The solar wind: A turbulent magnetohydrodynamic medium

MHD turbulence properties in the solar wind are briefly reviewed. The evolution of fluctuations of alfvénic type in near-ecliptic regions of the inner heliosphere is described. The role of interplanetary sources and the influence of interactions with structures convected by the solar wind are discussed. Turbulence features at high latitudes and in the outermost regions of the heliosphere are finally highlighted.     

Magnetic field reconnection theory and the solar wind — Magnetosphere interaction: A review

This review considers the theory of the magnetic field line reconnection and its application to the problem of the interaction between the solar wind and the Earth's magnetosphere. In particular, we discuss the reconnection models by Sonnerup and by Petschek (for both incompressible and compressible plasmas, for the asymmetric and nonsteady-state cases), the magnetic field annihilation model by Parker; Syrovatsky's model of the current sheet; and Birn's and Schindler's solution for the plasma sheet structure. A review of laboratory and numerical modelling experiments is given.Results concerning the field line reconnection, combined with the peculiarities of the MHD flow, were used in investigating the solar wind flow around the magnetosphere. We found that in the presence of a frozen-in magnetic field, the flow differs significantly from that in a pure gas dynamic case; in particular, at the subsolar. part of the magnetopause a stagnation line appears (i.e., a line along which the stream lines are branching) instead of a stagnation point. The length and location of the stagnation line determine the character of the interaction of the solar wind with the Earth's magnetosphere. We have developed the theory of that interaction for a steady-state case, and compare the results of the calculations with the experimental data.In the last section of the review, we propose a qualitative model of the solar wind — the Earth's magnetosphere interaction in the nonsteady-state case on the basis of the solution of the problem of the spontaneous magnetic field line reconnection.     

Self-consistent Simulations of Alfv��n Wave Driven Winds from the Sun and Stars

We review our recent results of Alfvén wave-driven winds. First, we present the result of self-consistent 1D MHD simulations for solar winds from the photosphere to interplanetary region. Here, we emphasize the importance of the reflection of Alfvén waves in the density stratified corona and solar winds. We also introduce the recent Hinode observation that might detect the reflection signature of transverse (Alfvénic) waves by Fujimura and Tsuneta (Astrophys. J. 702:1443, 2009). Then, we show the results of Alfvén wave-driven winds from red giant stars. As a star evolves to the red giant branch, the properties of stellar winds drastically change from steady coronal winds to intermittent chromospheric winds. We also discuss how the stellar evolution affects the wave reflection in the stellar atmosphere and similarities and differences of accretion disk winds by MHD turbulence.     

Hybrid Simulations of Wave Propagation and Ion Cyclotron Heating in the Expanding Solar Wind

We present results from hybrid (particle ions, fluid electrons) simulations of the evolution of Alfvén waves close to the ion cyclotron frequency in the solar wind, which take into account the basic properties of the background solar wind flow, i.e., the spherical expansion and the consequent decrease in magnetic field and cyclotron frequency with increasing distance from the Sun. We follow the evolution of a plasma parcel in a frame of reference moving with the solar wind using a 1D expanding box hybrid model; use of the hybrid model yields a fully self-consistent treatment of the resonant cyclotron wave-particle interaction. This model is related to a previous MHD model (Velli et al. 1992), which allows the use of a simple Cartesian geometry with periodic boundary conditions. The use of stretched expanding coordinates in directions transverse to the mean radial solar wind flow naturally introduces an anisotropic damping effect on velocity and magnetic field. We present results for the case of a single circularly polarized Alfvén wave propagating radially outward. Initially, the wave is below the cyclotron frequency for both the alpha partcles and protons. As the wind expands, the wave frequency (as seen in the solar wind frame) decreases more slowly than the cyclotron frequencies and the wave comes into resonance. With only protons, heating occurs as the wave frequency approaches the proton cyclotron frequency. With both alphas and protons, the alphas, which come into resonance first, are observed to be preferentially heated and accelerated. This revised version was published online in June 2006 with corrections to the Cover Date.     

