We treat, both analytically and numerically, small-amplitude, undamped, toroidal Alfv6n waves in a model of axisymmetric solar wind flow in which solar rotation is neglected. There is no restriction to WKB waves; the waves may have any frequency. By transforming in simple ways the equations governing the waves we are able to obtain exact formal solutions to the general time-dependent problem as well as to the Fourier-analyzed problem. We discuss the equations and their solutions in terms of coupled inward and outward propagating waves. One integral of the equations for the Fourier amplitudes is obtained; it relates the amplitudes of the ingoing and outgoing waves. The integral is a special case of a general law of conservation of wave action, which we show to hold for finite wavelengths. The statement of the conservation of wave action is shown to be analogous to the conservation of particle-antiparticle pairs in relativistic quantum theory. We obtain the condition required for WKB waves and show that it depends on the coupling of waves in a flowing medium. The solar wind problem is discussed in terms of the Fourier amplitudes. It is shown that there is a singularity in the equations, at the Alfv6n point, which determines physically acceptable solar wind solutions. A qualitative account of the amplitudes far from the sun is given based on an exact solution for a model with constant solar wind flow speed. A conservation equation for the wave energy is obtained, and the relations among the wave energy density, energy flux density, force, and acceleration are stated. Numerical solutions, based on realistic solar wind profiles, are given. We show that non-WKB waves with wave periods of about a day or two have somewhat greater wave energy densities, up to a factor of 2 or so, in the corona than do WKB waves with the same amplitude at I A.U. On the other hand, non-WKB waves of any wave period are no more effective in accelerating the plasma than are WKB waves; they are much less effective for wave periods of a day or more. We conclude that, for conditions actually existing in the corona, WKB estimates quite accurately account throughout the corona for the wave energy density, energy flux density, and wave acceleration of the plasma for Alfv6n waves with periods less than about 0.05, 1, and 0.01 day, respectively; the corresponding periods in the solar wind are about 1, 1, and 0.5 day. INTRODUCTIONAlfv6n waves have long been known to be a conspicuous feature of the solar wind plasma [Belcher et al., 1969; Belcher and Davis, 1971]. They dominate the microscale structure of the solar wind at least 50% of the time; magnetoacoustic wave modes, if they occur, contribute much less power to the plasma fluctuations than does the Alfv6n mode [Belcher and Davis, 1971). The Alfv6n waves can contribute to the dynamics of the solar wind. They exert a pressure on the plasma and are capable, in principle, of driving the solar wind [Alazraki and Couturier, 1971; Belcher, 1971; Belcher and Olbert, 1975; Dewar, 1970; Hollweg, 1973a, b, 1...

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A new detailed first principle kinetic theory for electrons is presented which is neither a classical fluid treatment nor an expospheric calculation. This new theory illustrates the global and local properties of the solar wind expansion that shape the observed features of the electron distribution function fe, such as its bifurcation, its skewness, and the ‘differential’ temperatures of the thermal and suprathermal subpopulations. Our approach starts with the Boltzmann equation and retains the effects of Coulomb collisions via a Krook collision operator without recourse to wave‐particle effects. We conclude that Coulomb collisions determine the population and shape of fe in both the thermal (E kT) energy regimes. We find that electrons with E >7kT constitute a special subpopulation of the suprathermals, insofar as Coulomb collisions are concerned; these we call ‘extrathermals.’ The electrons in the thermal portion of fe have undergone ∼10‐20 Coulomb collisions for cumulative momentum transfer en route to the observer at 1 AU; this population is thus more removed from the properties of coronal electrons than the suprathermal population. This latter group retains a strong memory of coronal conditions, since they have undergone only a few momentum transfer collisions. The thermal population is most nearly in collisional contact with the local dynamics (compressions, rarefactions, etc.) of the solar wind. The suprathermal portion of fe is determined by Coulomb collisional interactions with the distribution of solar wind material on radial scale of the heliopause itself. In this respect the suprathermal portion of fe is found to be responsive to the consequences of the global dynamics of the solar wind expansion. We find that this subpopulation is an attenuated vestige of collisional populations deep in the corona (1.03–10 Rs) which has been redistributed via Coulomb multiple pitch angle scattering on magnetically open field lines. The suprathermal particles moving toward the sun are computed to be observed as a result of Coulomb‐collision‐induced backscattering at larger (1–10 AU) heliocentric distances than that of the observer. Based on this theoretical picture, quantitative estimates for the partition of thermal and suprathermal phase density, the break in the velocity distribution, and the magnitude of the skewness (heat flux density) agree well with those typically observed near 1 AU. These calculations predict that the extrathermal fraction of the phase density, the extrathermal temperature, and the net heat flux density carried by electrons should be anticorrelated with the local bulk speed in quasi‐steady‐state flows and that the radial variation of extrathermal temperature inside 1 AU should be essentially independent of heliocentric distance. Our work also shows that the observation of suprathermal particles cannot be taken as a priori evidence for in situ wave particle interaction(s), since we can theoretically calculate a suprathermal population of solar wind electrons at 1 AU b...

Both wire-wound solenoids and cylindrical magnets can be approximately modeled as ideal, azimuthally symmetric solenoids. We present here an exact solution for the magnetic field of an ideal solenoid in an especially easy to use form. The field is expressed in terms of a single function that can be rapidly computed by means of a compact, highly efficient algorithm, which can be coded as an add-in function to a spreadsheet, making field calculations accessible even to introductory students. In computational work these expressions are not only accurate but also just as fast as most approximate expressions. We demonstrate their utility by numerically simulating the experiment of dropping a cylindrical magnet through a nonmagnetic conducting tube and then comparing the calculation with data obtained from experiments suitable for an undergraduate laboratory.

Extensive measurements of low-energy plasma electrons and positive ions were made during the Voyager 1 encounter with Saturn and its satellites. The magnetospheric plasma contains light and heavy ions, probably hydrogen and nitrogen or oxygen; at radial distances between 15 and 7 Saturn-radii (Rs) on the inbound trajectory, the plasma appears to corotate with a velocity within 20 percent of that expected for rigid corotation. The general morphology of Saturn's magnetosphere is well represented by a plasma sheet that extends from at least 5 to 17 Rs, is symmetrical with respect to Saturn's equatorial plane and rotation axis, and appears to be well ordered by the magnetic shell parameter L (which represents the equatorial distance of a magnetic field line measured in units of Rs). Within this general configuration, two distinct structures can be identified: a central plasma sheet observed from L = 5 to L = 8 in which the density decreases rapidly away from the equatorial plane, and a more extended structure from L = 7 to beyond 18 Rs in which the density profile is nearly flat for a distance +/- 1.8 Rs off the plane and falls rapidly thereafter. The encounter with Titan took place inside the magnetosphere. The data show a clear signature characteristic of the interaction between a subsonic corotating magnetospheric plasma and the atmospheric or ionospheric exosphere of Titan. Titan appears to be a significant source of ions for the outer magnetosphere. The locations of bow shock crossings observed inbound and outbound indicate that the shape of the Saturnian magnetosphere is similar to that of Earth and that the position of the stagnation point scales approximately as the inverse one-sixth power of the ram pressure.