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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Three-dimensional Features of the Outer Heliosphere Due to Coupling between the Interstellar and Heliospheric Magnetic Field. V. The Bow Wave, Heliospheric Boundary Layer, Instabilities, and Magnetic Reconnection

The heliosphere is formed due to interaction between the solar wind (SW) and local interstellar medium (LISM). The shape and position of the heliospheric boundary, the heliopause, in space depend on the parameters of interacting plasma flows. The interplay between the asymmetrizing effect of the interstellar magnetic field and charge exchange between ions and neutral atoms plays an important role in the SW–LISM interaction. By performing three-dimensional, MHD plasma/kinetic neutral atom simulations, we determine the width of the outer heliosheath—the LISM plasma region affected by the presence of the heliosphere—and analyze quantitatively the distributions in front of the heliopause. It is shown that charge exchange modifies the LISM plasma to such extent that the contribution of a shock transition to the total variation of plasma parameters becomes small even if the LISM velocity exceeds the fast magnetosonic speed in the unperturbed medium. By performing adaptive mesh refinement simulations, we show that a distinct boundary layer of decreased plasma density and enhanced magnetic field should be observed on the interstellar side of the heliopause. We show that this behavior is in agreement with the plasma oscillations of increasing frequency observed by the plasma wave instrument onboard Voyager 1. We also demonstrate that Voyager observations in the inner heliosheath between the heliospheric termination shock and the heliopause are consistent with dissipation of the heliospheric magnetic field. The choice of LISM parameters in this analysis is based on the simulations that fit observations of energetic neutral atoms performed by Interstellar Boundary Explorer .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric Boundary

In this study, we performed numerical calculations to test the suggestion by Desiati and Lazarian that the anisotropies of TeV cosmic rays may arise from their interactions with the heliosphere. For this purpose, we used a magnetic field model of the heliosphere and performed direct numerical calculations of particle trajectories. Unlike earlier papers testing the idea, we did not employ time-reversible techniques that are based on Liouville's theorem. We showed numerically that for scattering by the heliosphere, the conditions of Liouville's theorem are not satisfied, and the adiabatic approximation and time-reversibility of the particle trajectories are not valid. Finally, our results indicate sensitivity to the magnetic structure of the heliospheric magnetic field, and we expect that this will be useful for probing this structure in future research.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

VOYAGER OBSERVATIONS OF MAGNETIC SECTORS AND HELIOSPHERIC CURRENT SHEET CROSSINGS IN THE OUTER HELIOSPHERE

Voyager 1 ( V1 ) has passed through the heliosheath and is in the local interstellar medium. Voyager 2 ( V2 ) has been in the heliosheath since 2007. The role of reconnection in the heliosheath is under debate; compression of the heliospheric current sheets (HCS) in the heliosheath could lead to rapid reconnection and a reconfiguration of the magnetic field topology. This paper compares the expected and actual amounts of time the Voyager spacecraft observe each magnetic sector and the number of HCS crossings. The predicted and observed values generally agree well. One exception is at Voyager 1 in 2008 and 2009, where the distribution of sectors is more equal than expected and the number of HCS crossings is small. Two other exceptions are at V1 in 2011–2012 and at V2 in 2012, when the spacecraft are in the opposite magnetic sector less than expected and see fewer HCS crossings than expected. These features are consistent with those predicted for reconnection, and consequently searches for other reconnection signatures should focus on these times.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Oblique and rippled heliosphere structures from the Interstellar Boundary Explorer

