We study how a high-speed solar wind stream embedded in a slow solar wind affects the transport and energy changes of solar energetic protons in interplanetary space, assuming different levels of cross-field diffusion. This is done using a particle transport model that computes directional particle intensities and first order parallel anisotropies in a background solar wind generated by the magnetohydrodynamic model EUHFORIA. In particular, we consider a mono-energetic 4 MeV proton injection over an extended region located at a heliographic radial distance of 0.1 AU. By using different values for the perpendicular proton mean free path, we study how cross-field diffusion may affect the energetic particle spread and intensity profiles near a high-speed solar wind stream and a corotating interaction region (CIR). We find that both a strong cross-field diffusion and a solar wind rarefaction region are capable of dispersing SEPs efficiently, producing overall low particle intensities which can in some cases prevent the SEPs from being detected in-situ, since their intensity may drop below the detected pre-event intensity levels. We also discuss how accelerated particle populations form on the reverse and forward shock waves, separated by the stream interface inside the CIR. Under strong levels of cross-field diffusion, particles cross the SI and hence both accelerated particle populations merge together.
In the near future, Parker Solar Probe and Solar Orbiter will provide the first comprehensive in-situ measurements of the solar wind in the inner heliosphere since the Helios mission in the 1970s. We describe a reprocessing of the original Helios ion distribution functions to provide reliable and reproducible data to characterise the proton core population of the solar wind in the inner heliosphere. A systematic fitting of bi-Maxwellian distribution functions was performed to the raw Helios ion distribution function data to extract the proton core number density, velocity, and temperatures par…
Global gradients for cosmic-ray (CR) protons in the heliosphere are computed with a comprehensive modulation model for the recent prolonged solar minimum of Cycle 23/24. Fortunately, the PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) and Ulysses/KET (Kiel Electron Telescope) instruments simultaneously observed proton intensities for the period between July 2006 and June 2009. Radial and latitudinal gradients are calculated from measurements, with the latter possible because Ulysses changed its position significantly in the heliocentric meridional plane during …
Using one-dimensional hybrid expanding box model we investigate properties of the solar wind in the outer heliosphere. We assume a proton-electron plasma with a strictly transverse ambient magnetic field and, beside the expansion, we take into account influence of a continuous injection of cold pick-up protons through the charge-exchange process between the solar wind protons and hydrogen of interstellar origin. The injected cold pick-up protons form a ring distribution function that rapidly becomes unstable and generate Alfvén cyclotron waves. The Alfvén cyclotron waves scatter pick-up proton…
We have determined the interstellar spectra of cosmic ray protons and electrons from a few MeV to ~10 GeV. These interstellar spectra are based on Voyager data and a normalization of specific galactic propagation model calculations of both protons and electrons to PAMELA data at the Earth at 10 GeV, where the solar modulation is small. These resulting interstellar spectra are then compared with spectra of protons and electrons measured at lower energies at the Earth by PAMELA in 2009. The total amount of modulation at lower rigidities (energies) is found to be nearly the same at the same rigid…
We combine different measurements of the polytropic index of the proton plasma in the heliosphere: i) near-adiabatic index in the inner heliosphere ~1AU, ii) subadiabatic indices in the outer heliosphere ~20-40AU, and iii) near-zero indices in the inner heliosheath. These observations are unified by a single theoretical model of the polytropic index throughout its radial extent in the heliosphere; the corresponding fitting reveals the decreasing trend of the polytropic index with increasing heliocentric distance R. We anticipate that with increasing R, (i) the Debye length and mean-free-path d…
We report proton temperature anisotropy variations in the inner heliosphere with Parker Solar Probe (PSP) observations. Using a linear fitting method, we derive proton temperature anisotropy with temperatures measured by the Solar Probe Cup (SPC) from the SWEAP instrument suite and magnetic field observations from the FIELDS instrument suite. The observed radial dependence of temperature variations in the fast solar wind implies stronger perpendicular heating and parallel cooling than previous results from Helios measurements made at larger radial distances. The anti-correlation between proton…
Galactic cosmic rays (GCRs) inside the heliosphere are affected by magnetic turbulence and Solar wind disturbances which result in the so-called solar modulation effect. To investigate this phenomenon, we have performed a data-driven analysis of the temporal dependence of the GCR flux over the solar cycle. With a global statistical inference of GCR data collected in space by AMS-02, PAMELA, and CRIS on monthly basis, we have determined the dependence of the GCR diffusion parameters upon time and rigidity. In this conference, we present our results for GCR protons and nuclei, we discuss their i…
