On the stability of the solar wind

The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist.     

On neutral sheets in the solar wind

The structure and dynamics of neutral sheets in the solar wind is examined. The internal magnetic topology of the sheet is argued to be that of thin magnetic tongues greatly distended outward by the expansion inside the sheet. Due to finite conductivity effects, outward flow takes place across field lines but is retarded relative to the ambient solar wind by the reverse J×B force. The sheet thickness as well as the internal transverse magnetic field are found to be proportional to the electrical conductivity to the inverse one third power. Estimating a conductivity appropriate for a current carried largely by the ions perpendicular to the magnetic field, we find sheet dimensions of the order of 500km representative for the inner solar corona. For a radial field of strength 1/2G at 2R , the transverse field there is about 2 × 10^–3G and decreases outward rapidly.The energy release in the form of Joulean dissipation inside the sheet is estimated. It is concluded that ohmic heating in current sheets is not a significant source of energy for the overall solar wind expansion, mainly because these structures occupy only a small percentage of the total coronal volume. However, the local energy release through this mechanism is found to be large - in fact, over 7 times that expected to be supplied by thermal conduction. Therefore, ohmic heating is probably a dominant energy source for the dynamical conditions within the sheet itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the north-south asymmetry in the solar wind

The orientations of tangential discontinuities seen by Mariner 4 are interpreted as implying a sector dependent asymmetry in the north-south component of the solar-wind flow. In two sectors, fast solar wind streams had a southward motion relative to slow streams, in one sector the reverse obtained, and in the remaining sector the asymmetry was not clearly defined. We interpret this as being due to greater pressure in the north hemisphere in two sectors and greater pressure in the south hemisphere in one. It is possible this asymmetry could produce a small average southward magnetic field component.     

On the occurrence rate of high-speed solar wind events

We have investigated the rate of occurrence of solar wind phenomena observed between 1972–1984 using power-spectrum analysis. The data have been taken from the high-speed solar wind (HSSW) stream catalogue published by Mavromichalaki, Vassilaki, and Marmatsouri (1988). The power-spectrum analysis of HSSW events indicates that HSSW stream events have a periodicity of 9 days. This periodicity of HSSW events is of the 27-day period of coronal holes, which are major sources of solar wind events. In our opinion, the 9-day period may be the energy build-up time for coronal hole regions to produce the HSSW stream events.     

On the propagation of magnetic disturbances in the solar wind

Under the geometrical optics approximation we discuss the propagation of a polarized magnetic profile, made up of Alfvén waves, in the solar wind. We show that (i) the profile propagates at an angle to the radial direction (the direction of the solar wind flow), (ii) the radial half-width of the profile stays essentially constant, or even diminishes a little, with distance from the Sun, (iii) the half-width in a direction transverse to the radial direction increases without limit as the magnetic profile moves outward from the Sun. Thus the profile stretches out into a ‘ribbon’ which could, of course, be experimentally identified as a discontinuity. We also give equations for the variation of polarization of the profile, and illustrate the behavior of polarization in a simple case. We have done these calculations to show that the production of ‘discontinuities’ in the solar wind can arise from propagation effects on irregularly shaped ‘blobs’ of magnetic field, as well as from other causes.     

On the collisional theory of the anisotropic solar wind plasma

The collisional equations for the solar wind assuming steady, spherically symmetric flow and including thermal conduction and an anisotropic proton temperature are analysed in the absence of a heat source function. The equations are cast in a form that involves one dimensionless parameter, effectively equal to the inverse Péclet number for protons, and the small quantity , the square-root of the electron-proton mass ratio. Analytic forms for the proton temperature anisotropy and other flow variables are derived by applying the limit 0, and using asymptotic techniques. It is found that the model based purely on Coulomb collisions predicts values for the proton temperature anisotropy in the vicinity of the Earth that are much smaller than those observed, and that increasing the coronal base temperature serves to decrease the predicted anisotropy still further.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the heliographic latitude dependence of the solar wind velocity

Plasma data from Pioneers 6–7 and from a variety of satellites operating near the Earth are used to investigate the heliographic latitude dependence of the solar wind bulk speed near the sunspot maximum. No evidence is found for a latitude effect: the latitudinal gradient, if any, turns out to be 2 km (sec degree)^–1, to be compared with the gradient of 10 km (sec degree)^–1 observed in periods of low or moderate solar activity.     

