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International audience; The Magnetospheric Multiscale (MMS) spacecraft obtained unprecedented high-time resolution multipoint particle and field measurements of an interplanetary shock event on 8 January 2018. The spacecraft encountered the supercritical forward shock of a forward/reverse shock pair in the pristine solar wind upstream of the bow shock near the subsolar point as they neared apogee at 25 RE. The high-time resolution measurements from the four spacecraft, separated by only 20 km, allowed direct measurement of particle distributions revealing evidence of electron heating and near specularly reflected ions. The cross-shock potential is calculated directly from 3-D electric field measurements. This is the first reported direct high temporal resolution (

We quantify the effects of combined precipitating solar protons and magnetospheric electrons on nighttime odd hydrogen density enhancements during two solar energetic particle (SEP) events accompanied by strong geomagnetic storms. We perform detailed modeling of ionization rates for 7–17 November 2004 and 20–30 August 2005 intervals with improved version 1.6 of the Atmospheric Ionization Module Osnabruck model. Particle measurements from Geostationary Operational Environmental Satellites and Polar Orbiting Environmental Satellites are sorted and combined in 2 h intervals to create realistic particle precipitation maps that are used as the modeling input. We show that modeled atmospheric ionization rates and estimated peak odd hydrogen (primarily hydroxyl) production from 0.001 hPa to 0.1 hPa atmospheric pressure levels during these intervals are consistent with enhancements in nighttime averaged zonal odd hydrogen densities derived from newly reprocessed and improved data set of Microwave Limb Sounder instrument on board Aura satellite. We show that both precipitating SEPs and magnetospheric electrons contribute to mesospheric ionization and their relative contributions change throughout the intervals. Our event-based modeling results underline the importance of the combined ionization sources for odd hydrogen chemistry in the middle atmosphere.

It is well established that large solar energetic particle (SEP) events affect ozone in the middle atmosphere through chemical reactions involving odd hydrogen (HOx) species. We analyze global middle atmospheric effects at local nighttime for two large SEP events during the intervals of 7–17 November 2004 and 20–30 August 2005. Properties of the SEP events and concomitant geomagnetic storms are discussed using in situ measurements. Temporal dynamics and latitudinal distribution of HOx and ozone densities inferred from measurements by the Aura/MLS (Microwave Limb Sounder) instrument are analyzed. We show statistically significant increases of nighttime hydroxyl (OH) density in the middle atmosphere up to 5°106 cm−3 in the latitude range from 70° down to 50° latitude in northern and to −40° latitude in southern hemispheres in connection with peaks in proton fluxes of >10 MeV energy range measured by GOES spacecraft. During the storm main phases, the nighttime OH density increases were observed around ±50° in southern and northern hemispheres in the altitude range of 65–80 km. There is a correspondence between averaged nighttime OH partial column density (in 0.005 to 0.1 hPa pressure range) in the polar latitudes and energetic proton (>10 MeV) fluxes. Corresponding statistically significant nighttime ozone destructions up to 45% are observed from 70° down to 60° latitude in the northern and southern hemispheres. The SEP impulsive phases correspond to onsets of ozone density depletions. Larger relative ozone destructions are observed in the northern hemisphere in November and in the southern hemisphere in August. Simultaneous measurements of ozone density by the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED/SABER) instrument independently confirm the MLS results.

We extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)-driven shock. We model the propagation of a CME-driven shock in the ecliptic plane using the ZEUS-3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME-driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2-D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock-obliquity dependent. Following the procedure used in Li, Shalchi, et al. (2012), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2-D shell model in an approach similar to Zank et al. (2000). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross-field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.