During the transition from solar cycle 23 to 24 from 2006 to 2009, the Sun was in an unusual solar minimum with very low activity over a long period. These exceptional conditions included a very low interplanetary magnetic field (IMF) strength and a high tilt angle, which both play an important role in the modulation of galactic cosmic rays (GCR) in the heliosphere. Thus, the radial and latitudinal gradients of GCRs are very much expected to depend not only on the solar magnetic epoch, but also on the overall modulation level. We determine the non-local radial and the latitudinal gradients of …
Understanding the time-dependent relationship between the Sun's variability and cosmic rays (GCR) is essential for developing predictive models of energetic radiation in space. When traveling inside the heliosphere, GCRs are affected by magnetic turbulence and solar wind disturbances which result in the so-called solar modulation effect. To investigate this phenomenon, we have performed a data-driven analysis of the temporal dependence of the GCR flux over the solar cycle. With a global statistical inference of GCR data collected in space by AMS-02 and PAMELA on monthly basis, we have determin…
After six years of continuous observations in space, the Alpha Magnetic Spectrometer experiment has released new data on the temporal evolution of the proton and helium fluxes in cosmic rays. These data revealed that the ratio between proton and helium fluxes at the same value of rigidity $R=p/Z$ (momentum/charge ratio) is not constant at $R\lesssim$ 3 GV. In particular, the ratio is found to decrease steadily during the descending phase of Solar Cycle 24 toward the next minimum. We show that such a behavior is a remarkable signature of the $β\timesλ(R)$ dependence in the diffusion of cosmic r…
Switchbacks are discrete angular deflections in the solar wind magnetic field that have been observed throughout the heliosphere. Recent observations by Parker Solar Probe (PSP) have revealed the presence of patches of switchbacks on the scale of hours to days, separated by 'quieter' radial fields. We aim to further diagnose the origin of these patches using measurements of proton temperature anisotropy that can illuminate possible links to formation processes in the solar corona. We fitted 3D bi-Maxwellian functions to the core of proton velocity distributions measured by the SPAN-Ai instrume…
Models play an important role in our understanding of the global structure of the solar wind and its interaction with the interstellar medium. A critical ingredient in many types of models are the charge-exchange collisions between ions and neutrals. Some ambiguity exists in the charge-exchange cross-section for protons and hydrogen atoms, depending on which experimental data is used. The differences are greatest at low energies, and for the plasma-neutral interaction in the outer heliosheath may exceed 50\%. In this paper we assess a number of existing data sets and formulae for proton-hydrog…
Differential flows among different ion species are often observed in the solar wind, and such ion differential flows can provide the free energy to drive Alfvén/ion-cyclotron and fast-magnetosonic/whistler instabilities. Previous works mainly focused on ion beam instability under the parameters representative of the solar wind nearby 1 au. In this paper we further study proton beam instability using the radial models of the magnetic field and plasma parameters in the inner heliosphere. We explore a comprehensive distribution of proton beam instability as functions of the heliocentric distance …
Thanks to space-borne experiments of cosmic-ray (CR) detection, such as the AMS and PAMELA missions in low-Earth orbit, or the Voyager-1 spacecraft in the interstellar space, a large collection of multi-channel and time-resolved CR data has become available. Recently, the AMS experiment has released new precision data, on the proton and helium fluxes in CRs, measured on monthly basis during its first six years of mission. The AMS data reveal a remarkable long-term behavior in the temporal evolution of the proton-to-helium ratio at rigidity $R = p/Z <$ 3 GV. As we have argued in a recent work, …
Galactic cosmic rays (CRs) inside the heliosphere are affected by solar modulation. To investigate this phenomenon and its underlying physical mechanisms, we have performed a data-driven analysis of the temporal dependence of the CR proton flux over the solar cycle. The modulation effect was modeled by means of stochastic simulations of cosmic particles in the heliosphere. The model were constrained using measurements of CR protons made by AMS-02 and PAMELA experiments on monthly basis from 2006 to 2017. With a global statistical analysis of these data, we have determined the key model paramet…
The recovery of cosmic ray protons of energy ~150-250 MeV/nuc in solar cycle #23 from 2004 to 2010 has been followed at the Earth using IMP, ACE and balloon data and also at V2 between 74-92 AU and at V1 beyond the heliospheric termination shock (91-113 AU). The correlation coefficient between the intensities the Earth and V1 during this time period, is 0.936, allowing for a ~0.9 year delay due to the solar wind propagation time from the Earth to the outer heliosphere. To describe these intensity changes and to predict the absolute intensities measured at all three locations we have used a sim…
