The solar magnetic field plays a crucial role in the heating of the solar corona. MHD waves generated in the convection zone propagate upward along magnetic flux tubes and deposit their energy in the upper atmosphere. The random intermixing of coronal field lines by foot-point motions in coronal loops is expected to produce magnetic stresses that can only be released via field-line reconnection. I will discuss different aspects of the coronal heating problem, including the generation of MHD waves in the solar magnetic network, the dissipation of Alfven waves in the extended corona, and the effects on non-thermal electrons on energy transport in coronal loops.

The theory of heating the solar corona by a DC mechanism has had a turbulent history with a number of seemingly decisive setbacks. Since it was proposed in rough form by Parker in 1972, the theory has evolved through a number of steps. Major setbacks came from first an attempt to quantify the amount of available energy and later the observable effect of the intermittent nano-flare heating. These setbacks relies on assumptions that might not be accurate, and lately the DC heating mechanism has had a revival in the form of more direct models with very few assumptions that by forward modelling reproduces a number of observables.

One of the basic properties of the fast solar wind, that is its high speed, is still not self-consistently explained. This is mainly due to the theoretical difficulty of treating weakly collisional plasmas. The fluid approach implies that the medium is collision dominated and that the particle velocity distributions are close to Maxwellians. However the electron velocity distributions observed in the solar wind depart significantly from Maxwellians, indicating the limited validity of this hypothesis. In this work, we present new results obtained over a wide range of parameters with two basically different models: a) a kinetic collisionless model (called exospheric) and b) a numerical simulation including collisions. Both models assume electron velocity distributions in the corona with suprathermal tails, but make no assumption on the heat flux, which is calculated self-consistently. We show that these approaches yield a similar variation of the wind speed with the basic solar parameters, producing the high speeds observed in the fast solar wind.

We will discuss a mechanism of dissipation that allows us to explain several key features of the turbulent fluctuations in the in situ solar wind. The observational data suggest that the solar wind turbulence is dominated by fluctuations whose wave vector is perpendicular to the background magnetic field. This is in agreement with numerical simulations showing that the turbulent cascade tends to produce small spatial scales across the magnetic field rather than along it. The dissipation of the turbulent fluctuations is thought to be responsible for the observed perpendicular heating of the solar wind protons. The problem, however, is that the perpendicular heating is usually a signature of the cyclotron resonance, while the cross-field fluctuations cannot be immediately cyclotron-resonant with the protons because of their low frequency. We suggest that the velocity shear associated with the cross-field fluctuations excites a proton cyclotron instability. These unstable waves then transfer the energy from the cross-field fluctuations to the protons thus dissipating the cascade and producing the perpendicular heating. We will analyze the turbulence spectra reduced from the Wind and ACE spacecraft data and show that the onset of the instability is consistent with the spectral break separating the inertial and dissipation ranges of the turbulence. In particular, the dissipation sets in at the same shear under very different conditions of the solar wind plasma. The observed turbulence spectra often have power-law dissipation ranges, which are inconsistent with the direct cyclotron damping of the turbulent fluctuations. We demonstrate that the power-law spectra are simply a consequence of a marginal state of the instability in the dissipation range.

Resonant interaction between ions (oxygen ions OVI and protons) and ion cyclotron waves is investigated using a one dimensional hybrid code. Ion cyclotron waves are self-consistently generated by an ion cyclotron anisotropy instability. We focus on the detailed acceleration process of ions. The energization of oxygen ions due to waves is found to have two stages. During the first stage, oxygen ions are accelerated by ion cyclotron waves in the direction perpendicular to the background magnetic field that a perpendicular fluid velocity can be 4.7 times of thermal velocity in an initially low beta plasma (beta value at 0.01). During this stage, oxygen ions do not show an appreciable bulk acceleration along the background magnetic field. The large perpendicular (to the background magnetic field) fluid velocity could be wrongly identified as a large perpendicular thermal speed in hybrid simulations and a false extremely large temperature anisotropy could be found. In the second stage, a large bulk acceleration of oxygen ions (as large as 0.3 Alfven speed) is observed. The non-linear nature of wave particle interaction produces highly complex velocity distribution functions in the oxygen ions: oxygen ions are strongly heated in both the perpendicular and parallel directions. It is found that it is not possible to distingish the large perpendicular fluid velocity from the random perpendicular thermal motions of oxygen ions. Both of them can contribute to the line profile broadening in coronal observations. In contrast, the heating and acceleration behavior of the major species, protons, is quite different. The velocity distribution functions of protons are less complex than the oxygen velocity distributions. Protons can also develop a large temperature anisotropy with preferential heating in the perpendicular direction. A bulk acceleration of protons (much smaller than the acceleration of oxygen ions) along the background magnetic field is observed to develop simultaneously with the development of a proton temperature anisotropy. We will dicuss the implications of this study to observations above coronal holes.

