S. A. Markovskii

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.

Generation of Ion Cyclotron Waves in Coronal Holes by a Global Resonant Magnetohydrodynamic Mode

The damping of ion cyclotron waves is a process that can provide effective coronal heating and solar wind acceleration. However, the mechanism of generation of these waves in the solar corona remains unclear. We suggest that the ion cyclotron waves in coronal holes are excited by plasma instability that is driven by current fluctuations of a global resonant magnetohydrodynamic (MHD) mode. The frequency of the MHD mode is much lower than the proton gyrofrequency, so that its direct cyclotron damping is absent. At the same time, this frequency must be high enough to effectively generate the instability. We discuss the sources of such MHD waves in the coronal holes. The generated ion cyclotron waves are highly oblique with respect to the background magnetic field. We present qualitative arguments that these waves contribute to coronal heating and solar wind acceleration in a manner similar to that of the parallel-propagating waves usually used to explain the heating and acceleration. The scales of spatial inhomogeneity suggested by the observations and the amplitudes of the magnetic field fluctuations put limitations on the currents associated with MHD waves. We show that even with these limitations the current can still be large enough to drive the instability.

A SHORT-TIMESCALE CHANNEL OF DISSIPATION OF THE STRONG SOLAR WIND TURBULENCE

Hybrid numerical simulations of a turbulent cascade nearly perpendicular to the background magnetic field are carried out at the proton kinetic scales. It is shown that the cascade produces exponentially growing current sheets previously observed in fluid simulations. In the kinetic limit, the sheets are developing on a timescale as fast as the proton gyration. The rapid variations of the electric field associated with the sheets can demagnetize the protons and increase their thermal energy preferentially across the mean magnetic field. The relevance of this mechanism to the solar wind heating is discussed.

PROTON HEATING BY NONLINEAR FIELD-ALIGNED ALFVÉN WAVES IN SOLAR CORONAL HOLES

Field-aligned Alfven waves are often viewed as a source of the proton heating that accelerates the fast solar wind. However, the energy that they can inject into the protons in the limit of cyclotron-resonant quasi-linear diffusion is insufficient to account for the observed acceleration. To test the validity of this limit in coronal holes, nonlinear Alfven waves are modeled using a hybrid code. It is found that the nonlinearity is particularly strong when the intensity of antisunward-propagating waves is comparable to that of sunward waves. The sunward waves can be generated by the proton distribution as it evolves with the heliocentric distance. The ponderomotive force and beat interaction are identified as the most important nonlinear effects. The nonlinearity of the field-aligned Alfven waves produces density fluctuations. In the simulations, the amplitude of the density fluctuations was kept within the observed constraints from the interplanetary scintillation measurements in the corona. In this case, the characteristic time of the proton heating is almost 2 orders of magnitude smaller than the solar wind expansion time. Therefore, it can contribute to the energization of the solar wind on the global scale. The nonlinear wave damping operating alone cannot be responsible for the energization because it only causes particle diffusion parallel to the magnetic field. However, it can relax the limitation on the perpendicular diffusion imposed by the cyclotron resonance condition. The nonlinear damping combined with the linear one can then inject the additional thermal energy needed to accelerate the solar wind.

Intermittent Heating of the Solar Corona by Heat Flux-generated Ion Cyclotron Waves

Recently, we suggested that the source of ion heating in solar coronal holes is small-scale reconnection events (microflares) at the coronal base. The microflares launch intermittent heat flux up into the corona exciting ion cyclotron waves through a plasma microinstability. The ions are heated by these waves during the microflare bursts and then evolve with no energy input between the bursts. In this paper, we show that the structure of the proton distribution in the relatively long time periods between the microflares is determined by collisions at small heliocentric distances. At greater distances, the collisional processes can be replaced by similar processes due to secondary instabilities. These are excited by the distortion of the distribution under the action of the mirror force. At the same time, the heating during the microflare bursts is not affected by either the collisions or the secondary instabilities because of the short duration of the bursts. We demonstrate that in each intermittent heating event the protons diffuse approximately along one-dimensional curves in the phase space and can develop a quasi-plateau. The corresponding temperature increase can then be calculated without solving the diffusion equations. The overall coronal heating by this mechanism is a summed effect of all microflare bursts during the expansion time of the solar wind and adiabatic cooling between the microflares. The calculations for the collision-dominated region suggest that the overall heating is efficient enough to account for the acceleration of the fast solar wind in this region.