The propagation of the July 14, 2000 (Bastille Day), shock complex is modeled throughout the heliosphere, including its interaction with the solar wind termination shock and subsequent propagation into the inner heliosheath. The model includes pickup ions and the ionization cavity explicitly. The Bastille Day shock is used (1) to predict the time when the Voyager spacecraft can expect to observe 2- to 3-kHz radiation and (2) to place constraints on the distance to the heliopause in the upwind or nose direction. On the basis of the most widely accepted model for the generation of the 2- to 3-kHz radiation, we predict that the Bastille Day shock, were it to produce observable radiation in the outer heliosheath, would turn on in mid-October 2001. The distance to the heliopause at the nose is then estimated to be < 120–130 AU, and the distance to the termination shock is estimated to be

We test a theory presented previously to account for the turbulent transport of magnetic fluctuation energy in the solar wind and the related dissipation and heating of the ambient ion population. This theory accounts for the injection of magnetic energy through the damping of large-scale flow gradients, such as wind shear and compression, and incorporates the injection of magnetic energy due to wave excitation by interstellar pickup ions. The theory assumes quasi-two-dimensional spectral transport of the fluctuation energy and subsequent dissipation that heats the thermal protons. We compare the predictions of this theory with Voyager 2 and Pioneer 11 observations of magnetic fluctuation energy, magnetic correlation lengths, and ambient proton temperatures. Near-Earth Omnitape observations are used to adjust for solar variability, and the possibility that high-latitude effects could mask possible radial dependences is considered. We find abundant evidence for in situ heating of the protons, which we quantify, and show that the observed magnetic energy is consistent with the ion temperatures.

A new approach to the time-dependent anisotropic propagation of interstellar pickup ions in the interplanetary medium is presented. The model includes the effects of adiabatic focusing in a radial magnetic field, adiabatic deceleration, anisotropic pitch angle scattering, convection in the solar wind, and the continual injection of newly ionized particles. It is assumed that pickup ions experience difficulty in scattering through 90°. A two-timescale scattering operator is introduced together with a generalized hemispherical model for the transport of pickup ions. The approach described here significantly extends the previous studies by Isenberg (1997) and Schwadron (1998) in that the pitch angle dependence of the pickup ions is not assumed to be of the form ƒ(r, v, t, μ) = ƒ_(r, v, t)H(μ) + ƒ+(r, v, t)H(−μ) (H(μ) is the Heaviside step function) from the outset. Specifically, (1) a higher-order truncation of the underlying Boltzmann equation is used here, thus allowing a more careful analysis of the evolving pickup ion distribution; (2) we include a finite scattering rate for particles within each hemisphere and therefore present a more accurate treatment of pitch angle evolution; and (3) we do not assume instantaneous “isotropization” of the newborn pickup ion distribution within the sunward hemisphere but instead allow it to evolve into a scattered distribution on a timescale τ-, thus preserving the pitch angle characteristics of the ring beam. The anisotropic pitch angle scattering is found to result in the sunward accumulation of pickup ions, and particles moving sunward suffer more efficient cooling than those moving antisunward. Compared with the steepness at 90° pitch angle, the pitch angle dependence is not important within each hemisphere for moderately anisotropic scattering. However, for highly anisotropic scattering, the particle distribution is dominated by particles moving sunward, adiabatic cooling is more efficient, and the deviation of sunward moving particle distribution from a homogeneous hemisphere may be large at high velocities.

There is increasing evidence to suggest that energetic particles observed in “gradual” solar energetic particle (SEP) events are accelerated at shock waves driven out of the corona by coronal mass ejections. Energetic particle abundances suggest too that SEPs are accelerated from in situ solar wind or coronal plasma rather than from high-temperature flare material. A dynamical time-dependent model of particle acceleration at a propagating, evolving interplanetary shock is presented here. The theoretical model includes the determination of the particle injection energy (injection here refers to the injection of particles into the diffusive shock acceleration mechanism), the maximum energy of particles accelerated at the shock, energetic particle spectra at all spatial and temporal locations, and the dynamical distribution of particles that escape upstream and downstream from the evolving shock complex. As the shock evolves, energetic particles are trapped downstream of the shock and diffuse slowly away. In the immediate vicinity of the shock, broken power law spectra are predicted for the energetic particle distribution function. The escaping distribution consists primarily of very energetic particles initially with a very hard power law spectrum (harder than that at the shock itself) with a rollover at lower energies. As the shock propagates further into the solar wind, the escaping ion distribution fills in at lower energies, and the overall spectrum remains hard. Downstream of the shock, the shape of the accelerated particle spectrum evolves from a convex, broken power law shape near the shock to a concave spectrum far downstream of the shock. Intensity profiles for particles of different energies are computed, and the relation between arrival times, maximum predicted energies, and shock propagation characteristics are described. These results are of particular importance in the context of predictive space weather studies.

