Spectroscopic Constraints on Models of Ion-cyclotron Resonance Heating in the Polar Solar Corona

Using empirical velocity distributions derived from UVCS and SUMER ultraviolet spectroscopy, we construct theoretical models of anisotropic ion temperatures in the polar solar corona. The primary energy deposition mechanism we investigate is the dissipation of high frequency (10-10000 Hz) ion-cyclotron resonant Alfvén waves which can heat and accelerate ions differently depending on their charge and mass. We find that it is possible to explain the observed high perpendicular temperatures and strong anisotropies with relatively small amplitudes for the resonant waves. There is suggestive evidence for steepening of the Alfvén wave spectrum between the coronal base and the largest heights observed spectroscopically. Because the ion-cyclotron wave dissipation is rapid, even for minor ions like O⁵⁺, the observed extended heating seems to demand a constantly replenished population of waves over several solar radii. This indicates that the waves are generated gradually throughout the wind rather than propagated up from the base of the corona. This revised version was published online in June 2006 with corrections to the Cover Date.     

Kinetic Models for Whistler Wave Scattering of Electrons in the Solar Corona and Wind

Kinetic models are necessary to describe the physical processes associated with non-Maxwellian velocity distribution functions (VDFs) of electrons or ions in the solar corona and wind. It is shown that pitch-angle scattering of electrons in the solar wind needs to be considered in kinetic solar wind models. Coulomb collisions are not efficient enough to provide this scattering, but resonant interaction with whistler waves is. A solar wind model for undisturbed fast wind is presented, and the influence of scattering on flare electron propagation is investigated. Furthermore, it is found that resonant interaction of electrons with whistler waves is capable of producing suprathermal tails of electron distributions even under quiet conditions without flare activity.     

Hybrid Simulations of Wave Propagation and Ion Cyclotron Heating in the Expanding Solar Wind

We present results from hybrid (particle ions, fluid electrons) simulations of the evolution of Alfvén waves close to the ion cyclotron frequency in the solar wind, which take into account the basic properties of the background solar wind flow, i.e., the spherical expansion and the consequent decrease in magnetic field and cyclotron frequency with increasing distance from the Sun. We follow the evolution of a plasma parcel in a frame of reference moving with the solar wind using a 1D expanding box hybrid model; use of the hybrid model yields a fully self-consistent treatment of the resonant cyclotron wave-particle interaction. This model is related to a previous MHD model (Velli et al. 1992), which allows the use of a simple Cartesian geometry with periodic boundary conditions. The use of stretched expanding coordinates in directions transverse to the mean radial solar wind flow naturally introduces an anisotropic damping effect on velocity and magnetic field. We present results for the case of a single circularly polarized Alfvén wave propagating radially outward. Initially, the wave is below the cyclotron frequency for both the alpha partcles and protons. As the wind expands, the wave frequency (as seen in the solar wind frame) decreases more slowly than the cyclotron frequencies and the wave comes into resonance. With only protons, heating occurs as the wave frequency approaches the proton cyclotron frequency. With both alphas and protons, the alphas, which come into resonance first, are observed to be preferentially heated and accelerated. This revised version was published online in June 2006 with corrections to the Cover Date.     

Two-fluid 2.5D MHD Simulations of the Fast Solar Wind in Coronal Holes and the Relation to UVCS Observations

Recent SOHO/UVCS observations indicate that the perpendicular proton and ion temperatures are much larger than electron temperatures. In the present study we simulate numerically the solar wind flow in a coronal hole with the two-fluid approach. We investigate the effects of electron and proton temperatures on the solar wind acceleration by nonlinear waves. In the model the nonlinear waves are generated by Alfvén waves with frequencies in the 10^-3 Hz range, driven at the base of the coronal hole. The resulting electron and proton flow profile exhibits density and velocity fluctuations. The fluctuations may steepen into shocks as they propagate away from the sun. We calculate the effective proton temperature by combining the thermal and wave velocity of the protons, and find qualitative agreement with the proton kinetic temperature increase with height deduced from the UVCS Ly-α observations by Kohl et al. (1998). This revised version was published online in June 2006 with corrections to the Cover Date.     

MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.     

Kinetic Excitation Mechanisms for ION-Cyclotron Kinetic Alfvén Waves in Sun-Earth ConnectionI

We study kinetic excitation mechanisms for high-frequency dispersive Alfvén waves in the solar corona, solar wind, and Earth's magnetosphere. The ion-cyclotron and Cherenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (ICKAWs). Ion beams, anisotropic particles distributions and currents provide free energy for the excitation of ICKAWs in space plasmas. As particular examples we consider ICKAW instabilities in the coronal magnetic reconnection events, in the fast solar wind, and in the Earth's magnetopause. Energy conversion and transport initiated by ICKAW instabilities is significant for the whole dynamics of Sun-Earth connection chain, and observations of ICKAW activity could provide a diagnostic/predictive tool in the space environment research. This revised version was published online in August 2006 with corrections to the Cover Date.     

