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Using Parker Solar Probe data from orbits 8 through 17, we examine fluctuation amplitudes throughout the critical region where the solar wind flow speed approaches and then exceeds the Alfv\'en wave speed, taking account of various exigencies of the plasma data. In contrast to WKB theory for non-interacting Alfv\'en waves streaming away from the Sun, the magnetic and kinetic fluctuation energies per unit volume are not monotonically decreasing. Instead, there is clear violation of conservation of standard WKB wave action, which is consistent with previous indications of strong in-situ fluctuation energy input in the solar wind near the Alfv\'en critical region. This points to strong violations of WKB theory due to nonlinearity (turbulence) and major energy input near the critical region, which we interpret as likely due to driving by large-scale coronal shear flows.

The transition from subAlfv\'enic to superAlfv\'enic flow in the solar atmosphere is examined by means of Parker Solar Probe (PSP) measurements during solar encounters 8 to 14. Around 220 subAlfv\'enic periods with a duration $\ge$ 10 minutes are identified. The distribution of their durations, heliocentric distances, and Alfv\'en Mach number are analyzed and compared with a global magnetohydrodynamic model of the solar corona and wind, which includes turbulence effects. The results are consistent with a patchy and fragmented morphology, and suggestive of a turbulent Alfv\'en zone within which the transition from subAlfv\'enic to superAlfv\'enic flow occurs over an extended range of helioradii. These results inform and establish context for detailed analyses of subAlfv\'enic coronal plasma that are expected to emerge from PSP's final mission phase, as well as for NASA's planned PUNCH mission.

The solar wind is the extension of the Sun's hot and ionized corona, and it exists in a state of continuous expansion into interplanetary space. The radial distance at which the wind's outflow speed exceeds the phase speed of Alfvenic and fast-mode magnetohydrodynamic (MHD) waves is called the Alfven radius. In one-dimensional models, this is a singular point beyond which most fluctuations in the plasma and magnetic field cannot propagate back down to the Sun. In the multi-dimensional solar wind, this point can occur at different distances along an irregularly shaped "Alfven surface." In this article, we review the properties of this surface and discuss its importance in models of solar-wind acceleration, angular-momentum transport, MHD waves and turbulence, and the geometry of magnetically closed coronal loops. We also review the results of simulations and data analysis techniques that aim to determine the location of the Alfven surface. Combined with recent perihelia of Parker Solar Probe, these studies seem to indicate that the Alfven surface spends most of its time at heliocentric distances between about 10 and 20 solar radii. It is becoming apparent that this region of the heliosphere is sufficiently turbulent that there often exist multiple (stochastic and time-dependent) crossings of the Alfven surface along any radial ray. Thus, in many contexts, it is more useful to make use of the concept of a topologically complex "Alfven zone" rather than one closed surface. This article also reviews how the Polarimeter to Unify the Corona and Heliosphere (PUNCH) mission will measure the properties of the Alfven surface and provide key constraints on theories of solar-wind acceleration., Comment: Accepted for publication in Solar Physics, part of the topical collection titled "The Polarimeter to Unify the Corona and Heliosphere (PUNCH) Mission: An Overview." 30 pages, 8 figures

The solar wind (SW) and local interstellar medium (LISM) are turbulent media. Their interaction is governed by complex physical processes and creates heliospheric regions with significantly different properties in terms of particle populations, bulk flow and turbulence. Our knowledge of the solar wind turbulence \nature and dynamics mostly relies on near-Earth and near-Sun observations, and has been increasingly improving in recent years due to the availability of a wealth of space missions, including multi-spacecraft missions. In contrast, the properties of turbulence in the outer heliosphere are still not completely understood. In situ observations by Voyager and New Horizons, and remote neutral atom measurements by IBEX strongly suggest that turbulence is one of the critical processes acting at the heliospheric interface. It is intimately connected to charge exchange processes responsible for the production of suprathermal ions and energetic neutral atoms. This paper reviews the observational evidence of turbulence in the distant SW and in the LISM, advances in modeling efforts, and open challenges., Comment: 82 pages, 31 figures. Paper accepted by Space Science Reviews (collection: The Heliosphere in the Local Interstellar Medium: Into the Unknown), and presented at the ISSI Workshop on November 8-12, 2021

