Asymptotic solutions of the viscous solar wind equations

There is one and only one solution of the viscous solar wind equations which is asymptotically represented for large distances from the sun by a formal solution of Y. C. Whang, C. K. Liu, and C. C. Chang as a power series in the inverse one third power of the distance.     

On viscous attenuation of Alfvenic fluctuations in the solar wind

It is shown that the viscous attenuation of Alfvenic fluctuations is anisotropic and is proportional to the fluctuation component parallel to the mean magnetic field. If the ratio between the parallel and perpendicular components is a constant, then the viscous attenuation experienced by waves with wavelengths larger than the collisional free-path will be concentrated within 20 $\text{R?}$. Between 0.3 AU and l AU, no Alfvenic fluctuations of any frequency is appreciably damped by viscosity determined by Coulomb collision. The mechanism of viscous attenuation caonot explain the observed radial development of the spectrum. If, near the Sun, the Alfvenic fluctuations do have a parallel component, then the viscous damping will have an important accelerating effect on the solar wind in fast diverging stream tubes. If the parallel component is negligible, then the Alfvenic fluctuation will not be attenuated by any classical viscosity.     

A simulation study of the solar wind including the solar rotation effect

An axisymmetric solar wind structure including the solar rotation effect is studied by the method of MHD computer simulation. For the case of the radial magnetic field configuration, the simulation result is fairly well coincident with the steady-state solution. For the case of the dipole magnetic field configuration, the properties of the solution depend on the ratio of the gas pressure to the magnetic pressure-ratio) in the model. If the-ratio is small, a clearly defined stagnation region appears in the wind, in which the flow speed is very small and the azimuthal magnetic field is very weak because of the corotation of the plasma. If the-ratio is greater than 1, the plasma is not effectively trapped by the magnetic field so that the stagnation region is not clearly defined in the solution.     

On the role of plasma parameters and the Kelvin-Helmholtz instability in a viscous interaction of solar wind streams

We examine a mechanism for breaking down solar wind (SW) speed shears within 1 astronomical unit (a.u.), initiated by the development of the Kelvin-Helmholtz (K-H) instability for typical parameters of the plasma and magnetic field in the interplanetary medium. A semi-empirical SW model has been invoked to derive a distribution of the plasma parameters β = 8πP/B² and M_A² = (ρν²/2)/(B²/8π) between the Sun and 1 a.u. It is shown that in the vicinity of the Sun, up to heliocentric distances r ≈ 0.1 a.u., the parameters β ? 1, and M²_A ? 1 and therefore the magnetic field here may be considered a very strong one. Because of the stabilizing effect of the magnetic field the K-H instability in this region does not develop and a presence of great shears in SW speed with large velocity gradients is possible here.At distances r > 0.1 a.u. the parameters β ? 1, and M²_A > 1. Examination of a variety of SW speed profiles showed that the presence of plasma flow velocity shears in this region leads to an excitation of the K-H instability. Numerical analysis results indicate that a principal role in the excitation of this instability is played by oblique waves that propagate at an angle α ≈ 45° to the stream velocity vector.The question of the evolution of the leading front of a high speed SW streams within 1 a.u. is discussed, with a proper account of the influence of competing effects of kinematic steepening and turbulent viscosity, the latter being due to the development of the K-H instability. It is shown that the turbulent viscosity effect in this region is substantial and is capable of ensuring an expansion of the leading front of the high speed SW stream as this moves from 0.3 to 1 a.u., in agreement with experimental evidence reported by Rosenbauer et al. (1977).     

Wave-trains in the solar wind

Applying an Alfvén-Wave-Extended-QRH-approximation and the method of characteristics, we solve the equations of motion for outwardly propagating Alfvén waves analytically for three different cases of an azimuthal dependence of the background solar wind, (a) for a pure fast-slow stream configuration, (b) for the situation where the high-speed stream originates from a diverging magnetic field region, and (c) for the case of (b) and an initially decreasing density configuration (‘coronal hole’). The reaction of these waves on the background state as well as mode-mode coupling effects are neglected. These three solar wind models are discussed shortly. For the superimposed Alfvén waves we find, on an average, that there is a strong azimuthal dependence of all relevant wave parameters which, correlated with the azimuthal distributions of the solar wind variables, leads to good agreements with observations. The signature of high-speed streams and these correlations could clearly indicate solar wind streams originating from ‘coronal holes’. Contrary to the purely radial dependent solar wind, where outwardly propagating Alfvén waves are exclusively refracted towards the radial direction, we now find a refraction nearly perpendicular to the direction of the interplanetary magnetic field in the compression region and closely towards the magnetic field direction down the trailing edge and in the low-speed regime.     