Upstream Ion Cyclotron Waves at Venus and Mars

The occurrence of waves generated by pick-up of planetary neutrals by the solar wind around unmagnetized planets is an important indicator for the composition and evolution of planetary atmospheres. For Venus and Mars, long-term observations of the upstream magnetic field are now available and proton cyclotron waves have been reported by several spacecraft. Observations of these left-hand polarized waves at the local proton cyclotron frequency in the spacecraft frame are reviewed for their specific properties, generation mechanisms and consequences for the planetary exosphere. Comparison of the reported observations leads to a similar general wave occurrence at both planets, at comparable locations with respect to the planet. However, the waves at Mars are observed more frequently and for long durations of several hours; the cyclotron wave properties are more pronounced, with larger amplitudes, stronger left-hand polarization and higher coherence than at Venus. The geometrical configuration of the interplanetary magnetic field with respect to the solar wind velocity and the relative density of upstream pick-up protons to the background plasma are important parameters for wave generation. At Venus, where the relative exospheric pick-up ion density is low, wave generation was found to mainly take place under stable and quasi-parallel conditions of the magnetic field and the solar wind velocity. This is in agreement with theory, which predicts fast wave growth from the ion/ion beam instability under quasi-parallel conditions already for low relative pick-up ion density. At Mars, where the relative exospheric pick-up ion density is higher, upstream wave generation may also take place under stable conditions when the solar wind velocity and magnetic field are quasi-perpendicular. At both planets, the altitudes where upstream proton cyclotron waves were observed (8 Venus and 11 Mars radii) are comparable in terms of the bow shock nose distance of the planet, i.e. in terms of the size of the solar wind-planetary atmosphere interaction region. In summary, the upstream proton cyclotron wave observations demonstrate the strong similarity in the interaction of the outer exosphere of these unmagnetized planets with the solar wind upstream of the planetary bow shock.     

Empirical Solar Proton Model for Orbiting Spacecraft Applications

An empirical model for energetic solar proton fluxes is presented. With this model the effects of such protons on geocentric space missions, to be flown during the next solar active period (1977-1983), and with orbits involving partial magnetospheric shielding, may be estimated. A synoptic background review is given, followed by a detailed discussion of the model's use, errors, uncertainties, and limitations, including sample calculations which demonstrate the application of specific or general project missions. Finally, for circular trajectories, percentage exposure maps are presented, depicting fractional mission times spent outside particular L shells as functions of orbit altitude and inclination. The distinguishing assumptions of this analysis are: 1) that the solar proton flux in the 10-100 MeV energy range, as accumulated over solar cycle 20 due to several discrete events, will be accumulated at a uniform rate for the seven active years of solar cycle 21; and 2) that all protons in the energy range of interest have a common geomagnetic latitude cutoff.     

MHD waves in coronal flux tubes

The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona.     

Abundances,Ionization States,Temperatures, and FIP in Solar Energetic Particles

The relative abundances of chemical elements and isotopes have been our most effective tool in identifying and understanding the physical processes that control populations of energetic particles. The early surprise in solar energetic particles (SEPs) was 1000-fold enhancements in \({}^{3}\mbox{He}/{}^{4}\mbox{He}\) from resonant wave-particle interactions in the small “impulsive” SEP events that emit electron beams that produce type III radio bursts. Further studies found enhancements in Fe/O, then extreme enhancements in element abundances that increase with mass-to-charge ratio \(A/Q\), rising by a factor of 1000 from He to Au or Pb arising in magnetic reconnection regions on open field lines in solar jets. In contrast, in the largest SEP events, the “gradual” events, acceleration occurs at shock waves driven out from the Sun by fast, wide coronal mass ejections (CMEs). Averaging many events provides a measure of solar coronal abundances, but \(A/Q\)-dependent scattering during transport causes variations with time; thus if Fe scatters less than O, Fe/O is enhanced early and depleted later. To complicate matters, shock waves often reaccelerate impulsive suprathermal ions left over or trapped above active regions that have spawned many impulsive events. Direct measurements of ionization states \(Q\) show coronal temperatures of 1–2 MK for most gradual events, but impulsive events often show stripping by matter traversal after acceleration. Direct measurements of \(Q\) are difficult and often unavailable. Since both impulsive and gradual SEP events have abundance enhancements that vary as powers of \(A/Q\), we can use abundances to deduce the probable \(Q\)-values and the source plasma temperatures during acceleration, ≈3 MK for impulsive SEPs. This new technique also allows multiple spacecraft to measure temperature variations across the face of a shock wave, measurements otherwise unavailable and provides a new understanding of abundance variations in the element He. Comparing coronal abundances from SEPs and from the slow solar wind as a function of the first ionization potential (FIP) of the elements, remaining differences are for the elements C, P, and S. The theory of the fractionation of ions by Alfvén waves shows that C, P, and S are suppressed because of wave resonances during chromospheric transport on closed magnetic loops but not on open magnetic fields that supply the solar wind. Shock waves can accelerate ions from closed coronal loops that easily escape as SEPs, while the solar wind must emerge on open fields.     