A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during the process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on-board Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We also address a …
We present a comprehensive study of energetic neutral atoms (ENAs) of 10 eV to 2.5 keV from the downwind hemisphere of the heliosphere. These ENAs are believed to originate mostly from pickup protons and solar wind protons in the inner heliosheath. This study includes all low-energy observations made with the Interstellar Boundary Explorer over the first 8 years. Since the protons around 0.1 keV dominate the plasma pressure in the inner heliosheath in downwind direction, these ENA observations offer the unique opportunity to constrain the plasma properties and dimensions of the heliosheath whe…
We provide evidence that the sunward-propagating half of the solar wind electron halo distribution evolves without scattering in the inner heliosphere. We assume the particles conserve their total energy and magnetic moment, and perform a "Liouville mapping" on electron pitch angle distributions measured by the Parker Solar Probe SPAN-E instrument. Namely, we show that the distributions are consistent with Liouville's theorem if an appropriate interplanetary potential is chosen. This potential, an outcome of our fitting method, is compared against the radial profiles of proton bulk flow energy…
Since the beginning of the space exploration era, solar activity was observed at its lowest level during 2006 to 2009. During this period, the PAMELA space experiment observed spectra for galactic cosmic rays, specifically for protons, electrons and positrons over a wide energy range, during what is called an A < 0 solar magnetic polarity cycle. Drift theory predicts a difference in the behaviour for these oppositely charge particles during A < 0 cycles. An opportunity was thus created to study the predicted charge-sign-dependent modulation, also now for very quiet heliospheric conditions. A c…
The solar wind proton temperature at 1-au has been found to be correlated with small-scale intermittent magnetic structures, i.e., regions with enhanced temperature are associated with coherent structures such as current sheets. Using Parker Solar Probe data from the first encounter, we study this association using measurements of radial proton temperature, employing the Partial Variance of Increments (PVI) technique to identify intermittent magnetic structures. We observe that the probability density functions of high-PVI events have higher median temperatures than those with lower PVI, The r…
Instabilities described by linear theory characterize an important form of wave-particle interaction in the solar wind. We diagnose unstable behavior of solar wind plasma between 0.3 and 1 au via the Nyquist criterion, applying it to fits of $\sim1.5$M proton and $α$ particle Velocity Distribution Functions (VDFs) observed by \emph{Helios I} and \emph{II}. The variation of the fraction of unstable intervals with radial distance from the Sun is linear, signaling a gradual decline in the activity of unstable modes. When calculated as functions of the solar wind velocity and Coulomb number, we ob…
The outer heliosphere is a dynamic region shaped largely by the interaction between the solar wind and the interstellar medium. While interplanetary magnetic field and plasma observations by the Voyager spacecraft have significantly improved our understanding of this vast region, modeling the outer heliosphere still remains a challenge. We simulate the three-dimensional, time-dependent solar wind flow from 1 to 80 astronomical units (AU), where the solar wind is assumed to be supersonic, using a two-fluid model in which protons and interstellar neutral hydrogen atoms are treated as separate fl…
The main sources of solar energetic particle (SEP) events are solar flares and shocks driven by coronal mass ejections (CMEs). While it is generally accepted that energetic protons can be accelerated by shocks, whether or not these shocks can also efficiently accelerate solar energetic electrons is still debated. In this study we present observations of the extremely widespread SEP event of 26 Dec 2013. To the knowledge of the authors, this is the widest longitudinal SEP distribution ever observed together with unusually long-lasting energetic electron anisotropies at all observer positions. F…
A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations, is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. To this end, the dfferences in the modulation brought about by each of three choices for the heliospheric magnetic field, i.e. the unmodified Parker field, the Smith-Bieber modified field, and the Jokipii-Kota modified field, are studied. It is illustrated that both the Jokipii-Kota and Smith-Bieber modifications are effective in modify…
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 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 hy…