In the lower solar coronal regions where the magnetic field is dominant, the Alfven speed is much higher than the wind speed. In contrast, the near-Earth solar wind is strongly super-Alfvenic, i.e., the wind speed greatly exceeds the Alfven speed. The transition between these regimes is classically described as the "Alfven point" but may in fact occur in a distributed Alfven critical region. NASA's Parker Solar Probe (PSP) mission has entered this region, as it follows a series of orbits that gradually approach more closely to the sun. During its 8th and 9th solar encounters, at a distance of 16 solar radii from the Sun, PSP sampled four extended periods in which the solar wind speed was measured to be smaller than the local Alfven speed. These are the first in-situ detections of sub-Alfvenic solar wind in the inner heliosphere by PSP. Here we explore properties of these samples of sub-Alfvenic solar wind, which may provide important previews of the physical processes operating at lower altitude. Specifically, we characterize the turbulence, anisotropy, intermittency, and directional switchback properties of these sub-Alfvenic winds and contrast these with the neighboring super-Alfvenic periods., Comment: Accepted for publication in the Astrophysical Journal Letter

Motivated by theoretical, numerical, and observational evidence, we explore the possibility that the critical transition between sub-Alfv\'enic flow and super-Alfv\'enic flow in the solar atmosphere takes place in fragmented and disconnected subvolumes within a general Alfv\'en critical zone. The initial observations of sub-Alfv\'enic periods by Parker Solar Probe near \(16~R_\odot\) do not yet provide sufficient evidence to distinguish this possibility from that of a folded surface that separates simply-connected regions. Subsequent orbits may well enable such a distinction, but here we use a global magnetohydrodynamic model of the solar wind, coupled to a turbulence transport model, to generate possible realizations of such an Alfv\'en critical zone. Understanding this transition will inform theories of coronal heating, solar wind origin, solar angular momentum loss, and related physical processes in stellar winds beyond the Sun.

Neutron diffraction studies of HoFeO$_3$ single crystal were performed under external magnetic fields. The interplay between the external magnetic field, Dzyaloshinsky-Moria antisymmetric exchange and isotropic exchange interactions between Fe and Ho sublattice and inside Fe sublattice provides a rich phase diagram. As the result of the balance of exchange interactions inside crystal and external magnetic field we found 8 different magnetic phases, produced or suppressed by the field., Comment: 15 pages, 11 figures, 4 tables

Simulation results from a global magnetohydrodynamic model of the solar corona and solar wind are compared with Parker Solar Probe (PSP) observations during its first five orbits. The fully three-dimensional model is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model includes the effects of electron heat conduction, Coulomb collisions, turbulent Reynolds stresses, and heating of protons and electrons via a turbulent cascade. Turbulence transport equations for average turbulence energy, cross helicity, and correlation length are solved concurrently with the mean-flow equations. Boundary conditions at the coronal base are specified using solar synoptic magnetograms. Plasma, magnetic field, and turbulence parameters are calculated along the PSP trajectory. Data from the first five orbits are aggregated to obtain trends as a function of heliocentric distance. Comparison of simulation results with PSP data shows good agreement, especially for mean-flow parameters. Synthetic distributions of magnetic fluctuations are generated, constrained by the local rms turbulence amplitude given by the model. Properties of this computed turbulence are compared with PSP observations.