Abstract Past analysis has shown that the heliosphere structure can be deduced from correlations between long-scale solar wind pressure evolution and energetic neutral atom emissions. However, this required spatial and temporal averaging that smoothed out small or dynamic features of the heliosphere. In late 2014, the solar wind dynamic pressure increased by roughly 50% over a period of 6 months, causing a time and directional-dependent rise in around 2–6 keV energetic neutral atom fluxes from the heliosphere observed by the Interstellar Boundary Explorer. Here, we use the 2014 pressure enhancement to provide a simultaneous derivation of the three-dimensional heliospheric termination shock (HTS) and heliopause (HP) distances at high resolution from Interstellar Boundary Explorer measurements. The analysis reveals rippled HTS and HP surfaces that are oblique with respect to the local interstellar medium upwind direction, with significant asymmetries in the heliosphere structure compared to steady-state heliosphere models. We estimate that the heliosphere boundaries contain roughly ten astronomical unit-sized spatial variations, with slightly larger variations on the HTS surface than the HP and a large-scale, southwards-directed obliquity of the surfaces in the meridional plane. Comparisons of the derived HTS and HP distances with Voyager observations indicate substantial differences in the heliosphere boundaries in the northern versus southern hemispheres and their motion over time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Magnetized jets driven by the Sun: The structure of the heliosphere revisited—Updates

As the solar system moves through the interstellar medium, the solar wind is deflected forming the heliosphere. The standard picture of the heliosphere is a comet-shape like structure with the tail extending for 1000s of astronomical units. This standard picture stems from a view where magnetic forces are negligible and the solar magnetic field is convected passively down the tail. Recently, we showed that the magnetic tension of the solar magnetic field plays a crucial role on organizing the solar wind in the heliosheath into two jet-like structures. The two jets are separated by the interstellar medium that flows between them. The heliosphere then has a “croissant”-like shape where the distance to the heliopause downtail is almost the same as towards the nose. This new view of the heliosphere is in agreement with the energetic neutral atoms maps taken by the Interstellar Boundary Explorer and INCA/CASSINI. We developed as well an analytic model of the heliosheath in the axisymmetric limit that shows how the magnetic tension force is the driver for the north and south jets. We confirmed that the formation of these jets with magnetohydrodynamic (MHD) simulations. The main reason why previous global MHD simulations did not see these jets is due to spurious magnetic dissipation that was present at the heliospheric current sheet. We instead kept the same polarity for the interplanetary (solar) magnetic field in both the northern and southern hemispheres, eliminating spurious magnetic dissipation effects at the heliospheric current sheet. In this paper, we extend these previous results to include additional cases where we used: (a) weaker solar magnetic field; (b) solar magnetic field that reverses polarity at the solar equator in the axisymmetric limit; and (c) slower motion through the interstellar system. We discuss as well future challenges regarding the structure of the heliosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Inferring the Heliospheric Magnetic Field Back through Maunder Minimum

Recent solar conditions include a prolonged solar minimum (2005–2009) and a solar maximum that has not fully recovered in terms of the Heliospheric Magnetic Field (HMF) strength when compared to the previous maximum values. These anomalies may indicate that we are entering an era of lower solar activity than observed at other times during the space age. We study past solar grand minima, especially the Maunder period (1645–1715) to gain further insight into grand minima. We find the timescale parameters associated with three processes attributed to the magnetic flux balance in the heliosphere using chi-square analysis. We use HMF time series reconstructed based on geomagnetic data and near-Earth spacecraft measurements (OMNI) data to find the fundamental timescales that influence heliospheric field evolution through conversion or opening of magnetic flux from coronal mass ejections (CMEs) into the ambient heliospheric field, removal or loss of the ambient heliospheric field through magnetic reconnection, and interchange reconnection between CME magnetic flux and ambient heliospheric magnetic flux. We also investigate the existence of a floor in the heliospheric magnetic flux, in the absence of CMEs, and show that a floor ⩽1.49nT is sufficient to successfully describe the HMF evolution. The minimum value for the HMF at 1 au in the model-predicted historic record is 3.13 ± 0.35 nT. Our model results favorably reproduce paleocosmic data and near-Earth spacecraft measurements data and show how the HMF may evolve through periods of extremely low activity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

