Session PM10: Mini-Conference on Solar Wind Turbulence II

Dynamics of transitional region of the solar wind turbulence with heliocentric distance

Scale-separation model of wave-particle interaction in divergent solar wind was applied to study the transitional region of solar wind turbulence.\footnote{Galinsky, V.L and V. I. Shevchenko, \textit{Phys. Rev. Letters}, \textbf{85, }90 (2000).} We concentrated on area from around the end of the inertial range to the region where proton cyclotron dumping is important. Our goal is to investigate how the transitional region changes due to change of the solar wind and plasma parameters (and most important due to the change of local cyclotron frequency) with heliocentric distance. Previously we discovered that shell distribution developed in solar wind due to wave-particle interaction is becoming unstable as solar wind expands.\footnote{Shevchenko et al., \textit{Phys. of Plasmas,}\textbf{11}, 4290 (2004).} Waves that are generated by this instability modify the transitional region of turbulence.   

Nearly Incompressible Modeling of the Solar Wind

We develop a three-dimensional time dependent numerical model of compressible magnetohydrodynamic fluids describing super-Alfv\'enic, supersonic and strongly magnetized space and laboratory plasmas show a nonlinear relaxation towards a state of near incompressibility. The latter is characterized essentially by a subsonic turbulent Mach number. This transition is mediated dynamically by disparate spectral energy dissipation rates in compressible magnetosonic and shear Alfv\'enic modes. Nonlinear cascades lead to super-Alfv\'enic turbulent motions decaying to a sub- Alfv\'enic regime that couples weakly with (magneto)acoustic cascades. Consequently, the supersonic plasma motion is transformed into highly subsonic motion and density fluctuations experience a passive convection. This model provides a self-consistent explaination of the ubiquitous nature of incompressible magnetoplasma fluctuations in the solar wind and the interstellar medium.   

Nonlinear aspects of inhomogeneous solar wind plasma

We have developed two dimensional, time dependent, nonlinear fluid simulations of freely expanding solar wind plasma. In our computational model, the small scale solar wind fluctuations are modeled in the presence of large scale background inhomogeneous flows. The background inhomogeneous flows are treated statically, whereas the fluctuations evolve according to MHD turbulence. We find that the large scale inhomogeneity introduces intrinsic compressibility in the evolution of characteristic turbulent fluctuations. Consequently, turbulence is dominated by compressible modes over the Aflvenic fluctuations. Energy cascades are slowed down by the inhomogeneous flows which further lead to the flattening of the turbulent spectra from the usual Kolmogorov-like 5/3 law. Finally, the large scale flows tend to introduce significant deviation from Guassianiaty in the nature of anisotropic and inhomogeneous solar wind MHD turbulence.   

Fast Mode Turbulence in Low-Beta Plasmas with Applications to Solar Wind

We study the fast mode turbulence in low-beta compressible plasmas with applications to the solar wind magnetic fluctuations and particle heating. We have performed both 2-D compressible MHD simulations and the full electromagnetic particle-in-cell simulations to examine the nonlinear evolution of an initial set of fast modes with long wavelengths. In the MHD regime, these waves produce a cascade to smaller scales, showing a faster cascade in the direction perpendicular to the initial magnetic field than in parallel. A small amount of slow modes are excited and shock damping is the predominant dissipation mechanism of magnetic fluctuations. As the fast modes enter the kinetic regime, the cascade continues to well beyond the ion cyclotron frequency. At the high frequency regime, the cascade exhibits strong anisotropy, with more power in the direction perpendicular to the initial magnetic field. Most of the fluctuation energy still remains in the fast wave oscillations. Collisionless damping on electrons is the main dissipation channel in damping the high frequency fast modes. Comparison with solar wind observations will be discussed.   

Kinetic Simulations of Solar Wind Turbulence and Heating

New high sampling rate solar wind observations have been extended into the dissipation range of the solar wind turbulence spectrum, where nearly power-law energy spectra are observed. Recent theoretical studies have demonstrated that the dissipation range of the solar wind is well modeled by a cascade of kinetic Alfv\'{e}n waves. As such, a fully nonlinear kinetic simulation code, AstroGK, is employed to model the turbulent cascade of energy in the solar wind and corona to accurately capture the dissipation range. Milestone simulations employing a realistic mass ratio and plasma $\beta = 0.01$, $0.1$, $1$, $10$, and $100$ spanning from MHD scales to the electron gyroradius are presented. The large dynamic range of the simulations and their kinetic nature capture both the splitting of the turbulent energy at the proton gyroradius scale into a kinetic Alfv\'{e}n wave cascade and ion entropy cascade and the physical dissipation of the turbulence below the proton gyroradius, providing novel insight into the heating of solar wind and coronal ions due to kinetic processes in the dissipation regime.   