Perpendicular Proton Heating Due to Energy Cascade of Fast Magnetosonic Waves in the Solar Corona

Observational data and theoretical models suggest that the wave spectrum in the solar wind and corona may contain a fast magnetosonic mode component. This paper presents two-dimensional hybrid simulations of the energy cascade among the fast waves in the vicinity of the proton inertial scale. The initial spectrum consists of modes propagating in the positive direction, defined by the mean magnetic field, and is allowed to evolve freely in time. The plasma beta is set to low values typical of the solar corona. The cascade proceeds from lower to higher wavenumbers and mostly in the direction across the magnetic field. The highly oblique fast waves are strongly dissipated on the protons. The resulting proton heating is preferentially perpendicular to the magnetic field. If the wave intensity is constrained by the observed density spectra in the corona, the heating is fast enough to generate the solar wind.

VELOCITY POWER SPECTRA FROM CROSS-FIELD TURBULENCE IN THE PROTON KINETIC REGIME

Numerical hybrid simulations with particle protons and fluid electrons are conducted for turbulent fluctuations with spatial variations in a plane perpendicular to the background magnetic field. In the turbulent phase, the proton bulk velocity spectrum has a dissipation range starting at a smaller wavenumber than the magnetic spectrum dissipation range. The steepened portion of the proton bulk velocity spectrum is constrained to a smaller wavenumber with an increasing ratio of background proton plasma to magnetic pressure {beta}{sub p}. The form of the magnetic spectrum does not depend on {beta}{sub p}. The collisionless proton and fluctuation interaction which heats protons mainly across the magnetic field is deemed to be the result of a viscous-like interaction based, in part, on the dependence of the velocity spectrum on {beta}{sub p}.

Nature of fluctuations on directional discontinuities inside a solar ejection: Wind and IMP 8 observations

A solar ejection passed the Wind spacecraft between December 23 and 26, 1996. On closer examination, we find a sequence of ejecta material, as identified by abnormally low proton temperatures, separated by plasmas with typical solar wind temperatures at 1 AU. Large and abrupt changes in field and plasma properties occurred near the separation boundaries of these regions. At the one boundary we examine here, a series of directional discontinuities was observed. We argue that Alfvenic fluctuations in the immediate vicinity of these discontinuities distort minimum variance normals, introducing uncertainty into the identification of the discontinuities as either rotational or tangential. Carrying out a series of tests on plasma and field data including minimum variance, velocity and magnetic field correlations, and jump conditions, we conclude that the discontinuities are tangential. Furthermore, we find waves superposed on these tangential discontinuities (TDs). The presence of discontinuities allows the existence of both surface waves and ducted body waves. Both probably form in the solar atmosphere where many transverse nonuniformities exist and where theoretically they have been expected. We add to prior speculation that waves on discontinuities may in fact be a common occurrence. In the solar wind, these waves can attain large amplitudes and low frequencies. We argue that such waves can generate dynamical changes at TDs through advection or forced reconnection. The dynamics might so extensively alter the internal structure that the discontinuity would no longer be identified as tangential. Such processes could help explain why the occurrence frequency of TDs observed throughout the solar wind falls off with increasing heliocentric distance. The presence of waves may also alter the nature of the interactions of TDs with the Earths bow shock in so-called hot flow anomalies.

Three-dimensional Hybrid Simulation Study of Anisotropic Turbulence in the Proton Kinetic Regime

Three-dimensional numerical hybrid simulations with particle protons and quasi-neutralizing fluid electrons are conducted for a freely decaying turbulence that is anisotropic with respect to the background magnetic field. The turbulence evolution is determined by both the combined root-mean-square (rms) amplitude for fluctuating proton bulk velocity and magnetic field and by the ratio of perpendicular to parallel wavenumbers. This kind of relationship had been considered in the past with regard to interplanetary turbulence. The fluctuations nonlinearly evolve to a turbulent phase whose net wave vector anisotropy is usually more perpendicular than the initial one, irrespective of the initial ratio of perpendicular to parallel wavenumbers. Self-similar anisotropy evolution is found as a function of the rms amplitude and parallel wavenumber. Proton heating rates in the turbulent phase vary strongly with the rms amplitude but only weakly with the initial wave vector anisotropy. Even in the limit where wave vectors are confined to the plane perpendicular to the background magnetic field, the heating rate remains close to the corresponding case with finite parallel wave vector components. Simulation results obtained as a function of proton plasma to background magnetic pressure ratio β p in the range 0.1-0.5 show that the wave vector anisotropy also weakly depends on β p .