Context:In 2020 May-June, six solar energetic ion events were observed by the Parker Solar Probe/ISoIS instrument suite at 0.35 AU from the Sun. From standard velocity-dispersion analysis, the apparent ion path length is 0.625 AU at the onset of each event. Aims:We develop a formalism for estimating the path length of random-walking magnetic field lines, to explain why the apparent ion pathlength at event onset greatly exceeds the radial distance from the Sun for these events. Methods:We developed analytical estimates of the average increase in pathlength of random-walking magnetic field lines, relative to the unperturbed mean field. Monte Carlo simulations of fieldline and particle trajectories in a model of solar wind turbulence are used to validate the formalism and study the path lengths of particle guiding-center and full-orbital trajectories. The formalism is implemented in a global solar wind model, and results are compared with ion pathlengths inferred from ISoIS observations. Results:Both a simple estimate and a rigorous theoretical formulation are obtained for fieldlines' pathlength increase as a function of pathlength along the large-scale field. From simulated fieldline and particle trajectories, we find that particle guiding centers can have pathlengths somewhat shorter than the average fieldline pathlength, while particle orbits can have substantially larger pathlengths due to their gyromotion with a nonzero effective pitch angle. Conclusions:The long apparent path length during these solar energetic ion events can be explained by 1) a magnetic field line path length increase due to the field line random walk, and 2) particle transport about the guiding center with a nonzero effective pitch angle. Our formalism for computing the magnetic field line path length, accounting for turbulent fluctuations, may be useful for application to solar particle transport in general.

The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20{\deg} - 60{\deg}. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20{\deg}. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slab-like fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances.

Motivated by prior remote observations of a transition from striated solar coronal structures to more isotropic ``flocculated'' fluctuations, we propose that the dynamics of the inner solar wind just outside the Alfv\'en critical zone, and in the vicinity of the first $\beta=1$ surface, is powered by the relative velocities of adjacent coronal magnetic flux tubes. We suggest that large amplitude flow contrasts are magnetically constrained at lower altitude but shear-driven dynamics are triggered as such constraints are released above the Alfv\'en critical zone, as suggested by global magnetohydrodynamic (MHD) simulations that include self-consistent turbulence transport. We argue that this dynamical evolution accounts for features observed by {\it Parker Solar Probe} ({\it PSP}) near initial perihelia, including magnetic ``switchbacks'', and large transverse velocities that are partially corotational and saturate near the local Alfv\'en speed. Large-scale magnetic increments are more longitudinal than latitudinal, a state unlikely to originate in or below the lower corona. We attribute this to preferentially longitudinal velocity shear from varying degrees of corotation. Supporting evidence includes comparison with a high Mach number three-dimensional compressible MHD simulation of nonlinear shear-driven turbulence, reproducing several observed diagnostics, including characteristic distributions of fluctuations that are qualitatively similar to {\it PSP} observations near the first perihelion. The concurrence of evidence from remote sensing observations, {\it in situ} measurements, and both global and local simulations supports the idea that the dynamics just above the Alfv\'en critical zone boost low-frequency plasma turbulence to the level routinely observed throughout the explored solar system.

The current progress in the detection of terrestrial type exoplanets has opened a new avenue in the characterization of exoplanetary atmospheres and in the search for biosignatures of life with the upcoming ground-based and space missions. To specify the conditions favorable for the origin, development and sustainment of life as we know it in other worlds, we need to understand the nature of astrospheric, atmospheric and surface environments of exoplanets in habitable zones around G-K-M dwarfs including our young Sun. Global environment is formed by propagated disturbances from the planet-hosting stars in the form of stellar flares, coronal mass ejections, energetic particles, and winds collectively known as astrospheric space weather. Its characterization will help in understanding how an exoplanetary ecosystem interacts with its host star, as well as in the specification of the physical, chemical and biochemical conditions that can create favorable and/or detrimental conditions for planetary climate and habitability along with evolution of planetary internal dynamics over geological timescales. A key linkage of (astro) physical, chemical, and geological processes can only be understood in the framework of interdisciplinary studies with the incorporation of progress in heliophysics, astrophysics, planetary and Earth sciences. The assessment of the impacts of host stars on the climate and habitability of terrestrial (exo)planets will significantly expand the current definition of the habitable zone to the biogenic zone and provide new observational strategies for searching for signatures of life. The major goal of this paper is to describe and discuss the current status and recent progress in this interdisciplinary field and to provide a new roadmap for the future development of the emerging field of exoplanetary science and astrobiology., Comment: 206 pages, 24 figures, 1 table; Review paper. International Journal of Astrobiology (2019)