Acceleration of the solar wind

In this review, we discuss critically recent research on the acceleration of the solar wind, giving emphasis to high-speed solar wind streams emanating from solar coronal holes. We first explain why thermally driven wind models constrained by solar and interplanetary observations encounter substantial difficulties in explaining high speed streams. Then, through a general discussion of energy addition to the solar wind above the coronal base, we indicate a possible resolution of these difficulties. Finally, we consider the question of what role MHD waves might play in transporting energy through the solar atmosphere and depositing it in the solar wind, and we conclude by examining, in a simple way, the specific mechanism of solar wind acceleration by Alfvén waves and the related problem of accelerating massive stellar winds with Alfvén waves.Paper presented at the IX-th Lindau Workshop The Source Region of the Solar Wind.On leave from the Auroral Observatory, Institute of Mathematical and Physical Sciences, University of Tromsø, N-9001 Tromsø, Norway.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Kinetic-Gasdynamic Modeling of the Heliospheric Interface

Heliospheric energetic neutral atoms (ENAs) that will be measured by the Interstellar Boundary Explorer (IBEX) originate from the heliosheath. The heliosheath is formed as a result of the interaction of the solar wind (SW) with the circum-heliospheric interstellar medium (CHISM). The expected fluxes of ENAs are strongly dependent on the nature of this interaction. In turn, the interaction of the solar wind with the local interstellar cloud has a complex and multi-component nature. Detailed theoretical modeling of the interaction between the SW and the local interstellar medium is required to understand the physics of the heliosheath and to predict and explain the heliospheric ENAs. This paper summarizes current state-of-art kinetic-gasdynamic models of the SW/CHISM interaction. We shall restrict our discussion to the kinetic-gasdynamic and kinetic-magnetohydrodynamic (MHD) models developed by the Moscow group. This paper summarizes briefly the main results of the first self-consistent, two-component, kinetic-gasdynamic model by Baranov and Malama (J. Geophys. Res. 98:15157–15163, 1993), presents new results obtained from the 3D kinetic-MHD model by Izmodenov et al. (Astron. Astrophys. 437:L35–L38, 2005a), describes the basic formulation and results of the model by Malama et al. (Astron. Astrophys. 445:693–701, 2006) as well as reports current developments in the model. This self-consistent model considers pickup protons as a separate non-equilibrium component. Then we discuss a stochastic acceleration model for pickup protons in the supersonic solar wind and in the heliosheath. We also present the expected heliospheric ENA fluxes obtained in the framework of the models.     

Kinetic-Hydrodynamic Models of the Solar Wind Interaction with the Partially Ionized Supersonic Flow of the Local Interstellar Gas: Predictions and Interpretations of the Experimental Data

At present there is no doubt that the local interstellar medium (LISM) is mainly partially ionized hydrogen gas moving with a supersonic flow relative to the solar system. The bulk velocity of this flow is approximately equal ～26 km/s. Although the interaction of the solar wind with the charged component (below plasma component) of the LISM can be described in the framework of hydrodynamic approach, the interaction of H atoms with the plasma component can be correctly described only in the framework of kinetic theory because the mean free path of H atoms in the main process of the resonance charge exchange is comparable with a characteristic length of the problem considered. Results of self-consistent, kinetic-hydrodynamic models are considered in this review paper. First, such the model was constructed by Baranov and Malama (J. Geophys. Res. 98(A9):15,157–15,163, 1993). Up to now it is mainly developed by Moscow group taking into account new experimental data obtained onboard spacecraft studying outer regions of the solar system (Voyager 1 and 2, Pioneer 10 and 11, Hubble Space Telescope, Ulysses, SOHO and so on). Predictions and interpretations of experimental data obtained on the basis of these models are presented. Kinetic models for describing H atom motion were later suggested by Fahr et al. (Astron. Astrophys 298:587–600, 1995) and Lipatov et al. (J. Geophys. Res. 103(A9):20,631–20,642, 1998). However they were not self-consistent and did not incorporate sources to the plasma component. A self-consistent kinetic-hydrodynamic model suggested by Heerikhuisen et al. (J. Geophys. Res. 111:A06110, 2006, Astrophys. J. 655:L53–L56, 2007) was not tested on the results by Baranov and Malama (J. Geophys. Res. 111:A06110, 1993) although it was suggested much later. Besides authors did not describe in details their Monte Carlo method for a solution of the H atom Boltzmann equation and did not inform about an accuracy of this method. Therefore the results of Heerikhuisen et al. (J. Geophys. Res. 111:A06110, 2006) are in open to question and will not be considered in this review paper. That is why below we will mainly consider a progress of the Moscow group on heliospheric modelling endeavours in the kinetic-hydrodynamic approach. Criticism of the models that treat interstellar hydrogen in the heliosphere as several fluids is given. It is shown that the multi-fluid models give rise to unreal results especially for distributions of neutral component parameters. Magnetohydrodynamic (MHD) modelling of the solar wind interaction with the LISM gas is also reviewed.     

