascade within the solar wind using Advanced Composition Explorer observations from 1 AU over the years 1998 through 2007. We find that a minimum of a year of data is normally required to get good convergence and statistically significant results. We then apply these findings to 10 years of observations spanning both solar minimum and solar maximum conditions. We compare the computed energy cascade rates with previously determined rates of proton heating at 1 AU as determined from the radial gradient of the proton temperature to be proportional to the product of wind speed and proton temperature. We find good agreement with a moderate excess of energy within the cascade that is consistent with previous estimates for thermal electron heating in the solar wind. In keeping with earlier analyses of the dissipation spectrum, we postulate that electron heating by the turbulent cascade is less than and at most equal to the rate of proton heating.

Formation of pressure‐balanced structures and fast waves from nonlinear Alfvén waves

In the solar wind, Alfvenic fluctuations are typically observed in association with small fluctuations of the density (ρ) and magnetic field strength (B), which tend to be anticorrelated and in approximate pressure balance. One would not expect any finite δρ and δB among pure Alfven waves propagating strictly outward from the Sun. Our paper shows how Alfven waves can nonlinearly produce structures in pressure balance. We present a second-order analysis of the pure magnetohydrodynamic equations and hybrid simulations which show that nonlinear Alfven waves traveling in different directions but with equal group velocity can generate pressure-balanced structures with wave vectors perpendicular to the background magnetic field B 0 . Homogeneous fast waves are also generated in this direction in order to satisfy initial conditions. They cannot be Landau or transit-time damped and so cause the values of B and ρ to vary with time as they beat with the pressure-balanced structures. However, we find δρδB < 0 is satisfied most of the time, and this can partly explain the tendency for anticorrelation observed in the solar wind. In directions away from the perpendicular one, Alfven waves produce driven fast waves which give constant B and ρ to second order. Homogeneous fast and slow waves are also produced in these directions but Landau damp away in large β plasmas. Thus an equilibrium or steady propagating waveform at second order can be produced where B and ρ vary only in the perpendicular direction. If transverse magnetic structures with wave vectors perpendicular to B 0 are included at the same order as the initial Alfven waves, then these evolve to pressure-balanced structures and can also coexist with the Alfven waves. However, an equilibrium is obtained generally only when these structures also have velocity fluctuations equivalent of those of the Alfven waves.

Formation of arc-shaped Alfvén waves and rotational discontinuities from oblique linearly polarized wave trains

The forms of Alfvenic fluctuations in the solar wind sometimes possess nearly constant magnetic intensities but have an approximate arc rather than circular polarization. They are also associated with layers of abrupt field rotation called rotational discontinuities (RDs) where the field changes direction by < 180°. Ion-sense and electron-sense rotations are observed in approximately equal numbers. To explore the origin of this form, we conduct a one-and-one-half-dimensional hybrid numerical simulation study of the evolution of obliquely propagating, low-frequency (≪ion cyclotron) Alfven wave trains. Starting from a linearly polarized wave train, an approximate arc polarization evolves rapidly where the magnetic field moves to and fro on a less than semicircular arc. Large-amplitude (|δB|/B ∼ 1) wave trains steepen and produce RDs which always rotate the field by < 180° with no preference for ion or electron sense of rotation. These properties correspond to those of Alfvenic fluctuations in the solar wind, and our model is the first which offers an explanation of the observed arc-shaped waves and imbedded RDs. At early times, a large density signal is also generated. For large plasma β, the signal rapidly damps, and the waveform varies little with time. For small plasma β, the generated constant-B Alfven wave is parametrically unstable and causes the density signal to grow further before the instability saturates. The wave train and density signal beat strongly giving a periodic time variation of the wave amplitude and waveform. Ion heating from steepening, RD formation, relaxation to constant B, and parametric processes occurs mainly parallel to the background magnetic field and cannot explain the perpendicular heating of ions observed in the solar wind.

OBSERVATIONAL CONSTRAINTS ON THE ROLE OF CYCLOTRON DAMPING AND KINETIC ALFVEN WAVES IN THE SOLAR WIND

Certain few intervals with high-β plasma (ratio of gas pressure to magnetic pressure) have been interpreted as containing turbulent fluctuations with wave vectors that are confined to very oblique angles with respect to the mean magnetic field. The fluctuations are theorized to be Kinetic Alfven Waves (KAWs) engaged in an energy cascade that dissipates primarily at electron scales. Dissipation by ions, and by cyclotron damping in particular, is argued to be minimal to non-existent. This interpretation is not supported, generally, by the analysis of larger data sets using other data analysis methods. These prior studies, however, were not conducted for specific β ranges. In this study, we reconsider the analysis for a moderately large set of high-β intervals. The analysis includes magnetic variance, the Bieber ratio test, the cross-helicity versus magnetic helicity correlation, and the implied break frequency versus angle relationship. In our analysis, the results do not support the exclusive KAW interpretation as applied generally to solar wind intervals of high-β while the results do support the presence of cyclotron damping at a significant level.

Preferential Perpendicular Heating of Coronal Hole Minor Ions by the Fermi Mechanism

We present a kinetic mechanism for the preferential perpendicular heating of minor ions in coronal holes, which may be responsible for the consistent observation in fast solar wind that the heavy ions are hotter and flow faster than the proton population. The basis of this mechanism is the familiar resonant cyclotron interaction between ions and parallel-propagating ion cyclotron waves. The preferential effects naturally arise from the ability of minor ions to simultaneously resonate with several modes in a spectrum of inward- and outward-propagating waves, while protons can encounter only a single resonance for a given particle parallel speed. The single resonance defines a marginally stable proton distribution which represents a limit on the wave dissipation and heating attainable by the proton population. Minor ions have no such limitation and may continue to be heated as long as the resonant wave power is maintained. The multiply resonant interaction available to minor ions is equivalent to a second-order Fermi acceleration of these thermal particles. In this paper, we derive the quasi-linear expressions for this interaction and present illustrative results for the evolution of an O+5 ion distribution in a spatially homogeneous system under various assumptions on the resonant wave spectra. These results demonstrate strong and continuous perpendicular heating to temperatures comparable to those seen in coronal holes.