Wave-trains in the solar wind

The equations of motion of all relevant parameters of Alfvén waves propagating from the sun outwardly into the expanding interplanetary medium are discussed for the case of a quiet, ideal, isotropic, one-fluid solar wind plasma. It is found that the frequency of the wave reamains constant, while the wave vector and the amplitudes depend, in general, on the evolution of the background medium and on the angle between the wave vector and the interplanetary magnetic field. This latter dependence cancels approximately for the evolution of the amplitudes in the case of a pure, overall spiral magnetic field. It is shown that in this case the results of earlier discussions can be derived by less decisive restrictions.     

Wave-trains in the solar wind

The main results of Whitham's averaged Lagrangian method for the treatment of linear wave-trains in a weakly inhomogeneous, moving medium are presented briefly. This method is then applied to an ideal, isotropic, one-fluid plasma which can be taken for the lowest order approximation for the interplanetary solar wind expansion.     

Heat transport in the solar wind

Heat transport is considered both for quiet and disturbed solar winds. It is shown that heat may be transferred during solar flares by sharp fronted thermal wave pulses. Energy dissipation in the wave front arises from the firehose instability excitation. The effects of ionosonic turbulence on heat transport in a quiet solar wind are also investigated. A quasi-steady state, in which there is a balance between wave-particle interations and particle collisions is found. It is shown that the effect of wave-particle ‘collisions’ is to produce a significant decrease of the electron heat flow and electron temperature, and increase of the ion temperature relative to calculations which take into account particle particle collisions only.     

Hydromagnetic shocks in the solar wind

The Rankine-Hugoniot relations are applied to shock-like discontinuities measured by both magnetic field and plasma instruments on the satellite Explorer 34 between May 30, 1967 and Jan. 11, 1968.Shock normals were either determined from the magnetic field observations, or from the times of occurrence of the discontinuity at Explorers 33, 34 and 35. The Rankine-Hugoniot relations are obeyed to the accuracy of the observations, and the values of shock velocities, density ratios, and Mach numbers indicate that at 1 AU the typical interplanetary shock is not strong, although all the events studied caused geomagnetic impulses.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

Minor ions in the solar wind

Ions heavier than ⁴He are treated as “minors” in the solar wind. This is justified for many applications since minor ions have no significant influence on the dynamics of the interplanetary plasma. However, minor ions carry information on many aspects of the formation, on the acceleration and on the transfer of solar plasma from the corona into the interplanetary space. This review concentrates on various aspects of minor ions as diagnostic tracers. The elemental abundance patterns of the solar wind are shaped in the chromosphere and in the lower transition region by processes, which are not fully understood at this moment. Despite this lack of detailed understanding, observed abundance patterns have been classified and are now commonly used to characterize the sources, and to trace back solar-wind flows to their origins in the solar atmosphere. Furthermore, the solar wind is the most important source of information for solar isotopic abundances and for solar abundances of volatile elements. In order to fully exploit this information, a comprehensive understanding of elemental and isotopic fractionation processes is required. We provide observational clues to distinguish different processes at work.     

Helium abundance in the solar wind

Observations of hydrogen and helium ions in the solar wind have been carried out by the Goddard Space Flight Center - University of Maryland plasma instrument on Explorer 34. These ions are completely separated by means of electrostatic and magnetic fields. The average value of the ratio of number densities is 0.051 ± .02, derived from over 3000 h of measurement. Variations about this value from about 0.01 up to greater than 0.15 occur, and there are more high values than can be explained by random variation. A tentative association with some geomagnetic storms is suggested. The above value of abundance, assuming that plasma emitted in the ecliptic plane is a fair sample of the output of the sun, combined with other recent work by other methods indicate that the solar abundance may be about half the previously quoted estimates of approximately 0.1.     

Corotating structure in the solar wind

The hydrodynamic equations which describe the radial solar wind expansion are linearized and specialized to treat corotating perturbations. Approximate solutions are found which are time stationary in the corotating reference frame. The solutions predict the behavior of corotating structures for a given boundary condition close to the sun. In particular, the structure resulting from the interaction of fast and slow streams is described. Comparison with sector structure data shows reasonable qualitative and quantitative agreement.     

Magnetic dips in the solar wind

Using magnetic data from the HELIOS-1 fluxgate magnetometer, with a 0.2 s resolution, we have investigated the structure of several interplanetary discontinuities involving magnetic dips and rotations of the magnetic field vector. A minimum variance analysis illustrates the behaviour of the magnetic field through the transition. Using this analysis, quite different structures have been isolated and, in particular, narrow transitions resembling almost one dimensional reconnected neutral sheets. For the thinner cases (scale lengths of the magnetic rotation of the order or smaller than 10³ km), we find that the observed structures can be the nonlinear effect of a resistive tearing mode instability having developed on an originally one dimensional neutral sheet at the solar corona.     

