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Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind
The PI (Cranmer) and Co-I (A. van Ballegooijen) made significant progress toward the goal of building a "unified model" of the dominant physical processes responsible for the acceleration of the solar wind. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a one-dimensional and time-independent model of plasma heating and acceleration. The accomplishments in the report period are thus divided into these two categories: 1a. Focused Study of Kinetic MHD Turbulence. We have developed a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. A turbulent cascade is one possible way of generating small-scale fluctuations (easy to dissipate/heat) from a pre-existing population of low-frequency Alfven waves (difficult to dissipate/heat). We modeled the cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique waves undergo Landau damping, which implies strong parallel electron heating. We thus investigated the nonlinear evolution of the electron velocity distributions (VDFs) into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which are an alternate means of heating protons via stochastic interactions similar to particle-particle collisions. 1b. Focused Study of the Multi-Mode Detailed Balance Formalism. The PI began to explore the feasibility of using the "weak turbulence," or detailed-balance theory of Tsytovich, Melrose, and others to encompass the relevant physics of the solar wind. This study did not go far, however, because if the "strong" MHD turbulence discussed above is a dominant player in the wind's acceleration region, this formalism is inherently not applicable to the corona. We will continue to study the various published approaches to the weak turbulence formalism, especially with an eye on ways to parameterize nonlinear wave reflection rates. 2. Building the Unified Model Code Architecture. We have begun developing the computational model of a time-steady open flux tube in the extended corona. The model will be "unified" in the sense that it will include (simultaneously for the first time) as many of the various proposed physical processes as possible, all on equal footing. To retain this generality, we have formulated the problem in two interconnected parts: a completely kinetic model for the particles, using the Monte Carlo approach, and a finite-difference approach for the self-consistent fluctuation spectra. The two codes are run sequentially and iteratively until complete consistency is achieved. The current version of the Monte Carlo code incorporates gravity, the zero-current electric field, magnetic mirroring, and collisions. The fluctuation code incorporates WKJ3 wave action conservation and the cascade/dissipation processes discussed above. The codes are being run for various test problems with known solutions. Planned additions to the codes include prescriptions for nonlinear wave steepening, kinetic velocity-space diffusion, and multi-mode coupling (including reflection and refraction).
Helium and minor ions in the corona and solar wind - Dynamics and charge states
A theoretical model of the acceleration region of the solar wind with major species (p, alpha, e) and minor ions (e.g., He-3, C, O, Mg, Si) is presented. Observed n(e)-profiles and the equations of continuity and momentum are used to calculate profiles of T, n, and u for all species, as well as charge states of minor ions. The disagreement of the results of a pure p-e model with observations is discussed in some detail, and it is shown that a model consistent with observations both in the corona and at 1 AU requires a finite abundance of He(2+). This model predicts a strong enhancement of He/H in the lower corona. The results for the frozen-in charge states in the p-alpha-e model are in agreement with measurements in the low speed solar wind, especially for the well determined pair O(6+)/O(7+). Finally, a model for a coronal hole is investigated and it is found that wave pressure is necessary to model successfully the observed solar wind speeds and abundances. Although various simplifying assumptions had to be introduced, care was taken to ensure that the model remains physically consistent, i.e., that the same physics is used for the major species as well as the minor ions.
Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind
The PI (Cranmer) and Co-I (A. van Ballegooijen) made substantial progress toward the goal of producing a unified model of the basic physical processes responsible for solar wind acceleration. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a 1D model of plasma heating and acceleration. The accomplishments in Year 2 are divided into these two categories: 1a. Focused Study of Kinetic Magnetohydrodynamic (MHD) Turbulence. lb. Focused Study of Non - WKB Alfven Wave Rejection. and 2. The Unified Model Code. We have continued the development of the computational model of a time-study open flux tube in the extended corona. The proton-electron Monte Carlo model is being tested, and collisionless wave-particle interactions are being included. In order to better understand how to easily incorporate various kinds of wave-particle processes into the code, the PI performed a detailed study of the so-called "Ito Calculus", i.e., the mathematical theory of how to update the positions of particles in a probabilistic manner when their motions are governed by diffusion in velocity space.