Simulation of three-dimensional solar wind disturbances and resulting geomagnetic storms

A kinematic method of representing the three-dimensional solar wind flow is devised by taking into account qualitatively the stream-stream interaction which leads to the formation of a shock pair. Solar wind particles move radially away from the Sun, satisfying the frozen-magnetic field condition. The uniqueness of the present approach is that one can incorporate both theoretical and observational results by adjusting the parameters involved and that a self-consistent data set can be simulated. One can then infer the three-dimensional structure of the solar wind which is vital in understanding the interaction between the solar wind and the magnetosphere, and it is for this reason that the present kinematic method is devised. In the first part of this paper, the present kinematic method is described in detail by demonstrating that the following solar wind features can be simulated: (i) Variations of the solar wind quantities (such as the solar wind speed, the density and the IMF vector), associated with the solar rotation, at the Earth; (ii) the solar wind flow pattern in the meridian planes; (iii) the three-dimensional structure of the corotating interaction region (CIR); and (iv) the three-dimensional structure of the warped solar current sheet.In Section 2, the three-dimensional structure of solar wind disturbances are studied by introducing a flare-generated high speed stream into the two-stream model of the solar wind developed in Section 1. The treatment of the stream-stream interaction is generalized to deal with a flare-generated high speed stream, yielding a shock pair. The shock pair causes three-dimensional distortion of the solar current sheet as it propagates outward from the Sun. It is shown that a set of characteristic time variations of the solar wind speed, density, the interplanetary magnetic field magnitude B and angles (theta) and gf (phi) result at the time of the passage at the location of the Earth for a given set of flare conditions. These quantities allow us to compute the solar wind-magnetosphere energy coupling function . Time variations of the two geomagnetic indices AE and Dst are then estimated from . The simulated geomagnetic storms are compared with observed ones.In the third part, it is shown that recurrent geomagnetic storms can reasonably be reproduced, if fluctuating components of the interplanetary magnetic field (IMF) are superposed on the kinematic model of the solar wind developed in the first part. As an example, we simulate the fluctuating components by linearly polarized Alfvén waves and by random variations of the IMF angle (theta). Characteristics of the simulated and observed geomagnetic storms are discussed in terms of the simulated and observed AE and Dst indices. If the fluctuating components of the IMF can generally be identified as hydromagnetic waves, they may be an important cause for individual magnetospheric substorms, while the IMF magnitude B and the solar wind speed V modulate partially the intensity of magnetospheric substorms and storms.     

Alfvenic fluctuations in the solar wind: A case study using Ulysses measurements

We present preliminary results of a study of solar wind Alfvénic fluctuations using magnetometer and plasma measurements from the spacecraft Ulysses. We focus on a particular case study, and use wave language to discuss the fluctuations. The observations are consistent with a mixture of convected structures and Alfvén wave trains. Furthermore, our results tend to suggest that the Alfvénic-fluctuations propagate in the radial direction.     

Magnetic fields,plasmas, and coronal holes: The inner solar system

This paper reviews the recent results concerning streams and magnetic fields in the inner solar system. Specifically, it discusses in situ magnetic field and plasma observations within 1 AU which describe MHD stream flows and Alfvénic fluctuations, and it discusses the latest theories of those phenomena. Observationally, there have been significant advances in our understanding of streams and fluctuations as the result of acquiring nearly complete sets of high resolution plasma and magnetic data simultaneously at two or more points by IMPs 6, 7, and 8, Mariner-Venus-Mercury, HELIOS-1, and HELIOS-2. HELIOS and IMP observations and coronal hole observations demonstrated that streams can have very thin boundaries in latitude and longitude near the Sun. This has necessitated a revision of earlier views of stream dynamics, for it is now clear that magnetic pressure is a major factor in the dynamics of stream in the inner solar system and that nonlinear phenomena are significant much closer to the Sun than previously believed. Simultaneous IMP 6, 7, and 8 observations of Alfvénic fluctuations have shown that they are probably not simply transverse Alfvén waves; they suggest that Alfvénic fluctuations are better described as nonplanar, large-amplitude, general Alfvén waves moving through an inhomogeneous and discontinuous medium, and coupled to a compressive mode.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Modelling of Solar Wind, CME Initiation and CME Propagation