The Parker Solar Probe (PSP) primary mission extends seven years and consists of 24 orbits of the Sun with descending perihelia culminating in a closest approach of ($\sim 9.8~R_\odot$). In the course of these orbits PSP will pass through widely varying conditions, including anticipated large variations of turbulence properties such as energy density, correlation scales and cross helicities. Here we employ global magnetohydrodynamics simulations with self-consistent turbulence transport and heating \citep{usmanov2018} to preview likely conditions that will be encountered by PSP, by assuming suitable boundary conditions at the coronal base. The code evolves large-scale parameters -- such as velocity, magnetic field, and temperature -- as well as turbulent energy density, cross helicity, and correlation scale. These computed quantities provide the basis for evaluating additional useful parameters that are derivable from the primary model outputs. Here we illustrate one such possibility in which computed turbulence and large-scale parameters are used to evaluate the accuracy of the Taylor "frozen-in" hypothesis along the PSP trajectory. Apart from the immediate purpose of anticipating turbulence conditions that PSP will encounter, as experience is gained in comparisons of observations with simulated data, this approach will be increasingly useful for planning and interpretation of subsequent observations.

The solar corona and young solar wind may be characterized by critical surfaces -- the sonic, Alfv\'en, and first plasma-$\beta$ unity surfaces -- that demarcate regions where the solar wind flow undergoes certain crucial transformations. Global numerical simulations and remote sensing observations offer a natural mode for the study of these surfaces at large scales, thus providing valuable context for the high-resolution in-situ measurements expected from the soon-to-be-launched Parker Solar Probe (PSP). The present study utilizes global three-dimensional magnetohydrodynamic simulations of the solar wind to characterize the critical surfaces and investigate the flow in propinquitous regions. Effects of solar activity are incorporated by varying source magnetic dipole tilts and employing magnetogram-based boundary conditions. A magnetohydrodynamic turbulence model is self-consistently coupled to the bulk flow equations, enabling investigation of turbulence properties of the flow in the vicinity of critical regions. The simulation results are compared with a variety of remote sensing observations. A simulated PSP trajectory is used to provide contextual predictions for the spacecraft in terms of the computed critical surfaces. Broad agreement is seen in the interpretation of the present results in comparison with existing remote sensing results, both from heliospheric imaging and from radio scintillation studies. The trajectory analyses show that the period of time that PSP is likely to spend inside the $\beta=1$, sonic and Alfv\'en surfaces depends sensitively on the degree of solar activity and the tilt of the solar dipole and location of the heliospheric current sheet., Comment: Accepted for publication in The Astrophysical Journal Supplement Series

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic ray diffusion coefficients throughout the inner heliosphere ($2~R_\odot - 3$ AU). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path is evaluated using quasi-linear theory, while the perpendicular mean free path is determined by non-linear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mean free path (mfp) is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp; in the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 AU; our estimations of the parallel mfp in the ecliptic region at 1 AU agree well with the Palmer "consensus" range of $0.08 - 0.3$ AU; solar activity increases perpendicular diffusion and reduces parallel diffusion; the parallel mfp varies with rigidity $(P)$ as $P^{.33}$, and the perpendicular mfp is weakly dependent on $P$; the mfps are weakly influenced by the choice of long wavelength power spectra.