We analyze measured proton and electron temperatures in the high-speed solar wind in order to calculate the separate rates of heat deposition for protons and electrons. When comparing with other regions of the heliosphere, the fast solar wind has the lowest density and the least frequent Coulomb collisions. This makes the fast wind an optimal testing ground for studies of collisionless kinetic processes associated with the dissipation of plasma turbulence. Data from the Helios and Ulysses plasma instruments were collected to determine mean radial trends in the temperatures and the electron hea…
Precise measurements of the time-dependent intensity of the low energy ($<50$ GeV) galactic cosmic rays are fundamental to test and improve the models which describe their propagation inside the heliosphere. Especially, data spanning different solar activity periods, i.e. from minimum to maximum, are needed to achieve comprehensive understanding of such physical phenomenon. The minimum phase between the 23$^{rd}$ and the 24$^{th}$ solar cycles was peculiarly long, extending up to the beginning of 2010 and followed by the maximum phase, reached during early 2014. In this paper, we present proto…
In this Paper, we present the first results from the Flux Angle operation mode of the Faraday Cup instrument onboard Parker Solar Probe. The Flux Angle mode allows rapid measurements of phase space density fluctuations close to the peak of the proton velocity distribution function with a cadence of 293 Hz. This approach provides an invaluable tool for understanding kinetic scale turbulence in the solar wind and solar corona. We describe a technique to convert the phase space density fluctuations into vector velocity components and compute several turbulence parameters such as spectral index, r…
The origins and generation mechanisms of the slow solar wind are still unclear. Part of the slow solar wind is populated by "number density structures", discrete patches of increased number density that are frozen in to and move with the bulk solar wind. In this paper we aimed to provide the first in-situ statistical study of number density structures in the inner heliosphere. We reprocessed in-situ ion distribution functions measured by Helios in the inner heliosphere to provide a new reliable set of proton plasma moments for the entire mission. From this new data set we looked for number den…
Wave-particle instabilities driven by departures from local thermodynamic equilibrium have been conjectured to play a role in governing solar wind dynamics. We calculate the statistical variation of linear stability over a large subset of Helios I and II fast solar wind observations using a numerical evaluation of the Nyquist stability criterion, accounting for multiple sources of free energy associated with protons and helium including temperature anisotropies and relative drifts. We find that 88\% of the surveyed intervals are linearly unstable. The median growth rate of the unstable modes i…
Solar Orbiter will observe the Sun and the inner heliosphere to study the connections between solar activity, coronal structure, and the origin of the solar wind. The plasma instruments on board Solar Orbiter will determine the three-dimensional velocity distribution functions of the plasma ions and electrons with high time resolution. The analysis of these distributions will determine the plasma bulk parameters, such as density, velocity, and temperature. This paper examines the effects of short-time-scale plasma variations on particle measurements and the estimated bulk parameters of the pla…
We investigate the solar wind energy flux in the inner heliosphere using 12-day observations around each perihelion of Encounter One (E01), Two (E02), Four (E04), and Five (E05) of Parker Solar Probe (PSP), respectively, with a minimum heliocentric distance of 27.8 solar radii ($R_\odot{}$). Energy flux was calculated based on electron parameters (density $n_e$, core electron temperature $T_{c}$, and suprathermal electron temperature $T_{h}$) obtained from the simplified analysis of the plasma quasi-thermal noise (QTN) spectrum measured by RFS/FIELDS and the bulk proton parameters (bulk speed …
Understanding the physical processes in the solar wind and corona which actively contribute to heating, acceleration, and dissipation is a primary objective of NASA's Parker Solar Probe (PSP) mission. Observations of coherent electromagnetic waves at ion scales suggests that linear cyclotron resonance and non-linear processes are dynamically relevant in the inner heliosphere. A wavelet-based statistical study of coherent waves in the first perihelion encounter of PSP demonstrates the presence of transverse electromagnetic waves at ion resonant scales which are observed in 30-50\% of radial fie…
Robustly identifying the solar sources of individual packets of solar wind measured in interplanetary space remains an open problem. We set out to see if this problem is easier to tackle using solar wind measurements closer to the Sun than 1 AU, where the mixing and dynamical interaction of different solar wind streams is reduced. Using measurements from the Helios mission, we examined how the proton core temperature anisotropy and cross helicity varied with distance. At 0.3 AU there are two clearly separated anisotropic and isotropic populations of solar wind, that are not distinguishable at …
