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.     

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.     

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.     

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.     

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     

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.     

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.     

α-particle observations in the solar wind

The plasma experiment on board of the ESRO satellite HEOS-1 detects solar wind positive ions in the energy range from 200 eV/Z–16000 eV/Z. -particles have been observed for 10% of the time, from December 1968 to March 1969, when in the interplanetary medium -particle and proton bulk velocities are on average equal. The average relative abundance of -particles is 5.5 %.Although in general the two species, hydrogen and helium, have a similar behaviour, very often -particles have an independent time history. Strong discontinuities may be observed in one species, without occurring in the other, or having different characteristics. At certain times, -particles seem to behave as an independent fluid.Well defined fluxes of -particles are observed within the magnetosheath: in several cases -particles, present in the unperturbed solar wind, are found with unchanged energy spectrum through a certain layer behind the proton shock front inside the magnetosheath. This suggests that thermalization of -particles does not occur at the same place as that of protons.     

Coronal heating and solar wind acceleration; gyrotropic electron-proton solar wind

In coronal holes the electron (proton) density is low, and heating of the proton gas produces a rapidly increasing proton temperature in the inner corona. In models with a reasonable electron density in the upper transition region the proton gas becomes collisionless some 0.2 to 0.3 solar radii into the corona. In the collisionless region the proton heat flux is outwards, along the temperature gradient. The thermal coupling to electrons is weak in coronal holes, so the heat flux into the transition region is too small to supply the energy needed to heat the solar wind plasma to coronal temperatures. Our model studies indicate that in models with proton heating the inward heat conduction may be so inefficient that some of the energy flux must be deposited in the transition region to produce the proton fluxes that are observed in the solar wind. If we allow for coronal electron heating, the energy that is needed in the transition region to heat the solar wind to coronal temperatures, may be supplied by heat conduction from the corona.     

Large velocity discontinuities in the solar wind

In the course of 3000 hours observation of the interplanetary plasma, the plasma and magnetic-field experiments on Explorer 34 have detected 11 discontinuous solar-wind speed changes, not associated with shocks, of more than 60 km/sec in less than 3 min. These events, called uD's, may show a velocity change of either sign, but the plasma density and temperature are not found to change appreciably across them. Each speed discontinuity occurs simultaneously with a directional discontinuity in the magnetic field. High-resolution magnetic-field data show that sometimes the directional changes occur as rotational fans, and at other times they are erratic or occur within the time resolution of the magnetic-field experiment, 2.6 sec. The flow direction of the solar wind changed at 2 of the 11 uD's. The quiet nature of the field and plasma on each side of these events gives the impression that they are stable. The existence of these uD's is shown to be consistent with the theory of the Helmholtz instability. In particular, the additional observation that the magnetic-field direction change, , at a uD tends to be near 90° is consistent with the theory, for uD's with small may become unstable as they move from the sun.     

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.     

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR ^–1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR ^–3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Ion cyclotron instability in the solar wind

An ion cyclotron instability, arising because of the relative drift between the beam and the main components of the proton distribution function in the solar wind at 1 AU, is studied. The instability is excited in a bounded range of wave numbers provided the relative drift exceeds a certain minimum value called instability threshold. For 1, the instability threshold is smaller than or equal to the threshold of magnetosonic and Alfvén instabilities. The growth rates are enhanced by increasing relative drift and ratio of beam to main proton number density and by decreasing the wave numbers.