Origins of the solar wind in the corona
The coronal origins of the solar wind are considered. Potential sources of low-speed wind which are consistent with current data, including streamers and the interfaces between them and other coronal regions, await mass flow measurements for confirmation. A Doppler-dimming technique utilizing a white-light coronagraph and UV coronal spectrometer is to be employed aboard the Space Shuttle SPARTAN program, and its usage on Ulysses may provide information on mass flows in streamers and their surroundings.
Theoretical studies on the chromosphere, corona, and solar wind
Papers published during the period from Jun. 1980 - Dec. 1990 are listed.
Fine Structure in the Corona and Solar Wind at High Heliographic Latitudes at Solar Maximum
Microstreams and pressure balance structures in fast solar wind were more easily detected at Ulysses at 2.2 AU over the poles than at Helios at 0.3 AU. This is because solar rotation brings sources of fast solar wind beneath sources of slow solar wind at a rate that depends on latitude, for the same size features. Dynamic interaction between the fast and slow wind tends to mix the flows and make features more difficult to detect with increasing distance from the Sun. A given sized feature takes proportionally longer to pass a longitude when it is at 80 degrees latitude than when it is at the equator. At solar maximum, Ulysses will mainly be sampling solar wind coming from above streamers and from near streamers. The data will provide information on fine structure at the tops of streamers - the stalks - and on the source of slow solar wind, The visibility of the boundaries between fast and slow wind and of the stalk will increase with increasing latitude. We will present quantitative calculations of the visibility of various sized features, with various differences in flow speed, at the location of Ulysses when it is over the south (in 2000) and north (in 2001) polar regions of the Sun.
Fine Structure in the Corona and Solar Wind at High Heliographic Latitudes at Solar Maximum
Microstreams and pressure balance structures in fast solar wind were more easily detected at Ulysses at 2.2 AU over the poles than at Helios at 0.3 AU. This is because solar rotation brings sources of fast solar wind beneath sources of slow solar wind at a rate that depends on latitude, for the same size features. Dynamic interaction between the fast and slow wind tends to mix the flows and make features more difficult to detect with increasing distance from the Sun. A given sized feature takes proportionally longer to pass a longitude when it is at 80 degrees latitude than when it is at the equator. At solar maximum, Ulysses will mainly be sampling solar wind coming from above streamers and from near streamers. The data will provide information on fine structure at the tops of streamers - the stalks - and on the source of slow solar wind. The visibility of the boundaries between fast and slow wind and of the stalk will increase with increasing latitude. I will present quantitative calculations of the visibility of various sized features, with various differences in flow speed, at the location of Ulysses when it is over the south (in 2000) and north (in 2001) polar regions of the Sun.
Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind
The paper discusses the following: 1. No-cost Extension. The no-cost extension is required to complete the work on the unified model codes (both hydrodynamic and kinetic Monte Carlo) as described in the initial proposal and previous annual reports. 2. Scientific Accomplishments during the Report Period. We completed a comprehensive model of Alfvtn wave reflection that spans the full distance from the photosphere to the distant heliosphere. 3. Comparison of Accomplishments with Proposed Goals. The proposal contained two specific objectives for Year 3: (1) to complete the unified model code, and (2) to apply it to various kinds of coronal holes (and polar plumes within coronal holes). Although the anticipated route toward these two final goals has changed (see accomplishments 2a and 2b above), they remain the major milestones for the extended period of performance. Accomplishments la and IC were necessary prerequisites for the derivation of "physically relevant transport and mode-coupling terms" for the unified model codes (as stated in the proposal Year 3 goals). We have fulfilled the proposed "core work" to study 4 general types of physical processes; in previous years we studied turbulence, mode coupling (Le., non-WKB reflection), and kinetic wave damping, and accomplishment lb provides the fourth topic: nonlinear steepening.
Observed associations between the solar interior, corona, and solar wind
Using polarized brightness (pB) measurements made by the High Altitude Observatory (HAO) Mauna Loa Mk III K-coronameter, we investigate the daily changes of path-integrated density at1.15 R-circle dot.
