Theoretical studies of the physics of the solar atmosphere

Significant advances in our theoretical basis for understanding several physical processes related to dynamical phenomena on the sun were achieved. We have advanced a new model for spicules and fibrils. We have provided a simple physical view of resonance absorption of MHD surface waves; this allowed an approximate mathematical procedure for obtaining a wealth of new analytical results which we applied to coronal heating and p-mode absorption at magnetic regions. We provided the first comprehensive models for the heating and acceleration of the transition region, corona, and solar wind. We provided a new view of viscosity under coronal conditions. We provided new insights into Alfven wave propagation in the solar atmosphere. And recently we have begun work in a new direction: parametric instabilities of Alfven waves

Magnetohydrodynamic Slow Mode with Drifting He++^{++}: Implications for Coronal Seismology and the Solar Wind

The MHD slow mode wave has application to coronal seismology, MHD turbulence, and the solar wind where it can be produced by parametric instabilities. We consider analytically how a drifting ion species (e.g. He$^{++}$) affects the linear slow mode wave in a mainly electron-proton plasma, with potential consequences for the aforementioned applications. Our main conclusions are: 1. For wavevectors highly oblique to the magnetic field, we find solutions that are characterized by very small perturbations of total pressure. Thus, our results may help to distinguish the MHD slow mode from kinetic Alfv\'en waves and non-propagating pressure-balanced structures, which can also have very small total pressure perturbations. 2. For small ion concentrations, there are solutions that are similar to the usual slow mode in an electron-proton plasma, and solutions that are dominated by the drifting ions, but for small drifts the wave modes cannot be simply characterized. 3. Even with zero ion drift, the standard dispersion relation for the highly oblique slow mode cannot be used with the Alfv\'en speed computed using the summed proton and ion densities, and with the sound speed computed from the summed pressures and densities of all species. 4. The ions can drive a non-resonant instability under certain circumstances. For low plasma beta, the threshold drift can be less than that required to destabilize electromagnetic modes, but damping from the Landau resonance can eliminate this instability altogether, unless $T_{\mathrm e}/T_{\mathrm p}\gg1$.Comment: 35 pages, 5 figures, accepted for publication in Astrophys.

Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment

We study the propagation, reflection, and turbulent dissipation of Alfven waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al, we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy, and assume that there is much more energy in waves propagating away from the Sun than waves propagating towards the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfven critical point - that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfven-wave reflection and turbulent heating into fluid models of the solar wind.Comment: 9 pages, 9 figures, accepted for publication in Ap

Deceleration of Alpha Particles in the Solar Wind by Instabilities and the Rotational Force: Implications for Heating, Azimuthal Flow, and the Parker Spiral Magnetic Field

Protons and alpha particles in the fast solar wind are only weakly collisional and exhibit a number of non-equilibrium features, including relative drifts between particle species. Two non-collisional mechanisms have been proposed for limiting differential flow between alpha particles and protons: plasma instabilities and the rotational force. Both mechanisms decelerate the alpha particles. In this paper, we derive an analytic expression for the rate $Q_{\mathrm{flow}}$ at which energy is released by alpha-particle deceleration, accounting for azimuthal flow and conservation of total momentum. We show that instabilities control the deceleration of alpha particles at $r< r_{\mathrm{crit}}$, and the rotational force controls the deceleration of alpha particles at $r> r_{\mathrm{crit}}$, where $r_{\mathrm{crit}} \simeq 2.5 \,\mathrm{AU}$ in the fast solar wind in the ecliptic plane. We find that $Q_{\mathrm{flow}}$ is positive at $r<r_{\mathrm{crit}}$ and $Q_{\mathrm{flow}} = 0$ at $r\geq r_{\mathrm{crit}}$, consistent with the previous finding that the rotational force does not lead to a release of energy. We compare the value of~$Q_{\mathrm{flow}}$ at $r< r_{\mathrm{crit}}$ with empirical heating rates for protons and alpha particles, denoted $Q_{\mathrm{p}}$ and $Q_{\alpha}$, deduced from in-situ measurements of fast-wind streams from the \emph{Helios} and \emph{Ulysses} spacecraft. We find that $Q_{\mathrm{flow}}$ exceeds $Q_{\alpha}$ at $r < 1\,\mathrm{AU}$, and that $Q_{\mathrm{flow}}/Q_{\rm p}$ decreases with increasing distance from the Sun from a value of about one at $r=0.29 - 0.42\,\mathrm{AU}$ to about 1/4 at 1 AU. We conclude that the continuous energy input from alpha-particle deceleration at $r< r_{\mathrm{crit}}$ makes an important contribution to the heating of the fast solar wind.Comment: 14 pages, 10 figures, submitted to Astrophys.

The Turbulent Heating Rate in Strong MHD Turbulence with Nonzero Cross Helicity

Different results for the cascade power in strong, incompressible MHD turbulence with nonzero cross helicity appear in the literature. In this paper, we discuss the conditions under which these different results are valid. We define z+ to be the rms amplitude of Alfven waves propagating parallel to the background magnetic field, and z- to be the rms amplitude of Alfven waves propagating anti-parallel to the background magnetic field. Nonzero cross helicity implies that z+ and z- differ, and we take z- to be less than z+. We find that the mechanism that generates the z- fluctuations strongly affects the cascade power, because it controls the coherence time for interactions between oppositely directed wave packets at the outer scale. In particular, for fixed values of z+ and z-, the cascade power is in many cases larger when the z- fluctuations are generated by the reflection of z+ fluctuations than when the z- fluctuations are generated by forcing that is only weakly correlated with the z+ fluctuations.Comment: 16 pages, 2 figures, accepted for publication in Ap

Coronal faraday rotation fluctuations and a wave/turbulence-driven model of the solar wind

Some recent models for coronal heating and the origin of the solar wind postulate that the source of energy and momentum consists of Alfven waves of solar origin dissipating via MHD turbulence. We use one of these models to predict the level of Faraday rotation fluctuations (FRFs) that should be imposed on radio signals passing through the corona. This model has the virtue of specifying the correlation length of the turbulence, knowledge of which is essential for calculating the FRFs; previous comparisons of observed FRFs with models suffered from the fact that the correlation length had to be guessed. We compare the predictions with measurements of FRFs obtained by the Helios radio experiment during occultations in 1975 through 1977, close to solar minimum. We show that only a small fraction of the FRFs are produced by density fluctuations; the bulk of the FRFs must be produced by coronal magnetic field fluctuations. The observed FRFs have periods of hours, suggesting that they are related to Alfven waves which are observed in situ by spacecraft throughout the solar wind; other evidence also suggests that the FRFs are due to coronal Alfven waves. We choose a model field line in an equatorial streamer which has background electron concentrations that match those inferred from the Helios occultation data. The predicted FRFs are found to agree very well with the Helios data. If the FRFs are in fact produced by Alfven waves with the assumed correlation length, our analysis leads us to conclude that wave-turbulence models should continue to be pursued with vigor. But since we cannot prove that the FRFs are produced by Alfven waves, we state the more conservative conclusion, still subject to the correctness of the assumed correlation length, that the corona contains long-period magnetic fluctuations with sufficient energy to heat the corona and drive the solar wind