The purpose of this paper is to report about a self-consistent study of acceleration of multiply reflected pickup protons at a quasi-perpendicular solar wind termination shock and the influence of these protons on the shock's structure. A time-dependent formulation is developed by treating the solar wind and low-energy pickup protons as one fluid under the influence of the accelerated pickup protons as a second fluid. The results suggest that the termination shock would experience significant mediation by such accelerated pickup protons if the width of the termination shock's (sub)ramp would be smaller than four times the thermal electron inertial length Le. There are examples in observations of the Earth's bow shock with a width close to such values. For a shock width of 2Le and a multiply reflected ion (MRI) distribution function fMRI ∝ v−a with a = 4, the shock compression ratio is reduced to ∼2.4 compared with the initial value of ∼3.1 and the fraction of reflected pickup protons is ∼11%. For this width the accelerated pickup protons reach a maximum energy of up to ∼ 51 keV, if a e [3,4]. Such extended MRI spectra for pickup protons, if realistic, might enable a direct injection of these particles into the process of diffusive shock acceleration at the termination shock. Therefore the model also provides a theoretical basis for a study of the formation of anomalous cosmic rays.

The theory for the perpendicular diffusion of cosmic rays is not well understood which hampers our understanding of cosmic ray modulation. In this paper, a spherically symmetric cosmic ray modulation model is used to evaluate three different theories for perpendicular cosmic ray diffusion in the ecliptic plane, subject to the limitation of negligible cosmic ray transport in the polar direction. In models for the perpendicular diffusion component, it is assumed that perpendicular diffusion due to large-scale field line wandering dominates resonant perpendicular diffusion. To test these models, observations of anomalous and galactic helium obtained during a time of relatively small latitudinal gradients (1996) are used as a guideline. The spatial dependence of the parallel and perpendicular cosmic ray diffusion coefficients is determined completely theoretically using a promising hydromagnetic model for the transport of combined slab plus two-dimensional turbulence in the solar wind [Zank et al., 1996]. The main result of the paper is that the nonperturbative model [Zank et al., 1998] yields the best results. Its success is determined by the following: (1) a perpendicular correlation length derived from two-dimensional solar wind turbulence that is much larger than the parallel correlation length associated with slab turbulence; (2) a modest radial dependence of the radial diffusion coefficient in the outer heliosphere; and (3) a three interval rigidity dependence of the radial diffusion coefficient in the outer heliosphere with the smallest rigidity dependence in the middle interval and a strong rigidity squared dependence in the other two intervals. The nonperturbative model gives a tentative theoretical basis for the cosmic ray modulation simulations by Moraal et al. [1999], who found empirically that a similar spatial and three stage rigidity dependence for the radial diffusion coefficient is important for reproducing observed anomalous and galactic cosmic ray spectra.

Using a one-dimensional gasdynamic model, it has previously been shown that pickup ions (PIs) play a significant role in the propagation of shock waves in the outer heliosphere. The effect of adding a magnetic field to the heliospheric model and the resultant effect on shock wave propagation are studied here. In the absence of PIs the addition of a magnetic field has a significant effect on shock wave propagation, yielding results very different from those obtained by simple gasdynamic models. When PIs are included, the difference between the gasdynamic case and the MHD case is quite small, indicating the dominant role played by the PIs. The difference between shock propagation characteristics when PIs are included and when they are ignored is not nearly as great in the MHD case as it is in the gasdynamic case. One of the main differences in the MHD case is the propagation of pressure-balanced structures (PBSs), which are shown to be more easily observed in the outer heliosphere when PIs are included. Besides PBSs, the inclusion of a magnetic field also allows for the investigation of structures such as magnetic clouds which can obviously not be studied using a gasdynamic model.

