Convergent solutions of the inviscid solar wind equations

Formal solutions of the inviscid solar wind equations as power series in the inverse one seventh power and in the inverse one fifth power of the distance from the sun are shown to be convergent.     

Viscous solutions of the two-fluid solar wind equations

The two-fluid equations describing the ideal, steady, viscous solar wind are examined, and supersonic solutions are sought in which the electron and ion temperatures vary as inverse powers of the radial distance from the Sun. Just two solutions are found, and these are analogous to those found by Whang et al. (1966) and Dahlberg (1970) in one-fluid theory.     

The asymptotic behavior of the supersonic solutions of the two-fluid solar wind equations

Three different asymptotic branches of the two-fluid equations are found with _e ^m , _p ⁿ , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Re-examination of the viscous effect in the solar wind

The Helios observations of the plasma and magnetic field in the high-speed solar wind streams between 1 AU and 0.3 AU are used to examine the radial distribution of the various forces exerted on the streams. It is shown that the classical expression of the viscosity derived under the condition of collision-dominated plasma is not suitable for describing the viscous effect in the high speed wind streams, and the viscous force appears to exist in order to balance the inertial force of the fluid element with a resulting force, which approximates to the solar gravity between 0.3 AU and 1 AU. The radial dependence of the real viscous force in the streams is deduced and the corresponding viscosity is derived by assuming the trend of the real viscosity to approach the classical viscosity at small heliocentric distances. It is found that the ratio of the real to the classical viscosity at 1 AU should be equal to or greater than one tenth.     

Solutions of the two-fluid solar wind equations: Adiabatic and conduction dominated solutions

The equations governing the two-fluid spherically symmetric models of the solar wind have been solved numerically for a wide range of base conditions. As predicted from an asymptotic analysis we find a whole domain of solutions which are asymptotically adiabatic with the proton and electron temperatures tending to equality and varying like r ^{- 4/3}. In these 4/3 solutions the electron and proton heat conduction is asymptotically negligible and if it is neglected the resulting equations can be integrated analytically and shown to have the 4/3, 4/3 behaviour.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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.     

Some solutions of Einstein's equations with viscous fluids

If we admit the bulk and shear viscosity coefficients to be homogeneous in all the stages of the cosmic evolution and the fact that these can be expressed in terms of the metric coefficients, we obtain some cosmological models that are exact solutions of Einstein's equations. The metric utilized is the one of Szekeres's class II and the curvature source is a viscous fluid without heat flux.     

Unique solutions of solar wind models with thermal conductivity

The solutions of a radially symmetrical solar wind model with thermal conductivity are discussed in the neighborhood of the loci of the critical points, called the critical line, and at infinity. It is shown that for constant mass and total energy flux the conditions at infinity are related uniquely to the conditions at the critical line. Furthermore the requirement that the solution is continuous and has the proper behavior at infinity will determine uniquely one specific point on the critical line through which the solution has to pass.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

A note on the solution of the saturation flux limited solar wind equations

The solution curves of the differential equations determining the behavior of the solar wind are calculated for the case where the heat flux has its maximum value 3/2 nkTv _th. All the supersonic solutions are asymptotically adiabatic, T r ^-4/3.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Restrictions on radial magnetic field and flow solutions for the solar wind

In Parker's original model, the solar wind is represented as a spherically symmetric hydrodynamic flow. The velocity is radially directed and decoupled from the magnetic field. The simple extension of this model to include a dependence on the polar angle, , is shown to be invalid for radial flow and radial magnetic field. This work demonstrates how ad hoc symmetry conditions imposed to simplify a non-linear problem can be incompatible with the basic hydromagnetic equations.     

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.     

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.     

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.     

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.     

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.     

The termination of the solar wind

It has previously been suggested that the solar wind might terminate at distances of 5 AU to 20 AU from the Sun, and that the solar wind might be drastically slowed down by charge exchange and photoionization of interstellar hydrogen atoms which approach the Sun. However, recent satellite measurements of resonantly scattered Lyman alpha radiation, together with pulsar dispersion and Faraday rotation measures, imply very small values for the interstellar hydrogen density (0.05 cm⁻³) and magnetic field strength (3 μG). As a result, the solar wind is not expected to be slowed down by more than about 30% inside the termination distance, which is expected to be about 100 AU.     

Magnetic field of the solar wind

Relationship between the geoefficiency of the solar flares as well as of the active regions passing the central meridian of the Sun and the configuration of the large scale solar magnetic field is studied.It is shown that if the tangential component of the large scale magnetic field at the active region or at the flare region is directed southwards, that region and that flare produce geomagnetic storm. In case when the tangential magnetic field is directed northward, the active region and the flares occurring at that region do not cause any geomagnetic disturbance.An index of the geoefficiency of the solar flares and of the active regions is proposed.     

Thermalization of solar wind

Three kinetic equations describing the linear and non-linear wave-particle interaction for an anisotropic solar wind plasma have been developed. These equations have been solved numerically to find the variation inT /T with respect to time, whereT andT are the perpendicular and parallel temperatures with respect to the ambient magnetic field of the solar wind. For wave energy greater than a critical value (strong turbulence), non-linear wave-particle interactions are important but do not lead to thermalization. On the other hand, weak nonlinear interactions tend to increaseT /T , but make only a negligible contribution in the quantitative sense. Thus, only the linear wave-particle interaction remains as the significant contributer to the increase ofT /T .