COUPLING OF CORONAL AND HELIOSPHERIC MAGNETOHYDRODYNAMIC MODELS: SOLUTION COMPARISONS AND VERIFICATION

Two well-established magnetohydrodynamic (MHD) codes are coupled to model the solar corona and the inner heliosphere. The corona is simulated using the MHD algorithm outside a sphere (MAS) model. The Lyon–Fedder–Mobarry (LFM) model is used in the heliosphere. The interface between the models is placed in a spherical shell above the critical point and allows both models to work in either a rotating or an inertial frame. Numerical tests are presented examining the coupled model solutions from 20 to 50 solar radii. The heliospheric simulations are run with both LFM and the MAS extension into the heliosphere, and use the same polytropic coronal MAS solutions as the inner boundary condition. The coronal simulations are performed for idealized magnetic configurations, with an out-of-equilibrium flux rope inserted into an axisymmetric background, with and without including the solar rotation. The temporal evolution at the inner boundary of the LFM and MAS solutions is shown to be nearly identical, as are the steady-state background solutions, prior to the insertion of the flux rope. However, after the coronal mass ejection has propagated through the significant portion of the simulation domain, the heliospheric solutions diverge. Additional simulations with different resolution are then performed and show that the MAS heliospheric solutions approach those of LFM when run with progressively higher resolution. Following these detailed tests, a more realistic simulation driven by the thermodynamic coronal MAS is presented, which includes solar rotation and an azimuthally asymmetric background and extends to the Earth’s orbit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Three-dimensional Map of the Heliosphere from IBEX

The Interstellar Boundary Explorer (IBEX) mission has shown that variations in the energetic neutral atom (ENA) flux from the outer heliosphere are associated with the solar cycle and longer-term variations in the solar wind (SW). In particular, there is a good correlation between the dynamic pressure of the outbound SW and variations in the later-observed IBEX ENA flux. The time difference between observations of the outbound SW and the heliospheric ENAs with which they correlate ranges from approximately 2 to 6 yr or more, depending on ENA energy and look direction. This time difference can be used as a means of "sounding" the heliosheath, that is, finding the average distance to the ENA source region in a particular direction. Here, we apply this method to build a 3D map of the heliosphere. We use IBEX ENA data collected over a complete solar cycle, from 2009 through 2019, corrected for survival probability to the inner heliosphere. Here we divide the data into 56 "macropixels" covering the entire sky. As each point in the sky is sampled once every 6 months, this gives us a time series of 22 points macropixel –1 on which to time-correlate. Consistent with prior studies and heliospheric models, we find that the shortest distance to the heliopause, d HP , is slightly south of the nose direction (d HP ~ 110–120 au), with a flaring toward the flanks and poles (d HP ~ 160–180 au). The heliosphere extends at least ~350 au tailward, which is the distance limit of the technique.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Modeling Emission of Heavy Energetic Neutral Atoms from the Heliosphere

Observations of energetic neutral atoms (ENAs) are a fruitful tool for remote diagnosis of the plasma in the heliosphere and its vicinity. So far, instruments detecting ENAs from the heliosphere were configured for observations of hydrogen atoms. Here, we estimate emissions of ENAs of the heavy chemical elements helium, oxygen, nitrogen, and neon. A large portion of the heliospheric ENAs is created in the inner heliosheath from neutralized interstellar pick-up ions (PUIs). We modeled this process and calculated full-sky intensities of ENAs for energies 0.2–130 keV/nuc. We found that the largest fluxes among considered species are expected for helium, smaller for oxygen and nitrogen, and smallest for neon. The obtained intensities are 50–10{sup 6} times smaller than the hydrogen ENA intensities observed by IBEX . The detection of heavy ENAs will be possible if a future ENA detector is equipped with the capability to measure the masses of observed atoms. Because of different reaction cross-sections among the different species, observations of heavy ENAs can allow for a better understanding of global structure of the heliosphere as well as the transport and energization of PUIs in the heliosphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Heliosphere Responds to a Large Solar Wind Intensification: Decisive Observations from IBEX