A mechanism for the acceleration of pickup ions by repeated reflection from the electrostatic cross-shock potential of a quasi-perpendicular shock was proposed independently by Zank et al. [1996b] and Lee et al. [1996]. The acceleration mechanism, known variously as Multiply Reflected Ion (MRI) acceleration or shock surfing, was studied by these authors in the limit of an idealized shock, which possessed neither fine-scale structure (distinct foot, ramp, or overshoot) nor pickup ion scattering turbulence. Here the acceleration of pickup ions at cometary and interplanetary shocks and at the termination shock is studied in the test particle limit on the basis of a particle-mesh simulation. All simulations assume a shell distribution for the pickup ions (either pickup protons or helium), and the dynamics of pickup ions propagating in a fixed electromagnetic field profile are investigated. The effect of a shock foot, ramp and overshoot on the acceleration of pickup ions at perpendicular and oblique shocks is described. The acceleration of pickup ions in the presence of strong turbulence inside the foreshock region is also addressed. For quasi-perpendicular shocks with structure, we obtained the following results. First, the accelerated H + and He + spectrum is a very hard power law E -k , k = 0.92 -1.2, which is much harder than that predicted by diffusive shock acceleration. Also, as θ bn , the angle between the upstream magnetic field and shock normal, decreases from 90°, the accelerated pickup ion spectrum flattens until MRI acceleration ceases. Second, the fine structure of the shock is found to reduce slightly the maximum energy gain for an accelerated pickup ion compared to that gained at an unstructured shock. Third, a flat turbulence spectrum is found to lead to an increase in the maximum energy for transmitted pickup ions, whereas a power law turbulence spectrum leads to a modest reduction in the maximum pickup ion energy gain. However, the basic MRI acceleration mechanism continues to operate in the presence of turbulent magnetic fluctuations and the characteristic hard spectra are preserved. Fourth, MRI acceleration is found to work only for those shocks for which θ bn > 60° - 70°. The results from the test particle simulations described here are also used to interpret particle acceleration in self-consistent hybrid simulations.

A nonstationary Boltzmann particle-mesh method for neutral hydrogen originating from either the interstellar medium, the heliosheath, or the solar wind has been developed to simulate the detailed interaction of the solar wind with the local interstellar medium (LISM). Such a Boltzmann description for the hydrogen serves to capture the complicated neutral distribution. The neutral component is coupled to a hydrodynamic plasma through charge exchange. The distribution of the ionized component was taken from a two-shock model [Zank et al., 1996b]. This approach is used (1) to elucidate the nature of the solar wind - LISM interaction more carefully than has been done previously in a multifluid approach [Zank et al., 1996b] and (2) to identify precisely the role played by the three identifiably distinct neutral populations in determining the global structure and dynamics of the heliosphere. The differences in the global neutral H distribution that exist between Boltzmann and multifluid gasdynamic models axe discussed briefly.

The radial and latitudinal dependence of the cosmic ray diffusion tensor is investigated on the basis of a recently developed model of magnetohydrodynamic turbulence in the expanding solar wind [Zank et al., 1996a,b; Matthaeus et al., 1996]. In the ecliptic plane, decaying magnetohydrodynamic turbulence is assumed to be replenished in situ by turbulence generated through the interaction of streams (both shear and compressional effects) and by the creation of pickup ions. In the polar region, at least during solar minimum, stream interaction driven turbulence is neglected and only pickup ion driven turbulence is included. To model the perpendicular and drift elements of the cosmic ray diffusion tensor, we employ both a quasi-linear theory (QLT) and a newly developed nonperturbative theory (NPT) to describe the field line wandering which drives perpendicular transport. A resonant quasi-linear description is applied to the parallel component. For the QLT approach, we find that in the solar wind ecliptic plane (1) the radial diffusive length scale or mean free path (mfp) is very nearly constant until some 10 AU, after which it experiences some variation with increasing heliocentric distance; (2) the radial mfp is dominated at all radial distances by the component parallel to the mean magnetic field and the perpendicular component is completely unimportant; (3) the length scale associated with the drift component of the cosmic ray diffusion tensor is only comparable to the radial mfp beyond ∼ 10 AU; and (4) the rigidity P dependence of the radial mfp within 10 – 20 AU is weak and proportional to P1/3, but in the far outer heliosphere it is proportional to P2. For the QLT model in the polar region of the solar wind, we find that the radial cosmic ray mfp is much greater than the corresponding mfp in the ecliptic region, consistent with observed mfps for pickup ions reported by Gloeckler et al. [1995]. The polar models are, however, preliminary and assume vanishing cross-helicity. The polar radial mfp is dominated by the parallel component, and drift length scales are never comparable to the radial mfp in the high polar latitudes. By using instead a nonperturbative model for the perpendicular and drift components of the cosmic ray diffusion tensor, it was found that the mfps for these coefficients could be significantly larger than their QLT counterparts. The increased perpendicular mfp was found to be important in the radial mfp only beyond ∼ 20 AU, which remains dominated by the parallel diffusion within this distance. Within the ecliptic, the nonperturbative model yields a radial mfp for cosmic rays that is almost constant with heliocentric distance. Similar order of magnitude differences between the radial mfps in the ecliptic and polar regions of the solar wind are found with the nonperturbative models.