MACS, An Instrument, and a Methodology for Simulations and Global Measurements of the Coronal Electron Temperature and the Solar Wind Velocity on the Solar Corona
The determination of the radial and latitudinal temperature and wind profiles of the solar corona is of great importance in understanding the coronal heating mechanism and the dynamics of coronal expansion. Cram presented the theory for the formation of the K-coronal spectrum and identified two important observations. He observed the existence of temperature sensitive anti-nodes at certain wavelengths in the theoretical K-coronal spectra. The anti-nodes are separated by temperature-insensitive nodes. Remarkably, Cram showed that the wavelengths of the nodes and anti-nodes are almost independent of altitude above the solar limb. Because of these features, Cram suggested that the intensity ratios at two anti-nodes could be used as a diagnostic of the electron temperature in the K-corona. Based on this temperature diagnostic technique prescribed by Cram a slit-based spectroscopic study was performed by Ichimoto et al. on the solar corona in conjunction with the total solar eclipse of 3 Nov 1994 in Putre, Chile to determine the temperature profile of the solar corona. In this thesis Cram's theory has been extended to incorporate the role of the solar wind in the formation of the K-corona, and we have identified both temperature and wind sensitive intensity ratios. The instrument, MACS, for Multi Aperture Coronal Spectrometer, a fiber optic based spectrograph, was designed for global and simultaneous measurement of the thermal electron temperature and the solar wind velocity in the solar corona. The first ever experiment of this nature was conducted in conjunction with the total solar eclipse of 11 Aug 1999 in Elazig, Turkey. In this instrument one end of each of twenty fiber optic tips were positioned in the focal plane of the telescope in such a way that we could observe conditions simultaneously at many different latitudes and two different radial distances in the solar corona. The other ends of the fibers were vertically aligned and placed at the primary focus of the collimating lens of the spectrograph to obtain simultaneous and global spectra on the solar corona. By isolating the K-coronal spectrum from the spectrum recorded by each fiber the temperature and the wind sensitive intensity ratios were calculated to obtain simultaneous and global measurements of the thermal electron temperature and the solar wind velocity. We were successful in obtaining reliable estimates of the coronal temperature at many positions in the corona. This is the first time that simultaneous measurements of coronal temperatures have been obtained at so many points. However due to instrumental scattering encountered during observations, reliable estimates of the wind velocity turned out to be impossible to obtain. Although remedial measures were taken prior to observation, this task proved to be difficult owing to the inability to replicate the conditions expected during an eclipse in the laboratory. The full extent of the instrumental scattering was apparent only when we analyzed the observational sequence. Nevertheless the experience obtained from this very first attempt to simultaneously and globally measure both the wind velocity and the temperature on the solar corona have provided valuable information to conduct any future observations successfully.
Plasma and space physics
Continuum plasma dynamics, and properties of corona, solar wind, magnetosphere, and transition region
The quiescent corona and slow solar wind
The observations of the ultraviolet coronagraph spectrometer (UVCS), operating onboard the Solar and Heliospheric Observatory (SOHO) spacecraft, are discussed. The purpose of the UVCS is the study of the quiescent coronal streamer and the slow solar wind. The observations started in January 1996. Polarized radiance data in the visible continuum were obtained. Some characteristics of the coronal streamer from the UVCS recorded data are discussed. A model for the source of the slow solar wind in the inner corona is proposed.
On the acceleration of thermal coronal ions by flare induced shock waves
The energy spectra of solar flare ions are calculated by assuming that the process which accelerates solar wind ions to MeV/ nucleon energies in the interplanetary corotating interaction region (CIR) also occurs in flare induced magnetosonic fast-mode (MFM) shocks in the corona. Solar wind ions are considered to be accelerated to MeV/nucleon energies by wave-particle interactions in the shock front and the downstream flow, being compressed between upstream and downstream magnetic field irregularities, and then accelerated by the shock drift acceleration mechanism. The energy spectra of the accelerated ions is calculated from the number of shock encounters as a function of the post- and preacceleration energies. A best fit by an exponential in momentum is determined for ions in the 50 MeV to a few GeV range, and from 20-80 MeV by a suitable power law in kinetic energy with a mean spectral index. Comparisons with observed solar protons show good agreement.