We study how a high-speed solar wind stream embedded in a slow solar wind influences the spread of solar energetic protons in interplanetary space. To model the energetic protons, we used a recently developed particle transport code that computes particle distributions in the heliosphere by solving the focused transport equation in a stochastic manner. The particles are propagated in a solar wind containing a CIR, which was generated by the heliospheric magnetohydrodynamic model, EUHFORIA. We study four cases in which we assume a delta injection of 4 MeV protons spread uniformly over different…
We investigate the radial dependence of the spectral break separating the inertial from the dissipation range in power density spectra of interplanetary magnetic field fluctuations, between $0.42$ and $5.3$ AU, during radial alignments between MESSENGER and WIND for the inner heliosphere and between WIND and ULYSSES for the outer heliosphere. We found that the spectral break moves to higher and higher frequencies as the heliocentric distance decreases. The radial dependence of the corresponding wavenumber is of the kind $κ_b\sim R^{-1.08}$ in good agreement with that of the wavenumber derived …
Solar Orbiter strives to unveil how the Sun controls and shapes the heliosphere and fills it with energetic particle radiation. To this end, its Energetic Particle Detector (EPD) has now been in operation, providing excellent data, for just over a year. EPD measures suprathermal and energetic particles in the energy range from a few keV up to (near-) relativistic energies (few MeV for electrons and about 500 MeV/nuc for ions). We present an overview of the initial results from the first year of operations and we provide a first assessment of issues and limitations. During this first year of op…
Heliospheric modulation conditions were unusually quite during the last solar minimum activity between Solar Cycles 23/24. Fortunately, the PAMELA space-experiment measured six-month averaged Galactic positron spectra for the period July 2006 to December 2009, over an energy range of 80 MeV to 30 GeV, which is important for solar modulation. The highest level of Galactic positrons was observed at Earth during the July-December 2009 period. A well-established, comprehensive three-dimensional (3D) numerical model is applied to study the modulation of the observed positron spectra. This model had…
Solar Energetic Particles (SEPs), a major component of space weather, propagate through the interplanetary medium strongly guided by the Interplanetary Magnetic Field (IMF). In this work, we analyse the implications a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP release sites to the Earth. We simulate proton propagation by integrating fully 3-D trajectories near an analytically defined flat current sheet, collecting comprehensive statistics into histograms, fluence maps and virtual observer time profiles within an energy range of 1--800 MeV. We show that protons exp…
We introduce a new solar energetic particle (SEP) transport code that aims at studying the effects of different solar wind configurations on SEP events. We focus on the influence of varying solar wind velocities on the energy changes of SEPs, and study how a non-Parker background solar wind can trap particles temporarily at small heliocentric radial distances (r<1.5 AU). Our model computes particle distributions by solving the focused transport equation (FTE) in a stochastic manner by propagating particles in a solar wind generated by the heliospheric MHD model EUHFORIA. We solve the FTE, incl…
We perform a validation study of the latest version of the Alfvén Wave Solar atmosphere Model (AWSoM) within the Space Weather Modeling Framework (SWMF). To do so, we compare the simulation results of the model with a comprehensive suite of observations for Carrington rotations representative of the solar minimum conditions extending from the solar corona to the heliosphere up to the Earth. In the low corona ($r < 1.25$ \Rs), we compare with EUV images from both STEREO-A/EUVI and SDO/AIA and to three-dimensional (3-D) tomographic reconstructions of the electron temperature and density based on…
Parker Solar Probe (PSP), NASA's latest and closest mission to the Sun, is on a journey to investigate fundamental enigmas of the inner heliosphere. This paper reports initial observations made by the Solar Probe Analyzer for Ions (SPAN-I), one of the instruments in the Solar Wind Electrons Alphas and Protons (SWEAP) instrument suite. We address the presence of secondary proton beams in concert with ion-scale waves observed by FIELDS, the electromagnetic fields instrument suite. We show two events from PSP's 2nd orbit that demonstrate signatures consistent with wave-particle interactions. We s…
Large solar proton events (SPEs) affect the solar-terrestrial space environment and become a very important aspect in space weather research. In this work, we statistically investigate 78 solar proton events of 1996-2011 and find that there exists a longitudinally asymmetric distribution of flare sources of the solar proton events observed near 1 AU, namely, with the same longitude separation between magnetic field line footpoint of observer and flare sources, the number of the solar proton events originating from sources located at eastern side of the nominal magnetic footpoint of observer is…