The interaction of the solar wind termination shock with disturbances incident from the upstream solar wind is considered using a one-dimensional MHD (both transverse and oblique) model. This paper extends the work of Story and Zank [1995] (Paper 1) to include the effects of the interplanetary magnetic field. A decay law is derived to describe the damping of compound rarefaction/shock structures. The inclusion of a parallel magnetic field component leads to the production of slow-mode rarefactions and shocks. Therefore, depending on parameters, the interaction of the termination shock with interplanetary disturbances may serve to generate both slow- and fast-mode magnetosonic waves that propagate through the heliosheath. Furthermore, it follows from the simulations presented here that slow-mode waves and rotational discontinuities can be expected to occur, at least to some extent, at any region of the solar system where collisions between oblique MHD shocks occur. Some discussion regarding the relative local orientation of the heliospheric magnetic field, with respect to the interstellar magnetic field, is presented to address the possibility of a global rotational discontinuity(s) which may be necessary to connect the interplanetary magnetic field to the interstellar field. Some further results concerning the interaction of waves and shocks reflected from heliosheath structure with the termination shock are also presented.

A distinct fluid description for neutral hydrogen originating from either the interstellar medium, the heliosheath, or the solar wind has been developed to describe the detailed interaction of the solar wind with the local interstellar medium (LISM) [Williams et al., 1995]. Such a multifluid description for the hydrogen serves to capture the highly anisotropic nature of the neutral distribution. The neutral multifluid is coupled to a hydrodynamic plasma through charge exchange and the time-dependent model is solved in two spatial dimensions. This approach is used (1) to elucidate the nature of the solar wind - LISM interaction more carefully and precisely than has been done previously; (2) to identify precisely the role played by the three identifiably distinct neutral populations in determining the global structure and dynamics of the heliosphere (it is found, for example, that the heliopause is weakly time-dependent for the two-shock model); (3) to contrast these results with those obtained from the simpler, computationally more efficient model developed by Pauls et al. [1995]; and (4) to investigate the differences in global heliospheric structure and neutral properties between a two-shock (which results from a supersonic interstellar wind impinging on the heliosphere) and a one-shock (i.e., for a subsonic interstellar wind) model. In particular, observational criteria are presented that may allow one to distinguish between a one-shock and a two-shock heliosphere.

Recent multidimensional numerical simulations [Pauls et al., 1995] of the solar wind interaction with the local interstellar medium have produced a self-consistent description of the interstellar neutral hydrogen at the heliopause. In this report, we develop a simple one-dimensional model of the solar wind interaction with interstellar hydrogen which is capable of describing the basic features of the interaction along the solar wind stagnation line that were obtained in the numerical simulations. It is shown that pickup ions in the subsonic solar wind can stagnate the plasma flow completely at a distance of 40 AU from the termination shock thus defining the position of the contact discontinuity relative to the termination shock. The plasma number density increases considerably but remains finite on the solar wind side of the contact discontinuity, for a finite velocity of the neutral hydrogen. For the interstellar wind, deceleration due to the interaction with solar hydrogen is found to be important, even though the solar hydrogen density flux is relatively small. The characteristic scale of this interaction is defined by the depth of penetration of the solar hydrogen atoms into the interstellar wind. We find that for observed solar wind and interstellar medium parameters, the deceleration is sufficient to stagnate the interstellar wind at the contact discontinuity.