Broken universality in MHD turbulence

We study three-dimensional MHD turbulence at unit magnetic Prandtl number in the absence of both forcing and uniform magnetic field and show that three different inertial ranges for the total energy spectrum emerge for three different initial magnetic fields with identical initial velocity field, equal kinetic and magnetic energy and negligible relative cross and magnetic helicities at t=0. The pseudo-spectral code implements the symmetries of the fields, allowing for sizable savings in computer time and memory. We reach equivalent grids of $2048^3$ points with Taylor Reynolds numbers up to 1500 at peak of dissipation. The selecting parameter for the three regimes is the ratio of nonlinear eddy to Alfv\'en time. Results are consistent with previous findings in the presence of forcing and a strong uniform magnetic field, as well as with solar observations. However, in contrast to previous numerical studies, here the ratio of characteristic time scales can only only be ascribed to the intrinsic nonlinear dynamics of the flows under study. A link to the exact laws that can be written in MHD is delineated and other examples of non-universality in turbulence are given.   

Fully kinetic simulations of weak turbulence in electron-positron plasma

Wave turbulence in electron-positron plasma is investigated using fully kinetic electromagnetic particle-in-cell (PIC) simulations. Electron-positron plasma supports two linear modes (Alfven-like and magnetosonic-like modes) and it is demonstrated that this model provides a convenient testbed for investigation of some of the kinetic effects pertinent to the short-wavelength domain of the solar wind turbulence. PIC simulations provide essentially first principle description of the plasma dynamics and allow these questions to be rigorously addressed. In the present work, the emphasis is placed on quantifying the ability of the numerical method to correctly capture elementary linear and nonlinear processes (such as the dispersion relation for the linear waves, Landau damping, three-wave coalescence/decay, nonlinear scattering of waves by plasma particles, etc) and the comparison of the numerical results with predictions of the weak turbulence theory. These results will be used to guide and interpret the full-spectra simulations of a decaying turbulence.   

Linear and Non-Linear Landau Resonance of Kinetic Alfven Waves: Consequences for Electron Distribution and Wave Spectrum in the Solar Wind

Kinetic Alfven wave turbulence in solar wind is considered and it is shown that non-Maxwellian electron distribution function has a significant effect on the dynamics of the solar wind plasmas. Linear Landau damping leads to the formation of a plateau in the parallel electron distribution function which diminishes the Landau damping rate significantly. Nonlinear scattering of waves by plasma particles is generalized to short wavelengths and it is found that for the solar wind parameters this scattering is the dominating process as compared to three wave decay and coalescence in the wave vector range $1/\rho _i [Preview Abstract]

Observations of Large Amplitude, Narrowband Whistlers at Stream Interaction Regions

We present the first solar wind observations of large amplitude, narrowband waveforms in the whistler frequency range 10-100 Hz. Amplitudes range from a few to $>$40 mV/m peak-to-peak, one to three orders of magnitude larger than any previous observations of whistler mode waves in the solar wind. The whistlers are obliquely propagating with a large electrostatic component and are right-hand elliptically polarized in the spacecraft frame. They occur in groups that are strongly correlated with stream interaction regions. The groups persist from a few seconds to minutes and are observed at 88{\%} of SIRs and 17{\%} of shocks from available data. A more detailed look shows that the whistler groups are observed near sudden disturbances of the solar wind magnetic field and plasma. Test particle simulations indicate that these whistlers may play an important role in the dynamics of solar wind electrons within SIRs and near some shocks.   

The strahl as a source of electrostatic whistler waves in the solar wind turbulence

According to observations, the solar wind electron distribution consists of a dense core component (95{\%} of the total electron density) and the suprathermal population (5{\%}) that consists of halo with Maxwellian distribution with hotter temperature and of so-called strahl with a narrow pitch angle distribution directed along the magnetic field. This distribution can be unstable with regards to excitation of lower hybrid waves at anomalous Doppler resonance when the energy source of instability is parallel motion of electrons.\footnote{Shevchenko V., and V. Galinsky, Nonlinear Processes in Geophysics (submitted) (2010).} We investigated the nonlinear dynamics of instability in local approximation by using a hybrid method on resonant numeric simulations. The dynamics of wave power spectrum as well as the strahl distribution function were studied for different distribution function over parallel velocities of strahl electrons. The halo formation is discussed.   

Transitions of solar wind in non-equilibrium states

The solar wind, like other space plasmas, is a system that exists in stationary states out of equilibrium. Empirical kappa distributions successfully describe these space plasmas, while the Tsallis formalism of non-extensive Statistical Mechanics offers a solid statistical foundation for generating and understanding these distributions. The Tsallis entropy can be expressed in terms of the kappa index that labels these distributions and characterizes each stationary state. In this talk, we show how following this entropy exposes the phenomenological paths by which space plasmas transit through stationary states toward, or away from, equilibrium. Starting near a fundamental stationary state with the minimum entropy, spontaneous procedures that can increase entropy, move the system toward equilibrium. On the other hand, external factors that decrease the entropy of the system, move it back into stationary states closer to the fundamental state. In the case of solar wind, newly formed pick-up ions may play just such a critical role because their motion is highly ordered. This motion is dictated by the relative orientation of the solar wind velocity and the interplanetary magnetic field, which become increasingly perpendicular on average as the solar wind moves out through the heliosphere.   

