S. Ranga Sreenivasan

RESISTIVE FORCE-FREE MAGNETIC FIELDS.

The properties of the function α characterizing force‐free fields through the relation ≇ × B = αB are studied, and it is shown that it has to be either a function of space and time or a constant independent of both. An initial integrability condition for α and B is found. Using this condition, it is demonstrated for cylindrically symmetric magnetic fields that α must be a constant.

Exact algebraic dispersion relations for wave propagation in hot magnetized plasmas

A new model is presented for the treatment of wave propagation along an external magnetic field in a hot collisionless plasma. The analysis is based on the so-called polynomial distribution functions along the magnetic field, and takes account of enhanced fractions of high-energy particles, which are characteristic of rarefied and magnetized astrophysical plasmas, in comparison with the bi-Maxwellian distributions. These new distributions permit the derivation of general dispersion relations that are exactly valid for waves with Im (ω) > 0, and represent good approximations for those with Im (ω) > 0. Furthermore, the explicit form of the dispersion relations is shown to be valid for distribution functions of different shapes. Because of their algebraic structure, the solution of the dispersion relations can be shown to be equivalent to the determination of the roots of complex-valued polynomials. The cold plasma, the Maxwellian plasma and the so-called quasi-Maxwellian plasma appear in this formalism as asymptotic and special cases. The reliability of the model is demonstrated with the calculation of dispersion curves, growth and damping rates for several standard modes, and by comparing it with previous calculations carried out using explicit Maxwellian distributions. Finally, the tendency of the solar wind to generate ion-cyclotron waves is investigated as a first, new application.

Signature of a three-dimensional heliosphere in the spectra of anomalous cosmic rays

Abstract A steady-state transport model of the Anomalous component of Cosmic Rays (ACRs) that takes into account convection, spatial diffusion and adiabatic deceleration in a three-dimensional heliosphere is applied to compute ACR spectra in the kinetic energy range 2 keV to several GeV. The spectra are investigated with respect to their longitudinal gradients due to the three-dimensional structure of the heliosphere, defined by a latitudinally varying solar wind that is terminated by a heliospheric shock. The results significantly refine earlier studies based on the integrated spectra, i.e. the cosmic ray pressure. With the full spectral information at our disposal, we can identify the spectral regimes exhibiting the largest longitudinal gradients.

Longitudinal gradients of the distribution of anomalous cosmic rays in the outer heliosphere

Recent results, both from observation and theory, suggest that the termination shock of the solar wind is not spherical. First, observations made with the Ulysses spacecraft have confirmed that the solar wind momentum flux increases with latitude, implying an elongation of the shock above the suns poles. Second, results of modeling the global structure of the heliosphere indicate that a so-called upwind-downwind asymmetry of the shock is probable. In view of these findings as well as the observed upwind-downwind asymmetry in pick-up ion fluxes, one might suspect the existence of longitudinal gradients in the distributions of anomalous cosmic rays, which are supposedly identical with the pick-up ions accelerated at the termination shock. We demonstrate that such longitudinal gradients should indeed be expected in the outer heliosphere and estimate their magnitude using a three-dimensional modulation model.

On the collisional energy transfer between the constituents of the coronal plasma

It has been suggested that the distribution functions characterizing the constituents of the solar coronal plasma are non-Maxwellian. If so, an accurate treatment of the collisional momentum and energy exchange between the plasma constituents within the framework of hydrodynamic models requires a re-evaluation of the general transfer integrals in multi-component plasmas. We have evaluated these integrals numerically for both Maxwellian and non-Maxwellian distribution functions of the plasma species avoiding the standard approximation for the collision cross sections frequently employed in the literature. Significant differences are shown to exist in the energy exchange rates for different distributions. We also demonstrate the inadequacy of the assumption of thermodynamic equilibrium in the innermost solar wind and reveal the importance of an accurate evaluation of the transfer integrals for the solar coronal plasma based on more realistic velocity distributions.

On the Off-Ecliptic Distributions of Anomalous Cosmic Rays and their Relation to the Large-Scale Geometry of the Heliospheric Shock

The scenario explaining the origin of the anomalous component of cosmic rays (ACR) implies a close relation between these high energy particles and the solar wind termination shock representing their main acceleration region. Consequently, one should expect the ACR distributions in the heliosphere to reflect some information about the structure as well as the large-scale geometry of the shock. We study the influence of a non-spherically symmetric heliospheric shock on the off-ecliptic — i.e. high latitude — ACR distributions using a two-dimensional model including their anisotropic diffusion and drift in the heliospheric magnetic field as well as a solar wind flow dependent on the heliographic latitude. The model calculations are used to investigate the probability of a possible polar elongation of the heliospheric shock from observations of the distributions of the ACR at high latitudes during solar minimum conditions.

On the Asymmetry of the Distribution of the Anomalous Cosmic-Ray Component in the Heliosphere

An analysis based on a fluid type equation for the spatial diffusion of the anomalous component of cosmic rays in the solar wind is presented. The source distributions of the high-energy particles are related to the pick-up ion flux intensities at the position of the heliospheric shock. Due to the strong asymmetric distributions of the different species of pick-up ions in the heliosphere and a possible aspherical termination shock of the solar wind, the source distributions are expected to exhibit element specific upwind-downwind asymmetries. An analytical treatment of the problem, using boundary conditions derived from observations by the Pioneer and Voyager satellites, leads to an estimate of the asymmetries of the anomalous component in the heliosphere. The investigation is performed in two stages: the problem is solved for an axially symmetric heliosphere in the first instance, and a latitudinal variation of the solar wind velocity as well as in the hydrodynamic diffusion coefficient is incorporated to model the effects of a heliospheric magnetic field in the second. Subject headings: acceleration of particles — cosmic rays — shock waves — solar wind

On the asymmetry of the distribution of the anomalous cosmic-ray component in the heliosphere

An analysis based on a fluid type equation for the spatial diffusion of the anomalous component of cosmic rays in the solar wind is presented. The source distributions of the high-energy particles are related to the pick-up ion flux intensities at the position of the heliospheric shock. Due to the strong asymmetric distributions of the different species of pick-up ions in the heliosphere and a possible aspherical termination shock of the solar wind, the source distributions are expected to exhibit element specific upwind-downwind asymmetries. An analytical treatment of the problem, using boundary conditions derived from observations by the Pioneer and Voyager satellites, leads to an estimate of the asymmetries of the anomalous component in the heliosphere. The investigation is performed in two stages: the problem is solved for an axially symmetric heliosphere in the first instance, and a latitudinal variation of the solar wind velocity as well as in the hydrodynamic diffusion coefficient is incorporated to model the effects of a heliospheric magnetic field in the second. Subject headings: acceleration of particles — cosmic rays — shock waves — solar wind