Simulations of coronal mass ejections (CMEs) evolving in the interplanetary (IP) space from the Sun up to 1 AU are performed in the framework of ideal magnetohydrodynamics (MHD) by the means of a finite-volume, explicit solver. The aim is to quantify the effect of the background solar wind and of the CME initiation parameters, such as the initial magnetic polarity, on the evolution and on the geo-effectiveness of CMEs. First, three different solar wind models are reconstructed using the same numerical grid and the same numerical scheme. Then, different CME initiation models are considered: Magnetic foot point shearing and magnetic flux emergence. For the fast CME evolution studies, a very simple CME model is considered: A high-density and high-pressure magnetized plasma blob is superposed on a background steady state solar wind model with an initial velocity and launch direction. The simulations show that the initial magnetic polarity substantially affects the IP evolution of the CMEs influencing the propagation velocity, the shape, the trajectory (and thus, the geo-effectiveness).     

Recent Observations of Plasma and Alfvénic Wave Energy Injection at the Base of the Fast Solar Wind

We take stock of recent observations that identify the episodic plasma heating and injection of Alfvénic energy at the base of fast solar wind (in coronal holes). The plasma heating is associated with the occurrence of chromospheric spicules that leave the lower solar atmosphere at speeds of order 100?km/s, the hotter coronal counterpart of the spicule emits radiation characteristic of root heating that rapidly reaches temperatures of the order of 1?MK. Furthermore, the same spicules and their coronal counterparts (“Propagating Coronal Disturbances”; PCD) exhibit large amplitude, high speed, Alfvénic (transverse) motion of sufficient energy content to accelerate the material to high speeds. We propose that these (disjointed) heating and accelerating components form a one-two punch to supply, and then accelerate, the fast solar wind. We consider some compositional constraints on this concept, extend the premise to the slow solar wind, and identify future avenues of exploration.     

A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows

A parallel adaptive mesh refinement (AMR) scheme is described for solving the governing equations of ideal magnetohydrodynamics (MHD) in three space dimensions. This solution algorithm makes use of modern finite-volume numerical methodology to provide a combination of high solution accuracy and computational robustness. Efficient and scalable implementations of the method have been developed for massively parallel computer architectures and high performance achieved. Numerical results are discussed for a simplified model of the initiation and evolution of coronal mass ejections (CMEs) in the inner heliosphere. The results demonstrate the potential of this numerical tool for enhancing our understanding of coronal and solar wind plasma processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Class of TVD Type Combined Numerical Scheme for MHD Equations With a Survey About Numerical Methods in Solar Wind Simulations

It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made. This revised version was published online in August 2006 with corrections to the Cover Date.     

Working Group 1 Report: Solar Wind Models from the Sun to 1 AU: Constraints by "in situ" and Remote Sensing Measurements

The goal of Working Group 1 was to discuss constraints on solar wind models. The topics for discussion, outlined by Eckart Marsch in his introduction, were: (1) what heats the corona, (2) what is the role of waves, (3) what determines the solar wind mass flux, (4) can stationary, multi-fluid models describe the fast and slow solar wind, or (5) do we need time dependent fluid models, kinetic models, and/or MHD models to describe solar wind acceleration. The discussion in the working group focused on observations of "temperatures" in the corona, mainly in coronal holes, and whether the observations of line broadening should be interpreted as thermal broadening or wave broadening. Observations of the coronal electron density and the flow speed in coronal holes were also discussed. There was only one contribution on observations of the distant solar wind, but we can place firm constraints on the solar wind particle fluxes and asymptotic flow speeds from observations with Ulysses and other spacecraft. Theoretical work on multi-fluid models, higher-order moment fluid models, and MHD models of the solar wind were also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

The heliospheric magnetic field

The heliospheric magnetic field (HMF) is an important component of the heliospheric medium. It has been the subject of extensive studies for the past thirty five years. There is a very large observational data base, mostly from the vantage point of the ecliptic plane, but now also from the solar polar regions, from the Ulysses mission. This review aims to present its most important large scale characteristics. A key to understand the HMF is to understand the source functions of the solar wind and magnetic fields close to the sun. The development of new modelling techniques for determining the extent and geometry of the open magnetic field regions in the corona, the sources of the solar wind and the HMF has provided a new insight into the variability of the source functions. These are now reasonably well understood for the state of the corona near solar minimum. The HMF at low-to-medium heliolatitudes is dominated, near solar minimum, by the Corotating Interaction Regions (CIRs) which arise from the interaction of alternating slow and fast solar wind streams, and which, in turn, interact in the outer heliosphere to form the large scale Merged Interaction Regions. The radial component of the HMF is independent of heliolatitude; the average direction is well organised by the Parker geometry, but with wide distributions around the mean, due, at high latitudes, to the presence of large amplitude, Alfvénic fluctuations. The HMF at solar maximum is less well understood, due in part to the complexity of the solar source functions, and partly to the lack of three dimensional observations which Ulysses is planned to remedy at the next solar maximum. It is suggested that the in-ecliptic conditions in the HMF, largely determined by the dynamics of transients (Coronal Mass Ejections) may also be found at high latitudes, due to the wide latitude distribution of the CMEs.     