Our heliosphere—the bubble in the local interstellar medium produced by the Sun's outflowing solar wind—has finally responded to a large increase in solar wind output and pressure in the second half of 2014. NASA's Interstellar Boundary Explorer ( IBEX ) mission remotely monitors the outer heliosphere by observing energetic neutral atoms (ENAs) returning from the heliosheath, the region between the termination shock and heliopause. IBEX observed a significant enhancement in higher energy ENAs starting in late 2016. While IBEX observations over the previous decade reflected a general reduction of ENA intensities, indicative of a deflating heliosphere, new observations show that the large (~50%), persistent increase in the solar wind dynamic pressure has modified the heliosheath, producing enhanced ENA emissions. The combination of these new observations with simulation results indicate that this pressure is re-expanding our heliosphere, with the termination shock and heliopause already driven outward in the locations closest to the Sun. The timing between the IBEX observations, a large transient pressure enhancement seen by Voyager 2 , and the simulations indicates that the pressure increase propagated through the heliosheath, reflected off the heliopause, and the enhanced density of the solar wind filled the heliosheath behind it before generating significantly enhanced ENA emissions. As a result, the coming years should see significant changes in anomalous cosmic rays, galactic cosmic radiation, and the filtration of interstellar neutral atoms into the inner heliosphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Whence the Interstellar Magnetic Field Shaping the Heliosphere?

Measurements of starlight polarized by aligned interstellar dust grains are used to probe the relation between the orientation of the ambient interstellar magnetic field (ISMF) and the ISMF traced by the ribbons of energetic neutral atoms discovered by the Interstellar Boundary Explorer spacecraft. We utilize polarization data, many acquired specifically for this study, to trace the configuration of the ISMF within 40 pc. A statistical analysis yields a best-fit ISMF orientation, B magpol , aligned with Galactic coordinates ℓ = 42°, b = 49°. Further analysis shows the ISMF is more orderly for "downfield" stars located over 90° from Bmagpol. The data subset of downfield stars yields an orientation for the nearby ISMF at ecliptic coordinates λ, β ≈ 219° ± 15°, 43° ± 9° (Galactic coordinates l, b ≈ 40°, 56°, ±17°). This best-fit ISMF orientation from polarization data is close to the field direction obtained from ribbon models. This agreement suggests that the ISMF shaping the heliosphere belongs to an extended ordered magnetic field. Extended filamentary structures are found throughout the sky. A previously discovered filament traversing the heliosphere nose region, "Filament A," extends over 300° of the sky, and crosses the upwind direction of interstellar dust flowing into the heliosphere. Filament A overlaps the locations of the Voyager kilohertz emissions, three quasar intraday variables, cosmic microwave background (CMB) components, and the inflow direction of interstellar grains sampled by Ulysses and Galileo. These features are likely located in the upstream outer heliosheath where ISMF drapes over the heliosphere, suggesting Filament A coincides with a dusty magnetized plasma. A filament 55° long is aligned with a possible shock interface between local interstellar clouds. A dark spot in the CMB is seen within 5° of the filament and within 10° of the downfield ISMF direction. Two large magnetic arcs are centered on the directions of the heliotail. The overlap between CMB components and the aligned dust grains forming Filament A indicates the configuration of dust entrained in the ISMF interacting with the heliosphere provides a measurable foreground to the CMB.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Calibration of the Voyager ultraviolet spectrometers and the composition of the heliosphere neutrals: reassessment