On the validity of the chapman-enskog description of the solar wind

The validity of the Chapman-Enskog method in the calculation of the heat conductivity of the solar wind is studied. The predictions of the Chapman-Enskog theory are compared with known results of rarefied gas kinetic theory. The results suggest that the use of the Chapman-Enskog theory to describe the transport processes in the solar wind is not strictly justified.     

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.     

On solar wind helium and heavy ion temperatures

Because of theoretical difficulties in predicting the behavior of multi-ionic plasmas, observation must serve as a guide to expectations concerning the results of further measurements of other parameters. Here we examine the support for the common belief that observations of the helium to hydrogen temperature ratio indicate that the thermal velocities of ionic species in the solar wind tend to be equal.     

On the modeling of the three-fluid structure of the quiet solar wind

The reciprocal influence of the electrons and protons, on one side, and the -particles, on the other side in the quiet solar wind is investigated within the framework of a conductive three-fluid model (with frictional forces included). For this purpose two mathematical methods are used, namely: I. Simultaneous solution of the fluid equations for all three species; and II. Solution of two-fluid equations (for electrons and protons) followed by that of a modified one-fluid equation for the -particles (in which the two-fluid solutions are used for electrons and protons).The results of our investigation indicate the following: (a)The macroscopic -particle characteristics as obtained from the two methods of solution are almost identical. Thus, the differences between the three-fluid and two-fluid characteristics of the electrons and protons represent a second order (and negligible) effect on the -particle characteristics. In both approaches, the frictional interaction between -particles and protons raises the (lower) -particle streaming velocity to that of the protons and decreases the relative to proton density ratio to a value about 0.035, as observed at 1 AU, (b)The electron and proton characteristics obtained from three-fluid and two-fluid solutions are similar, except for the proton temperature. The two-fluid solution providesT _p-values which, though within the observational error, are larger than those obtained from the simultaneous three-fluid solution (at 1 AU, the difference amounts to about 30%). Thus, the -particles affect the temperature profile of the protons in the solar wind through heat exchange (mainly), dynamical friction, as well as through their contribution to the interplanetary electrostatic field.     

On the correlation of coronal green-line intensity and solar wind velocity

Cross-correlation functions have been computed between green-line intensity (Kislovodsk) and Vela solar wind velocity January–June 1967. They are calculated separately for east and west limb observations in 5° latitude increments, and the solar wind velocites are correlated at their estimated emission times by correcting for the plasma Earth-Sun transit time using the observed velocities. The cross-correlation patterns appear to be dominated by two competing effects: a tendency of quasi-stationary green-line emission and solar wind velocity to anti-correlate; and a tendency of transient green-line emission and solar wind velocity enhancements to correlate positively. We also find evidence for simultaneous (same-day) emission brightenings over 2 to 4 limb quadrants. It is therefore recommended that, following a well-known practice in solar terrestrial studies, recurrent and transient events in both solar wind and green-line emissions should be studied separately.     

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

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 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.     

On solar wind interaction with the earth's magnetosphere

Hydrodynamic and electrodynamic problems of solar wind interaction with the Earth's magnetosphere on the day-side are investigated.The initial fact, well established, is that the density of the magnetic field energy in the solar wind is rather small. Magnetic field intensity and orientation are shown to determine the character of the solar wind flow around the magnetosphere. For mean parameters of the wind, if the tangential component of the magnetic field is more or equal 5γ, the flow in the magneto-sheath will be laminar. For other cases the flow is of a turbulent type.For turbulent flow, typical plasma parameters are estimated: mean free path, internal scale of inhomogeneities and dissipated energy. The results obtained are compared with experimental data.For the case of laminar flow, special attention is paid to the situation when magnetic fields of the solar wind and Earth are antiparallel. It is suggested, on the basis of solid arguments, that the southward interplanetary field diffuses from the magnetosheath into the Earth's magnetosphere. These ideas are used for the estimation of the distance to the magnetopause subsolar point. A detailed comparison with results of observation is made. The coincidence is satisfactory. Theoretical investigation has been made to a great extent for thin magnetopause with thickness δ ～ R_He-gyroradius of an electron.It is shown that during magnetospheric substorms relaxation oscillations with the period τ = 100–300 sec must appear. A theorem is proved about the appearance of a westward electrical field during the substorm development, when the magnetosphere's day-side boundary moves Earthward and about the recovery phase, when the magnetopause motion is away from the Earth, when there is an eastward electrical field.In the Appendix, plasma wave exitation in the magnetopause is considered and conductivity magnitudes are calculated, including the reduction due to the scattering by plasma turbulence.     

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 .