Element and Isotopic Fractionation in Closed Magnetic Structures

Recent papers have suggested that the slow solar wind is a super-position of material which is released by reconnection from large coronal loops. This reconnection process is driven by large-scale motions of solar magnetic flux driven by the non-radial expansion of the solar wind from the differentially rotating photosphere into more rigidly rotating coronal holes. The elemental composition of the slow solar wind material is observed to be fractionated and more variable than the fast solar wind from coronal holes. Recently, it has also been reported that fractionation also occurs in 3He/4He. This may be interpreted in the frame-work of an existing model for fractionation on large coronal loops in which wave-particle interactions preferentially heat ions thereby modifying their scale-heights. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Two Sources of Solar Energetic Particles

Evidence for two different physical mechanisms for acceleration of solar energetic particles (SEPs) arose 50 years ago with radio observations of type III bursts, produced by outward streaming electrons, and type II bursts from coronal and interplanetary shock waves. Since that time we have found that the former are related to “impulsive” SEP events from impulsive flares or jets. Here, resonant stochastic acceleration, related to magnetic reconnection involving open field lines, produces not only electrons but 1000-fold enhancements of ³He/⁴He and of (Z>50)/O. Alternatively, in “gradual” SEP events, shock waves, driven out from the Sun by coronal mass ejections (CMEs), more democratically sample ion abundances that are even used to measure the coronal abundances of the elements. Gradual events produce by far the highest SEP intensities near Earth. Sometimes residual impulsive suprathermal ions contribute to the seed population for shock acceleration, complicating the abundance picture, but this process has now been modeled theoretically. Initially, impulsive events define a point source on the Sun, selectively filling few magnetic flux tubes, while gradual events show extensive acceleration that can fill half of the inner heliosphere, beginning when the shock reaches ～2 solar radii. Shock acceleration occurs as ions are scattered back and forth across the shock by resonant Alfvén waves amplified by the accelerated protons themselves as they stream away. These waves also can produce a streaming-limited maximum SEP intensity and plateau region upstream of the shock. Behind the shock lies the large expanse of the “reservoir”, a spatially extensive trapped volume of uniform SEP intensities with invariant energy-spectral shapes where overall intensities decrease with time as the enclosing “magnetic bottle” expands adiabatically. These reservoirs now explain the slow intensity decrease that defines gradual events and was once erroneously attributed solely to slow outward diffusion of the particles. At times the reservoir from one event can contribute its abundances and even its spectra as a seed population for acceleration by a second CME-driven shock wave. Confinement of particles to magnetic flux tubes that thread their source early in events is balanced at late times by slow velocity-dependent migration through a tangled network produced by field-line random walk that is probed by SEPs from both impulsive and gradual events and even by anomalous cosmic rays from the outer heliosphere. As a practical consequence, high-energy protons from gradual SEP events can be a significant radiation hazard to astronauts and equipment in space and to the passengers of high-altitude aircraft flying polar routes.     

Coupling of the coronal he abundance to the solar wind

Models of the transition region — corona — solar wind system are investigated in order to find the coronal helium abundance and to study the role played by coronal helium in controlling the the solar wind proton flux. The thermal force on -particles in the transition region sets the flow of helium into the corona. The frictional coupling between -particles and protons and/or the electric polarization field determines the proton flux in the solar wind as well as the fate of the coronal helium content.     

Acceleration of the High Speed Solar Wind in Coronal Holes

We outline a theory for the origin and acceleration of the fast solar wind as a consequence of network microflares releasing a spectrum of high frequency Alfvén waves which heat (by cyclotron absorption) the corona close to the Sun. The significant features of our model of the fast wind are that the acceleration is rapid with the sonic point at around two solar radii, the proton temperatures are high (~ 5 million degrees) and the minor ions are correspondingly hotter, roughly in proportion to their mass. Moreover we argue that since the energy flux needed to power the quiet corona in closed field regions is about the same as that needed to drive the fast solar wind, and also because at deeper levels (< 2 × 10⁵ K) there is no great difference in the properties of supergranules and network in closed and open field regions, the heating process (i.e., dissipation of high frequency waves) must be the same in both cases. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formation and Evolution of Corotating Interaction Regions and their Three Dimensional Structure