On the basis of transport theories appropriate to a radially expanding solar wind, new results for the evolution of the energy density in solar wind fluctuations at MHD scales are derived. The models, which represent a departure from the well-known WKB description, include the effects of “mixing”, driving by stream-stream interactions (compression and shear) and interstellar pick-up ions as well as non-isotropic MHD turbulence. Magnetometer data from Voyager 1 and 2 and Pioneer 11 are compared to the turbulence-based models and close agreement is found between theory and data for a reasonable choice of parameters.

A new mechanism for the acceleration of pickup ions by repeated reflections from the electrostatic cross shock potential of a quasi-perpendicular shock is presented. The acceleration mechanism, multiply reflected ion (MRI) acceleration, offers a resolution to the issue of injecting pickup ions into an efficient particle energization scheme, and the injection efficiency for pickup ions is found to be inversely proportional to ion mass and proportional to charge. By studying the particle energy gain in the motional electric field (where a steady shock frame is assumed) the energized pickup ion spectrum can be computed. Extremely hard power law spectra (E −1.5 , for example) emerge from the upstream pickup ion distribution. The maximum energy that a reflected pickup ion can gain is found to be proportional to the square of the product of the Alfven speed and (r−1), where r is the shock compression ratio. For solar wind conditions at either interplanetary shocks or the termination shock the upper energy limit is typically in excess of 0.5 MeV. It is suggested here that MRI acceleration provides an efficient mechanism for injecting low-energy pickup ions into a subsequent acceleration process such as diffusive Fermi acceleration. Such a two-step acceleration scheme alleviates many of the difficulties which plague ion energization models at perpendicular shocks. The structure of a quasi-perpendicular shock modified by shock reflection of pickup ions is discussed in general terms. By way of application we present a detailed study of the MRI acceleration mechanism at the termination shock for a wide range of parameters and discuss the implications for the anomalous cosmic ray component. The acceleration of pickup ions by an interplanetary traveling shock is also discussed, and the observations made by Ulysses [Gloeckler et al., 1994] are addressed. The puzzling aspects of the Gloeckler et al. [1994] observations appear to be explained quite naturally by shock energization based on repeated pickup ion reflections. Observational tests of MRI acceleration may be possible by using pickup He + at either the terrestrial or Jovian bow shock or by using cometary ions at a cometary bow shock.

First results from a two-dimensional (axisymmetric) time-dependent gas dynamic model for the interaction of the solar wind with the local interstellar medium are presented. The model includes the mutual influence of the interstellar and interplanetary plasma (protons and electrons) and the neutral interstellar hydrogen atoms. Neutrals created by charge exchange with the solar wind are ignored; this allows us to approximate the dynamical evolution of the system with the isotropic fluid equations. A supersonic interstellar wind is assumed. The global structure of the heliosphere and interaction region is described for both the plasma and neutral gas. The self-consistent model is compared to a noninteracting gas dynamic model, and dramatic differences in the size of the heliosphere are found. The distribution of neutral hydrogen in the heliosphere is also discussed.