Four decades have gone by since the discovery that the solar wind at 1 AU seems to exist in two relatively distinct states: slow and fast. There is still no universal agreement concerning the primary physical cause of this apparently bimodal distribution, even in its simplest manifestation at solar minimum. In this presentation we review and extend a series of ideas that link the different states of solar wind to the varying superradial geometry of magnetic flux tubes in the extended corona. Past researchers have emphasized different aspects of this relationship, and we attempt to disentangle some of the seemingly contradictory results. We apply the hypothesis of Wang and Sheeley (as well as Kovalenko) that Alfven wave fluxes at the base are the same for all flux tubes to a recent model of non-WKB Alfven wave reflection and turbulent heating, and we predict coronal heating rates as a function of flux tube geometry. We compare the feedback of these heating rates on the locations of Parker-type critical points, and we discuss the ranges of parameters that yield a realistic bifurcation of wind solutions into fast and slow. Finally, we discuss the need for next-generation coronagraph spectroscopy of the extended corona -- especially measurements of the electron temperature above 1.5 solar radii -- in order to confirm and refine these ideas.

To understand coronal heating one has to describe microphysical processes at their intrinsic scales, where the energy (of waves, turbulence, nonuniform flows or currents) is dissipated. In standard fluid treatments this problem is often circumvented by artificially enhancing the dissipation, e.g. by increasing the Coulomb collision rates in the tenuous corona, or lowering the Reynolds number by orders of magnitude. We address the basic assumptions underlying collisional transport theory, and point out collisionless alternatives. We elucidate some kinetic aspects of coronal heating in association with Landau and cyclotron resonance damping of plasma waves, and discuss kinetic results which were numerically obtained by solving the Vlasov equation for ions and electrons in a coronal funnel.

We show that MHD waves naturally explain the heating and acceleration of the coronal plasma in open field regions by 1-dimensional numerical simulations from the photosphere to ~20Rsun. Alfvenic perturbations with dv~1km/s and period of 10s to 1000s are input at the photosphere. Through the upward propagation, the wave amplitude is amplified in the stratified atmosphere to generate compressive MHD waves by the nonlinear effects. The compressive waves steepen and eventually dissipate by both fast and slow shocks. Density fluctuations accompanying the compressive modes further contribute to reflection of the outgoing Alfven waves and the excited incoming waves eventually dissipate through wave-wave interactions. Thus, the most of the input Alfven wave energy effectively dissipate within the computational region, which directly leads to the heating (> 1MK) and acceleration (~800km/s) of the coronal plasma observed in high-speed solar wind from poles (see figure). We adopt 2nd-order MHD-Godunov scheme with taking into account radiative cooling and thermal conduction for the simulations. At the outer boundary, the outgoing (non-reflecting) boundary condition is properly prescribed by considering all the 7 MHD characteristics to avoid unphysical wave reflection.

Dissipation of turbulence is generally considered an important contributor for the heating and acceleration of the solar wind from the corona throughout the heliosphere, due to radially evolving dissipation mechanisms and/or cascading of the energy stored in the turbulence to dissipation scales. While the cascading can be modeled by using MHD simulations, they tend to be very computer-intensive. An alternative approach is to model the turbulence spectral evolution as a diffusion or convection of turbulence energy in wavenumber space. In this work, we will model the evolution of the solar wind using this approach. As an improvement to earlier models, the counterstreaming wave fields, required for the non-linear interactions which cause the spectral evolution, are modeled with higher consistency, by using a simple frequency-dependent model for the wave reflection from large-scale gradients. The cascade is taken to transfer energy to small perpendicular scales, and the predicted parallel extent of the spectral evolution is neglected. We apply the model to the inner heliosphere, and present the resulting solar wind profiles from the corona to interplanetary space.

Recent observations of the fast and slow solar wind close to the sun, as well as in-situ observations beyond 0.3AU show different temperatures and outflow speeds of protons and heavy ions. I will present the results of multi-fluid models of the solar wind that include explicit wave heating and acceleration. The models describes electrons, protons, and heavy ions as coupled fluids that are heated by different heating processes with the parameters constrained by observations. I will show the results of 2.5D three-fluid simulations of the fast solar wind plasma that combine the effects of MHD waves self-consistently, and ion-cyclotron waves parametrically on the acceleration and heating processes. I will show multi-fluid models of slow solar wind in coronal streamers, and discuss the relation between the models and observations. I will present the results of two-dimensional hybrid kinetic models of ion-cyclotron wave heating of the heavy ions in the solar wind plasma.

We present comparative measurements of He⁺², O⁺⁶, O⁺⁷ and Fe^+7-11 from the ACE/SWICS instrument and H⁺ from the SOHO/PM sensor. While it has been well established that alpha particles generally have a higher flow speed than protons, very little is known about the relative flow speeds of the heavier ions. Our preliminary results indicate that the average speeds of solar wind ions tend to increase in the order H, He, Fe, O⁺⁶, O⁺⁷. Although some of the speed differences are quite small, they are largest in coronal hole associated solar wind flows, decreasing to near zero in the high density low speed solar wind. We also find that the minor ions tend to have equal thermal speeds in coronal hole flows, and equal temperatures in low speed flows. We have also identified a number of interesting time intervals during which He and the heavier ions show dramatic density decreases while the proton density remains relatively steady.