Corotating interaction regions are a consequence of spatial variability in the coronal expansion and solar rotation, which cause solar wind flows of different speeds to become radially aligned. Compressive interaction regions are produced where high-speed wind runs into slower plasma ahead. When the flow pattern emanating from the Sun is roughly time-stationary these compression regions form spirals in the solar equatorial plane that corotate with the Sun, hence the name corotating interaction regions, or CIRs. The leading edge of a CIR is a forward pressure wave that propagates into the slower plasma ahead, while the trailing edge is a reverse pressure wave that propagates back into the trailing high-speed flow. At large heliocentric distances the pressure waves bounding a CIR commonly steepen into forward and reverse shocks. Spatial variation in the solar wind outflow from the Sun is a consequence of the solar magnetic field, which modulates the coronal expansion. Because the magnetic equator of the Sun is commonly both warped and tilted with respect to the heliographic equator, CIRs commonly have substantial north-south tilts that are opposed in the northern and southern hemispheres. Thus, with increasing heliocentric distance the forward waves in both hemispheres propagate toward and eventually across the solar equatorial plane, while the reverse shocks propagate poleward to higher latitudes. This paper provides an overview of observations and numerical models that describe the physical origin and radial evolution of these complex three-dimensional (3-D) heliospheric structures. This revised version was published online in August 2006 with corrections to the Cover Date.     

Langmuir Wave Activity: Comparing the Ulysses Solar Minimum and Solar Maximum Orbits

We examine the occurrence and intensity of Langmuir wave activity (electrostatic waves at the electron plasma frequency) during the solar minimum and solar maximum orbits of Ulysses. At high latitudes during the solar minimum orbit, occurrences of Langmuir waves in magnetic holes were frequent; in the second orbit, they were less common. This difference, in comparison with observations from the first Ulysses fast heliolatitude scan, suggests that Langmuir wave activity in magnetic holes is enhanced in solar wind from polar coronal holes. This revised version was published online in August 2006 with corrections to the Cover Date.     

A 16-moment Fast Solar Wind Model

A 16-moment fast solar wind model based on a bi-Maxwellian velocity distribution is presented. Although the proton heat flux density is found to be significantly smaller than the classical Spitzer-Härm value, it still plays a significant role in shaping the proton temperature anisotropy in the fast solar wind.     

Working Group 1 Report: Solar Wind Models from the Sun to 1 AU: Constraints by "in situ" and Remote Sensing Measurements

The goal of Working Group 1 was to discuss constraints on solar wind models. The topics for discussion, outlined by Eckart Marsch in his introduction, were: (1) what heats the corona, (2) what is the role of waves, (3) what determines the solar wind mass flux, (4) can stationary, multi-fluid models describe the fast and slow solar wind, or (5) do we need time dependent fluid models, kinetic models, and/or MHD models to describe solar wind acceleration. The discussion in the working group focused on observations of "temperatures" in the corona, mainly in coronal holes, and whether the observations of line broadening should be interpreted as thermal broadening or wave broadening. Observations of the coronal electron density and the flow speed in coronal holes were also discussed. There was only one contribution on observations of the distant solar wind, but we can place firm constraints on the solar wind particle fluxes and asymptotic flow speeds from observations with Ulysses and other spacecraft. Theoretical work on multi-fluid models, higher-order moment fluid models, and MHD models of the solar wind were also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Observations of the solar wind from coronal holes

The solar wind emanating from coronal holes (CH) constitutes a quasi-stationary flow whose properties change only slowly with the evolution of the hole itself. Some of the properties of the wind from coronal holes depend on whether the source is a large polar coronal hole or a small near-equatorial hole. The speed of polar CH flows is usually between 700 and 800 km/s, whereas the speed from the small equatorial CH flows is generally lower and can be <400 km/s. At 1 AU, the average particle and energy fluxes from polar CH are 2.5×10⁸ cm^–2 sec^–1 and 2.0 erg cm^–2 s^–1. This particle flux is significantly less than the 4×10⁸ cm^–2 sec^–1 observed in the slow, interstream wind, but the energy fluxes are approximately the same. Both the particle and energy fluxes from small equatorial holes are somewhat smaller than the fluxes from the large polar coronal holes.Many of the properties of the wind from coronal holes can be explained, at least qualitatively, as being the result of the effect of the large flux of outward-propagating Alfvén waves observed in CH flows. The different ion species have roughly equal thermal speeds which are also close to the Alfvén speed. The velocity of heavy ions exceeds the proton velocity by the Alfvén speed, as if the heavy ions were surfing on the waves carried by the proton fluid.The elemental composition of the CH wind is less fractionated, having a smaller enhancement of elements with low first-ionization potentials than the interstream wind, the wind from coronal mass ejections, or solar energetic particles. There is also evidence of fine-structure in the ratio of the gas and magnetic pressures which maps back to a scale size of roughly 1° at the Sun, similar to some of the fine structures in coronal holes such as plumes, macrospicules, and the supergranulation.