Magnetic discontinuities on small scales in MHD simulations and solar wind

Recent studies have compared properties of the magnetic field in simulations of MHD turbulence with spacecraft data, focusing on methods used to identify classical discontinuities and intermittency statistics. Comparison of solar wind data and simulations of 2D and 3D turbulence shows good agreement in waiting-time analysis of magnetic discontinuities, and in the related distribution of magnetic field increments. This supports the idea that the magnetic structures in the solar wind may emerge fast and locally from nonlinear dynamics that can be understood in the framework of nonlinear MHD theory. The analysis suggests that small scale current sheets form spontaneously and rapidly enough that some of the observed solar wind discontinuities may be locally generated, representing boundaries between interacting flux tubes. Some of these current sheets could be reconnection sites. Indeed, in turbulence strong reconnection events locally occur. Previous studies on discontinuities and theories of reconnection in turbulence could be combined in order to identify possible reconnection events between the intermittent events.   

Fisk-Gloeckler Suprathermal Proton Spectrum in the Heliosheath and the Local Interstellar Medium

Convergence of suprathermal keV-MeV proton and ion spectra approximately to the Fisk-Gloeckler (F-G) form j(E) = j$_{0}$ E$^{-1.5}$ in Voyager 1and 2 heliosheath measurements is suggestive of distributed acceleration in Kolmogorov turbulence, which may extend well beyond the heliopause into the local interstellar medium (LISM). Turbulence of this type is already indicated by interstellar radio scintillation measurements of electron density power spectra. Previously published extrapolations (Cooper et al., 2003, 2006) of the LISM proton spectrum from eV to GeV energies are highly consistent with the F-G power-law and further indicative of such turbulence and LISM effectiveness of the F-G cascade acceleration process. The LISM pressure computed from this spectrum well exceeds that from current estimates for the LISM magnetic field, so exchange of energy between the protons and the magnetic field would likely have a strong role in evolution of the turbulence as per the F-G theory and as long ago proposed for cosmic ray energies by Parker and others. Pressure-dependent estimates of the LISM field strength should not ignore this potentially strong and even dominant contribution from the plasma. Presence of high-beta suprathermal plasma on LISM field lines could significantly affect interactions with the heliospheric outer boundary region and might potentially account for distributed and more discrete features in ongoing measurements of energetic neutral emission from the Interstellar Boundary Explorer (IBEX) mission.   

MHD Turbulence and the FIP Effect

The First Ionization Potential (FIP) Effect is the by now well known abundance anomaly in the solar corona and slow speed solar wind, where elements with FIP less than about 10 eV (e.g. Fe, Mg, Si) are enhanced in abundance by a factor of about 3-4. High FIP elements (e.g. C, O, Ar) are essentially unchanged, while the highest FIP element, He, is depleted by a factor of about 0.5. A similar, though reduced abundance anomaly is found in the fast speed solar wind, and in coronal holes. These element fractionations are best explained by the action of the ponderomotive force in the solar chromosphere, arising as Alfv\'en waves reflect from the strong density gradients. Chromospheric ions, but not neutrals, are preferentially accelerated upwards. I will describe some recent developments, including the parametric generation of slow mode waves by the Alfv\'en wave driver, that now allows both the enhancement of Fe, Mg, S, etc, and the depletion of He to occur simultaneously.   

Interplay of MHD turbulence and discontinuities in the solar wind

Solar wind MHD turbulence has been studied for several decades, yet it still escapes full and unambiguous understanding. In particular, whether MHD discontinuities are ``intrinsic" turbulent structures or ``fossils" of initial conditions in the solar corona is a point of debate nowadays. Understanding of this issue is crucial for the correct interpretation of the solar wind turbulence in the inertial range, as the discontinuities can make a non-negligible contribution to the observed spectra. Here we will discuss a simple {\it ``structure-based"} model of collisionless, compressible MHD (Alfv\'enic) turbulence. In contrast to more familiar paradigms of turbulence, dissipation of nonlinear Alfv\'enic structures arises from collisioless dissipation of the associated (driven) compressible mode. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of the rates of nonlinear wave steepening and collisionless damping. The phases represent (1) a smooth turbulence dominated by the usual wave-wave cascade when damping is strong, and (2) a spiky turbulence dominated by small-scale structures (e.g., discontinuities) when damping is weak. The $T_e/T_p$--$\beta$ phase diagram of the solar wind turbulence will be presented. The turbulent spectrum is computed and shows a broken power-law structure.