Geoactive zones in the solar wind

Three parameters of the solar wind, proton number density n, Z-component of frozen-in magnetic field, in solar ecliptic coordinates and magnetic field variability ΔB, may be called geoactive parameters since each of them is responsible for a certain phase or stage of a geomagnetic storm.An undisturbed solar corpuscular stream differs from the quiet solar wind mainly in higher bulk velocity v; other parameters, in particular, n, Z and ΔB, are not enhanced in the stream. However, the examination of a number of geomagnetic storms shows that v is not a geoactive parameter. Hence the corpuscular stream itself is not more geoactive than the quiet solar wind.The retarding of corpuscular stream by the quiet solar wind results in various plasma deformations (compression, torsion, shear). This, in turn, leads to the creation, in the stream and ambient quiet solar wind, of geoactive zones. Each zone is characterized by the enhancement of some geoactive parameter. The entry of the Earth into a geoactive zone causes a corresponding phase or stage of a geomagnetic storm.The concept of geoactive zones is applied to the analysis of the geomagnetic storm of 8–10 July 1966.     

Tangential discontinuities in the solar wind

This paper considers six discontinuity surfaces which were observed by magnetometers on 3 spacecraft in the solar wind. It is shown that the actual surface orientations, determined from the measured time delays and solar wind speed, are consistent with the theoretical orientations which were computed from the relation , where is the normal to the surface of a hydromagnetic tangential discontinuity across which the magnetic field direction changes from to . The plasma and magnetic field data for these discontinuities are consistent with the pressure balance condition, and the magnetic field vectors in the associated current sheets are parallel to the discontinuity surface, as required theoretically. The 6 discontinuity surfaces extended without much distortion over ∼ 0.002 AU. A seventh surface is discussed which satisfies the condition but which extended without much distortion over 0.01 AU. This latter is not a typical surface, however, and its curvature is larger than average. Most of the surfaces tended to lie along the spiral direction, but one was nearly perpendicular to the spiral direction.     

The effect of solar wind latitudinal dependence on the cosmic-ray propagation in the heliosphere

We have investigated how the latitude dependence of the solar wind velocity (SWV) influenced the cosmic-ray (CR) modulation and distribution in the heliosphere. The dependence proposed by Fry and Akasofu (1987) is used:v _SW=v _O+v ₁(1-cos ⁿ _m , where the SWV,v _SW is a function of the heliomagnetic latitude _m andv ₀ andv ₁ are constants. An estimation of the diffusion and drift terms in the transport equation is made, which shows that towards the poles the effects of the drift transfer decrease, while the diffusion terms in the equation increase due to the change of the interplanetary magnetic field (IMF) geometry. The numerical solutions of the two-dimensional (2-D) transport equation show that when the SWV changes with latitude: (1) The CR intensities away from the neutral sheet are larger for both IMF polarity periods in comparison with the case when the SWV does not change with the latitude. (2) The latitude gradients are negative during negative magnetic polarity periods. (3) The Voyager 1 and Voyager 2 long-time observations showing greater galactic CR intensities nearer the Sun at greater distances, could be explained by the proposed model.     

The solar wind

The current status of our understanding of the nature and origin of the solar wind is briefly reviewed, with emphasis being placed on the need for wave-particle interactions to account for the main energy source as well as details of the particle distribution functions. There has been considerable progress in the theoretical treatment of various aspects of the physics of the solar wind but a complete understanding is not yet in sight. Arguments concerning the ultimate fate of the solar wind are reviewed, in particular those concerning the distance to the shock wave which marks the termination of supersonic flow. This is of particular significance in view of recent observations suggesting that the termination might occur at about 50 AU from the Sun.     

Variable solar wind

The solar wind in the heliosphere is a variable phenomenon on all spatial and time scales. It has been shown that there are two basic types of solar wind by the Strouhal number S = L/VT, which characterizes relative variations in the main parameters of the solar wind on the given time interval T and linear scale L for velocity V, which is never zero. The first type is transient (S > 1), which is usually the basic type for sufficiently small values of T and large values of L. The second type is quasi-stationary, when 1 > S > 0. The constant solar wind is nonexistent. The extreme case of S = 0 is physically impossible, as is the case of S = ∞. It is always necessary to indicate and justify the range of applicability for a special quasi-stationary case 1 ? S > 0. Otherwise, to consider the case of S = 0 is incorrect. Regarding this, the widely-spread views on the stationary state of the solar wind are very conditional. They either lack physical sense, or have a very limited range of applicability for time T and scale L.