Discontinuities in the solar wind

The nonuniform emission of the solar wind from the sun means that conditions are established which favor the development of discontinuities in the plasma parameters. Since the solar wind is in rapid proper motion with respect to the sun and the earth, examination of these discontinuities requires that the wind velocity be transformed away. Then it is found that they satisfy the conditions of magnetohydrodynamics and can be treated as shock waves and the stationary contact surfaces consisting of either tangential or contact discontinuities. The collision-free structure of the solar wind suggests that the tangential discontinuity is the more likely contact surface as it is more capable of inhibiting diffusion which is required for a lifetime sufficient for the structure to be carried to the neighborhood of the earth.Either the shock wave or the contact surface can create signals that are detectable at the surface of the earth. The simplest surface signal to detect is the sudden impulse (SI) but other signals may be found. The existence of a field of MHD discontinuities in the solar wind should make possible the generation of ensembles of shocks and contact surfaces. Various possibilities are explored and these are discussed from the standpoint of combinations of sudden impulses at the earth's surface which are both positive and negative. Some of these are recurrent with a 27-day period; the interplanetary M region shock ensemble associated with this is discussed and the development of these structures in space is reviewed.Lastly observational evidence for interplanetary shock waves is given together with the analytic technique for establishing their geometry and comparing the derived and measured jump parameters. The applicability of the geometrical construction of the general class of MHD discontinuity to their analysis is indicated and shows the way in which the structural content of the solar wind can be classified by the use of magnetometers and plasma probes. A parametric study of the jump conditions through a shock wave can be used to verify the correctness of field measurements because of the redundancy in measurements. This also allows the details of shock structure to be examined including the intrinsic partitioning of the internal energy of the shocked plasma.     

MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.     

Semi-empirical MHD Model of the Solar Wind and its Comparison with Ulysses

We have developed a 2D semi-empirical model (Sittler and Guhathakurta 1999) of the corona and the interplanetary medium using the time independent MHD equations and assuming azimuthal symmetry, utilizing the SOHO, Spartan and Ulysses observations. The model uses as inputs (1) an empirically derived global electron density distribution using LASCO, Mark III and Spartan white light observations and in situ observations of the Ulysses spacecraft, and (2) an empirical model of the coronal magnetic field topology using SOHO/LASCO and EIT observations. The model requires an estimate of solar wind velocity as a function of latitude at 1 AU and the radial component of the magnetic field at 1 AU, for which we use Ulysses plasma and magnetic field data results respectively. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, temperature T_eff, and heat flux Q_eff which are derived from the equations of conservation of mass, momentum and energy, respectively, in the rotating frame of the Sun. The term "effective" indicates possible wave contributions. The model can be used as a planning tool for such missions as Solar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind. This revised version was published online in June 2006 with corrections to the Cover Date.     

Heliospheric ENA fluxes: How Sensitive Are They to the Ionization State of LIC?

We explore the sensitivity of the fluxes of heliospheric energetic neutral atoms (ENA) at 1 AU to the ionization state of the local interstellar cloud (LIC). The solar wind plasma is compressed and heated in the termination shock transition. The shocked solar plasma is convected toward the heliospheric tail in the heliosheath, the region between the termination shock and the heliopause. The ENAs are produced in charge exchange of the plasma protons and background neutral gas and can be readily detected at 1 AU. The expected ENA fluxes depend on the shocked plasma density, temperature, and velocity in the heliosheath. The size and structure of the heliospheric interface region depend on the parameters of the interstellar medium. ENA fluxes would thus reveal the LIC parameters. We demonstrate the sensitivity of the heliospheric ENA fluxes to the ionization state of the LIC. The axi-symmetric model of the solar wind/LIC interaction includes the self-consistent treatment of the plasma-gas coupling and Monte Carlo simulations of the neutral gas distribution. This revised version was published online in August 2006 with corrections to the Cover Date.