[1] Hydromagnetic wave equations are derived for toroidal Alfven waves in a background, axi-symmetric magnetic field. In the case, where the spatial variations in the wave equations are along the background magnetic field, the equations can be re-cast in Klein-Gordon equation forms, with cut-off frequency ωc. For harmonic, constant frequency solutions, the Klein Gordon equation reduces to a Sturm-Liouville equation. We compute the eigenvalues and eigenfunctions appropriate for the Earth's dipole magnetic field, which are relevant for geomagnetic pulsations. It is suggested that the breather type Alfven eigenmodes, obtained from the analysis may describe ultra low frequency Alfvenic pulsations (e.g. Pc and Pi pulsations) observed in space and on the ground with frequencies ranging from a few milli-Herz (mHz) to a few Hz). The wave equations for the velocity and magnetic field perturbations can be re-written in terms of Elsasser variables. The resultant wave equations are a special case of the wave mixing equations for Alfvenic fluctuations used to describe locally incompressible turbulence in the solar wind. The canonical wave energy equation for the backward and forward waves, and wave reflection and transmission coefficients are briefly discussed. The equations can also be cast in the form of a Dirac equation, in the Weyl spinor form, in which the mass in the Dirac equation is identified with the wave mixing coefficient for the backward and forward waves.

[1] Homotopy formulas are obtained for the magnetic vector potential A, where B = ∇ × A is the magnetic induction, which gives alternative methods for calculating A for a given B, different from the Biot-Savart formulas. The homotopy formulas are used to obtain A for multipole potential fields and other potential fields, which are useful in relative helicity calculations. However, the formulas do not work for monopole and split monopole magnetic fields. In the latter case, there is no global continuous solution for A, but a global discontinuous A can be constructed, which is continuous on two open sets that cover the sphere. The differential and integral forms of the helicity and relative helicity transport equations using both Eulerian and Lagrangian perspectives are discussed. The approach to magnetic helicity and magnetic helicity injection, based on a toroidal-poloidal decomposition of the field, in which the field is represented by Euler potentials is also used in the analysis. The relative magnetic helicity and helicity injection rate for the Parker spiral interplanetary magnetic field, in which there is either a flat current sheet or a warped current sheet in the helioequatorial plane, are discussed. One of the homotopy formulas is used to provide an efficient way to calculate the relative helicity of interplanetary magnetic flux rope configurations observed by the WIND spacecraft.

A new two-fluid model which describes mass loading in the solar wind (e.g., the interaction of the solar wind with a cometary coma or the local interstellar medium) is presented. The self-consistent back-reaction of the mass-loaded ions is included through their effective scattering in low-frequency MHD turbulence and the invocation of a diffusive approximation. Such an approximation has the advantage of introducing self-consistent dissipation coefficients into the governing equations, thereby facilitating the investigation of the internal structure of shocks in mass-loading environments. To illustrate the utility of the new model, we consider the structure of cometary shocks in the hypersonic one-dimensional limit, finding that the incoming solar wind is slowed by both mass loading and the development of a large cometary ion pressure gradient. The shock is broadened and smoothed by the cometary ions with a thickness of the order of the cometary ion diffusion scale.

The Particle Acceleration and Transport in the Heliosphere (PATH) numerical code was developed to understand solar energetic particle (SEP) events in the near-Earth environment. We discuss simulation results for the 13 December 2006 SEP event. The PATH code includes modeling a background solar wind through which a CME-driven oblique shock propagates. The code incorporates a mixed population of both flare and shock-accelerated solar wind suprathermal particles. The shock parameters derived from ACE measurements at 1 AU and observational flare characteristics are used as input into the numerical model. We assume that the diffusive shock acceleration mechanism is responsible for particle energization. We model the subsequent transport of particles originated at the flare site and particles escaping from the shock and propagating in the equatorial plane through the interplanetary medium. We derive spectra for protons, oxygen, and iron ions, together with their time-intensity profiles at 1 AU. Our modeling results show reasonable agreement with in situ measurements by ACE, STEREO, GOES, and SAMPEX for this event. We numerically estimate the Fe/O abundance ratio and discuss the physics underlying a mixed SEP event. We point out that the flare population is as important as shock geometry changes during shock propagation for modeling time-intensity profiles and spectra at 1 AU. The combined effects of seed population and shock geometry will be examined in the framework of an extended PATH code in future modeling efforts.