Recent perspectives in solar physics - Elemental composition, coronal structure and magnetic fields, solar activity
Elemental abundances in the solar corona are studied. Abundances in the corona, solar wind and solar cosmic rays are compared to those in the photosphere. The variation in silicon and iron abundance in the solar wind as compared to helium is studied. The coronal small and large scale structure is investigated, emphasizing magnetic field activity and examining cosmic ray generation mechanisms. The corona is observed in the X-ray and EUV regions. The nature of coronal transients is discussed with emphasis on solar-wind modulation of galactic cosmic rays. A schematic plan view of the interplanetary magnetic field during sunspot minimum is given showing the presence of magnetic bubbles and their concentration in the region around 4-5 AU by a fast solar wind stream.
Study of the mechanism for solar wind formation
Observations of the corona and solar wind are analyzed and compared with generalized results derived from laboratory-scale experiments. It was shown that a thermal pressure gradient can make a major contribution to a precipitating plasma of the solar wind emanating from coronal holes. It is found that the divergence Phi = (R/R sub solar radius)f of the magnetic field lines, originating from coronal holes, is one of the factors governing solar wind velocity at Earth orbit (R= 1 AU). A decrease in the velocity V sub R = 1 AU from approx = 750 mk/sec down to approx = 450 km/sec may be attributable to an increase in superradial divergence f from approx = 7-9 to 20. The plasma energy flux density F at the base of the coronal holes representing the sources of the solar wind with V sub R=1AE = (450 to 750) km/sec, remains nearly constant, being F approx = (1.4 +/- 0.3) x 10 to the 6th power x ergs/sq cm/sec for the period 1973-1975.
A reexamination of two-fluid solar wind models
The two-fluid solar-wind equations have been solved by a method which is approximately 50 times faster than any previously developed, through the use of asymptotic expansions which are self-consistently iterated upon to find a solution that passes through the critical point. The energy assumptions in two-fluid solar-wind models are reexamined, and the conclusions are as follows: (1) proton thermal conduction may not be neglected, (2) the Coulomb logarithm must be calculated as a function of radius, and (3) the electron and proton temperatures at the base need not be equal, even when the time scale for energy exchange between the species is an order of magnitude smaller than the expansion time at the base. It is possible to reproduce reasonable quiet-time solar-wind parameters at 1 AU, but only if the proton temperature is approximately twice the electron temperature at 1 solar radius. This may indicate that extended proton heating is important in the outer solar corona. Winds with velocities at 1 AU of 450 km/s are generated without nonthermal energy deposition but require high proton temperatures as well as very low densities at the base. Higher-velocity solutions are not possible in a spherically symmetric geometry for reasonable particle fluxes at 1 AU, and it is suggested that these higher-velocity states probably require additional heating, acceleration mechanisms, or nonradial flow.
The Solar Probe Plus Mission: Humanity's First Visit to Our Star
Solar Probe Plus (SPP) will be the first spacecraft to fly into the low solar corona. SPPs main science goal is to determine the structure and dynamics of the Suns coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Understanding these fundamental phenomena has been a top-priority science goal for over five decades, dating back to the 1958 Simpson Committee Report. The scale and concept of such a mission has been revised at intervals since that time, yet the core has always been a close encounter with the Sun. The mission design and the technology and engineering developments enable SPP to meet its science objectives to: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles. The SPP mission was confirmed in March 2014 and is under development as a part of NASAs Living with a Star (LWS) Program. SPP is scheduled for launch in mid-2018, and will perform 24 orbits over a 7-year nominal mission duration. Seven Venus gravity assists gradually reduce SPPs perihelion from 35 solar radii (RS) for the first orbit to less than 10 RS for the final three orbits. In this paper we present the science, mission concept and the baseline vehicle for SPP, and examine how the mission will address the key science questions.