The data harvest from the Voyagers’ (V 1 and V 2) Ultraviolet Spectrometers (UVS) covers encounters with the outer planets, measurements of the heliosphere sky-background, and stellar spectrophotometry. Because their period of operation overlaps with many ultraviolet missions, the calibration of V1 and V2 UVS with other spectrometers is invaluable. Here we revisit the UVS calibration to assess the intriguing sensitivity enhancements of 243% (V1) and 156% (V2) proposed recently. Using the Lyα airglow from Saturn, observed in situ by both Voyagers, and remotely by International Ultraviolet Explorer (IUE), we match the Voyager values to IUE, taking into account the shape of the Saturn Lyα line observed with the Goddard High Resolution Spectrograph on board the Hubble Space Telescope. For all known ranges of the interplanetary hydrogen density, we show that the V1 and V2 UVS sensitivities cannot be enhanced by the amounts thus far proposed. The same diagnostic holds for distinct channels covering the diffuse He i 58.4 nm emission. Our prescription is to keep the original calibration of the Voyager UVS with a maximum uncertainty of 30%, making both instruments some of the most stable EUV/FUV spectrographs in the history of space exploration. In that frame, we reassess the excess Lyα emission detected by Voyager UVS deep in the heliosphere, to show its consistency with a heliospheric but not galactic origin. Our finding confirms results obtained nearly two decades ago—namely, the UVS discovery of the distortion of the heliosphere and the corresponding obliquity of the local interstellar magnetic field (∼40{sup ∘} from upwind) in the solar system neighborhood—without requiring any revision of the Voyager UVS calibration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cosmic-Ray Transport in Heliospheric Magnetic Structures. II. Modeling Particle Transport through Corotating Interaction Regions

The transport of cosmic rays (CRs) in the heliosphere is determined by the properties of the solar wind plasma. The heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the three-dimensional (3D) heliospheric CR transport are structures such as corotating interaction regions (CIRs), which, due to the enhancement of the magnetic field strength and magnetic fluctuations within and due to the associated shocks as well as stream interfaces, do influence the CR diffusion and drift. In a three-fold series of papers, we investigate these effects by modeling inner-heliospheric solar wind conditions with the numerical magnetohydrodynamic (MHD) framework Cronos (Wiengarten et al., referred as Paper I), and the results serve as input to a transport code employing a stochastic differential equation approach (this paper). While, in Paper I, we presented results from 3D simulations with Cronos, the MHD output is now taken as an input to the CR transport modeling. We discuss the diffusion and drift behavior of Galactic cosmic rays using the example of different theories, and study the effects of CIRs on these transport processes. In particular, we point out the wide range of possible particle fluxes at a given point in space resulting from these different theories. The restriction of this variety by fitting the numerical results to spacecraft data will be the subject of the third paper of this series.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cosmic-Ray Diffusion Coefficients throughout the Inner Heliosphere from a Global Solar Wind Simulation

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2 R{sub ⊙}−3 au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer “consensus” range of 0.08–0.3 au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P{sup .33}, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Energetic neutral atom and interstellar flow observations with IBEX: Implications for the global heliosphere

Since launch in Oct. 2008, IBEX, with its two energetic neutral atom (ENA) cameras, has provided humankind with the first-ever global images of the complex boundary separating the heliosphere from the local interstellar medium (LISM). IBEX’s energy-resolved all-sky maps, collected every six months, are yielding remarkable new insights into the heliospheres structure as it is shaped by the combined forces of the local interstellar flow, the local interstellar magnetic field (LISMF), and the evolving solar wind. IBEX has also acquired the first images of ENAs backscattered from the surface of the moon as well as global images of the magnetospheric response to solar wind disturbances. IBEX thus addresses all three Heliophysics science objectives set forth in the 2014 Science Plan for NASAs Science Mission Directorate (SMD) as well as the goals in the recent Solar and Space Physics Decadal Survey (NRC 2012). In addition, with the information it provides on the properties of the LISM and the LISMF, IBEX represents a unique bridge between heliophysics and astrophysics, and fills in critical knowledge for understanding the habitability of exoplanetary systems and the future habitability of Earth and the solar system. Because of the few-year time lag due to solar wind and ENA transport, IBEX observed the solar wind/ LISM interaction characteristic of declining phase/solar minimum conditions. In the continuing mission, IBEX captures the response of the interstellar boundaries to the changing structure of the solar wind in its transition toward the “mini” solar maximum and possibly the decline into the next solar minimum. The continuing IBEX mission affords never-to-be-repeated opportunities to coordinate global imaging of the heliospheric boundary with in-situ measurements by the Voyagers as they pass beyond the heliopause and start to directly sample the LISM.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