[1] The evolution of density fluctuations throughout the solar wind is investigated as the basis of a newly developed theory of nearly incompressible hydrodynamics for an inhomogeneous flow. The model is explored using two-dimensional numerical simulations. The lowest-order density fluctuations (absent in the original homogeneous nearly incompressible theory) obey a passive scalar evolution equation with an additional source term that results from coupling to the large-scale inhomogeneous mean density gradient. The importance of this source term is explored, and we estimate analytically an upper bound for the maximum possible effect of a source term for nearly incompressible flows with an inhomogeneous background (static and spherically symmetric). For typical solar wind parameters, we show that this effect is rather weak beyond 0.1 AU and that the density fluctuations can be described sufficiently accurately as a pure passive scalar. Our simulations identify the sensitive dependence of density fluctuation evolution on typical initial length-scale ratio of scalar (density) and velocity fields, an effect known from the theory of passive scalar decay and experimentally measured in grid-generated turbulence. It has long been thought that the variance in the density fluctuations (δρ)2 should decay in the manner analogous to the mean background density, implying that with heliocentric distance (δρ)2 ∝ R−4 throughout the heliosphere. Analysis of plasma data obtained by the Voyager spacecraft by Bellamy et al. (2005) showed that the density fluctuations decay much more slowly than R−4 and the decay rate exhibits a flattening between 20–30 AU and a possible rise afterward. A possible mechanism to reduce the decay rate within 30 AU was suggested to be turbulence driven by stream-stream interactions followed by more dominant pickup ion interactions beyond 30 AU. Here we show that the variance in the density fluctuations as described by the inhomogeneous nearly incompressible theory evolves essentially independently of the mean density background with a decay rate that reduces and possibly levels off with increasing heliocentric distance.

[1] Decades of interplanetary measurements of the solar wind and other space plasmas have established that the suprathermal ion intensity distributions (j) are non-Maxwellian and are characterized by high-energy power law tails (j ∼ E−κ). Recent analysis by Fisk and Gloeckler of suprathermal ion observations between 1–5 AU demonstrates that a particular differential intensity distribution function emerges universally between ∼2–10 times the solar wind speed with κ ∼ 1.5. This power law tail is particularly apparent in downstream distributions beyond reverse shocks associated with corotating interaction regions. Similar power law tails have been observed in the downstream flow beyond the termination shock by the Low Energy Charged Particle instrument on both Voyager 1 and Voyager 2. Using kappa distributions with internal energy, density, and bulk flow derived from large-scale magnetohydrodynamic models, we calculate the simulated flux of energetic neutral atoms (ENAs) produced in the heliosheath by charge exchange between solar wind protons and interstellar hydrogen. We then produce simulated ENA maps of the heliosheath, such as will be measured by the Interstellar Boundary Explorer Mission (IBEX). We also estimate the expected signal to noise and background ratio for IBEX. The solar wind suprathermal tail significantly increases the ENA flux within the IBEX energy range, ∼0.01–6 keV, by more than an order of magnitude at the highest energies over the estimates using a Maxwellian. It is therefore essential to consider suprathermal tails in the interpretation of IBEX ENA images and theoretical modeling of the heliospheric termination shock.

[1] Evidence now exists which suggests that in large solar energetic particle (SEP) events, particles are often accelerated to ∼ MeV energies (and perhaps up to GeV energies) at shock waves driven by coronal mass ejections (CMEs). These energetic particles are of considerable importance to space weather studies since they serve as a precursor signal for possible disruptive events at the Earth. As a CME-driven shock propagates, expands and weakens, particles accelerated diffusively at the shock can escape upstream and downstream into the interplanetary medium. The escaping energized particles propagate along the interplanetary magnetic field, experiencing only weak scattering from fluctuations in the interplanetary magnetic field (IMF). In this work, we study the time-dependent transport of energetic particles accelerated at a propagating shock using a Monte-Carlo approach. This treatment, together with our previous work on particle acceleration at shocks, allows us to investigate the characteristics (intensity profiles, angular distribution, particle anisotropies) of high-energy particles arriving at various distances from the sun. Such an approach is both easy to implement and allows us to study the affect of interplanetary turbulence on particle transport in a systematic manner. These theoretical models form an excellent basis on which to interpret observations of high-energy particles made in situ at 1 AU by spacecraft such as ACE and WIND.