Stellar winds from active solar type stars can play a crucial role in removal of stellar angular momentum and erosion of planetary atmospheres. However, major wind properties except for mass loss rates cannot be directly derived from observations. We employed a three dimensional magnetohydrodynamic Alfven wave driven solar wind model, ALF3D, to reconstruct the solar wind parameters including the mass loss rate, terminal velocity and wind temperature at 0.7, 2 and 4.65 Gyr. Our model treats the wind thermal electrons, protons and pickup protons as separate fluids and incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating to properly describe proton and electron temperatures of the solar wind. To study the evolution of the solar wind, we specified three input model parameters, the plasma density, Alfven wave amplitude and the strength of the dipole magnetic field at the wind base for each of three solar wind evolution models that are consistent with observational constrains. Our model results show that the velocity of the paleo solar wind was twice as fast, about 50 times denser and 2 times hotter at 1 AU in the Suns early history at 0.7 Gyr. The theoretical calculations of mass loss rate appear to be in agreement with the empirically derived values for stars of various ages. These results can provide constraints for wind dynamic pressures on magnetospheres of (exo)planets around the young Sun and other active stars, which is crucial in realistic assessment of the Joule heating of their ionospheres and corresponding effects of atmospheric erosion., Comment: 7 pages, 4 figures, accepted by Astrophysical Journal Letters

A displacement of the heliospheric current sheet (HCS) south of the helioequator by approx.10deg was proposed by Simpson et al. (1996) as a possible explanation of the north-south asymmetry in the galactic cosmic rays observed by Ulysses during its first fast transit in 1994-1995. The idea was not supported by magnetic field measurements on Ulysses and, on this ground, was dismissed by Simpson et al. (1996). In addition, Erdos & Balogh (1998) argued that any north-south symmetry was unlikely as there should be flux balance between the magnetic sectors of opposite polarity. Nonetheless, many in the scientific community have accepted the original suggestion of Simpson et al. (1996) that a displacement of the HCS was responsible for the cosmic ray asymmetry. In this paper, using a magnetohydrodynamic model of the solar corona and solar wind that includes both dipole and quadrupole magnetic source terms, we show that a north-south asymmetry of the magnetic field on the Sun does not give rise to a displacement of the HCS. The lack of displacement of the HCS results from a latitudinal redistribution of magnetic flux near the Sun where the plasma beta much < 1. The latitudinal redistribution is a direct consequence of the magnetic field gradient between pole and equator. Near the Sun, the latitudinal gradient in magnetic field generates meridional flows directed equatorward that tend to relax the gradient in the magnetic field (to make it more latitude-independent) as heliocentric distance increases. If there is an asymmetry between north and south magnetic field strength then the meridional flows are also asymmetric (i.e., stronger in the hemisphere of stronger magnetic field). Because the magnetic fluxes (positive and negative) in the hemispheres must be equal, the redistribution shifts the HCS into balance by approx. 16 R(solar mass). At larger distances, where the magnetic field is relatively weak (beta much > 1), the HCS can be displaced if there is a difference in total pressure between the hemispheres.

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

We have developed a three-fluid, fully three-dimensional magnetohydrodynamic model of the solar wind plasma in the outer heliosphere as a co-moving system of solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Our approach takes into account the effects of electron heat conduction and dissipation of Alfvenic turbulence on the spatial evolution of the solar wind plasma and interplanetary magnetic fields. The turbulence transport model is based on the Reynolds decomposition of physical variables into mean and fluctuating components and uses the turbulent phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. We solve the coupled set of the three-fluid equations for the mean-field solar wind and the turbulence equations for the turbulence energy, cross helicity, and correlation length. The equations are written in the rotating frame of reference and include heating by turbulent dissipation, energy transfer from interstellar pickup protons to solar wind protons, and solar wind deceleration due to the interaction with the interstellar hydrogen. The numerical solution is constructed by the time relaxation method in the region from 0.3 to 100 AU. Initial results from the novel model are presented.

I will describe a three-dimensional magnetohydrodynamic model of the solar wind that takes into account turbulent heating of the wind by velocity and magnetic fluctuations as well as a variety of effects produced by interstellar pickup protons. In this report, the interstellar pickup protons are treated as one fluid and the protons and electrons are treated together as a second fluid. The model equations include a Reynolds decomposition of the plasma velocity and magnetic field into mean and fluctuating quantities, as well as energy transfer from interstellar pickup protons to solar wind protons that results in the deceleration of the solar wind. The model is used to simulate the global steady-state structure of the solar wind in the region from 0.3 to 100 AU. Where possible, the model is compared with Voyager data. Initial results from generalization to a three-fluid model is described elsewhere in this session.