MULTIPLE CURRENT SHEET SYSTEMS IN THE OUTER HELIOSPHERE: ENERGY RELEASE AND TURBULENCE

In the outer heliosphere, beyond the solar wind termination shock, it is expected that the warped heliospheric current sheet forms a region of closely packed, multiple, thin current sheets. Such a system may be subject to the ion-kinetic tearing instability, and hence may generate magnetic islands and hot populations of ions associated with magnetic reconnection. Reconnection processes in this environment have important implications for local particle transport, and for particle acceleration at reconnection sites and in turbulence. We study this complex environment by means of three-dimensional hybrid simulations over long timescales, in order to capture the evolution from linear growth of the tearing instability to a fully developed turbulent state at late times. The final state develops from the highly ordered initial state via both forward and inverse cascades. Component and spectral anisotropy in the magnetic fluctuations is present when a guide field is included. The inclusion of a population of newborn interstellar pickup protons does not strongly affect these results. Finally, we conclude that reconnection between multiple current sheets can act as an important source of turbulence in the outer heliosphere, with implications for energetic particle acceleration and propagation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Helium Energetic Neutral Atoms from the Heliosphere: Perspectives for Future Observations

Observations of energetic neutral atoms (ENAs) allow for remote sensing of plasma properties in distant regions of the heliosphere. So far, most of the observations have concerned only hydrogen atoms. In this paper, we present perspectives for observations of helium energetic neutral atoms (He ENAs). We calculated the expected intensities of He ENAs created by the neutralization of helium ions in the inner heliosheath and through the secondary ENA mechanism in the outer heliosheath. We found that the dominant source region for He ENAs is the inner heliosheath. The obtained magnitudes of intensity spectra suggest that He ENAs can be observed with future ENA detectors, as those planned on Interstellar Mapping and Acceleration Probe . Observing He ENAs is most likely for energies from a few to a few tens of keV/nuc. Estimates of the expected count rates show that the ratio of helium to hydrogen atoms registered in the detectors can be as low as 1:10{sup 4}. Consequently, the detectors need to be equipped with an appropriate mass spectrometer capability, allowing for recognition of chemical elements. Due to the long mean free paths of helium ions in the inner heliosheath, He ENAs are produced also in the distant heliospheric tail. This implies that observations of He ENAs can resolve its structure, which seems challenging from observations of hydrogen ENAs since energetic protons are neutralized before they progress deeper in the heliospheric tail.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

We develop a numerical model to study the time-dependent modulation of galactic cosmic rays in the inner heliosphere. In the model, a time-delayed modified Parker heliospheric magnetic field (HMF) and a new diffusion coefficient model, NLGCE-F, from Qin and Zhang, are adopted. In addition, the latitudinal dependence of magnetic turbulence magnitude is assumed to be ∼(1+sin{sup 2}θ)/2 from the observations of Ulysses, and the radial dependence is assumed to be ∼r{sup S}, where we choose an expression of S as a function of the heliospheric current sheet tilt angle. We show that the analytical expression used to describe the spatial variation of HMF turbulence magnitude agrees well with the Ulysses, Voyager 1, and Voyager 2 observations. By numerically calculating the modulation code, we get the proton energy spectra as a function of time during the recent solar minimum, it is shown that the modulation results are consistent with the Payload for Antimatter-Matter Exploration and Light-nuclei Astrophysics measurements.

79 ASTRONOMY AND ASTROPHYSICS↗