We have developed a global fully three-dimensional magnetohydrodynamic solar wind model for the region that extends from the coronal base to 100 AU. The simulation domain consists of tree spherical shell subdomains with computational boundaries between them placed at 20 solar radii and 0.3 AU. The location of the first boundary ensures that the flow at the boundary is both supersonic and super-Alfvenic. A steady-state solution in the innermost (coronal) region is obtained by the time-relaxation method. The solution uses a tilted dipole model or solar magnetograms as the boundary condition at the coronal base and includes a flux of Alfven waves in the WKB approximation which provide additional acceleration for the coronal outflow in the open field regions. The intermediate region solution is constructed by the integration of steady-state equations along radius using a marching scheme. The outer region solution (0.3-100 AU) is obtained again by the time relaxation and takes into account turbulence transport and heating as well as heating, flow deceleration, and other effects due to the interstellar pickup protons treated as a separate fluid. We use the model to simulate the global steady-state structure of the solar wind from the coronal base to the heliospheric boundary and compare the results with Ulysses and Voyager observations.

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

Recently we have restructured our approach to simulating magnetohydrodynamic (MHD) turbulence in the solar wind. Previously, we had defined a 'virtual' heliosphere that contained, for example, a tilted rotating current sheet, microstreams, quasi-two-dimensional fluctuations as well as Alfven waves. In this new version of the code, we use the global, time-stationary, WKB Alfven wave-driven solar wind model developed by Usmanov and described in Usmanov and Goldstein [2003] to define the initial state of the system. Consequently, current sheets, and fast and slow streams are computed self-consistently from an inner, photospheric, boundary. To this steady-state configuration, we add fluctuations close to, but above, the surface where the flow become super-Alfvenic. The time-dependent MHD equations are then solved using a semi-discrete third-order Central Weighted Essentially Non-Oscillatory (CWENO) numerical scheme. The computational domain now includes the entire sphere; the geometrical singularity at the poles is removed using the multiple grid approach described in Usmanov [1996]. Wave packets are introduced at the inner boundary such as to satisfy Faraday's Law [Yeh and Dryer, 1985] and their nonlinear evolution are followed in time.

From time to time the density of the Solar Wind falls below unity for a day or so. Despite studies of these events, their cause has not been established. In the solar wind there are frequent rarefactions but these are much shallower than the ones we are discussing here. In particular any role that CMEs might play in forming more extreme rarefactions is not clear . We discuss 9 cases of extreme events, leading to sub-alfvenic flow and well observed by Wind, which occurred between 1999 and 2002, and look for corresponding CME events in the LASCO cotalog. The catalog gives a fitted speed , good out to 20 Rs ,as well as a speed lower down in the corona, and this is used to distinguish between a CME and an ICME. We find one of the events ,which was simulated by Usmanov et al.,cannot be associated with an ICME. The other eight events can plausibly be associated with fast ICMEs, identified by the prescence of bi-streaming electrons also seen by Wind SWE, and by other phenomena The implications of these observations are discussed but do not seem to be conclusive as to the cause of the extreme rarefactions.

We present simulation results from a tilted-dipole steady-state MHD model of the solar corona and solar wind and compare the output from our model with the Wang-Sheeley model which relates the divergence rate of magnetic flux tubes near the Sun (inferred from solar magnetograms) to the solar wind speed observed near Earth and at Ulysses. The boundary conditions in our model specified at the coronal base and our simulation region extends out to 10 AU. We assumed that a flux of Alfven waves with amplitude of 35 km per second emanates from the Sun and provides additional heating and acceleration for the coronal outflow in the open field regions. The waves are treated in the WKB approximation. The incorporation of wave acceleration allows us to reproduce the fast wind measurements obtained by Ulysses, while preserving reasonable agreement with plasma densities typically found at the coronal base. We find that our simulation results agree well with Wang and Sheeley's empirical model.