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A critical component of particle acceleration in astrophysical shocks is the non-resonant (Bell) instability, where the streaming of cosmic rays (CRs) leads to the amplification of magnetic fields necessary to scatter particles. In this work we use kinetic particle-in-cells simulations to investigate the high-CR current regime, where the typical assumptions underlying the Bell instability break down. Despite being more strongly driven, significantly less magnetic field amplification is observed compared to low-current cases, an effect due to the anisotropic heating that occurs in this regime. We also find that electron-scale modes, despite being fastest growing, mostly lead to moderate electron heating and do not affect the late evolution or saturation of the instability.

It has been suggested that Centaurus A (Cen A) could make a contribution to the observed ultrahigh-energy cosmic-ray (UHECR) flux. We calculate the flux of astrophysical neutrinos produced by UHECRs accelerated in the jet of Cen A, a close-by jetted active galactic nucleus. We use a bottom-up approach, in which we follow the energization of protons and heavier elements in a magnetohydrodynamic simulation of a relativistic jet with proper parameters of Cen A, also accounting for attenuation losses based on the observed photon fields. We compare the expected neutrino flux with the sensitivity of current and planned neutrino detectors. We find that the detection of $\sim 10^{17}$-$10^{18}$ eV neutrinos from Cen A would require ultimate neutrino detectors that reach a point source sensitivity of $\sim {\rm a~few}\times10^{-13}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$. Successful detection, though challenging, would be useful in constraining the Cen A contribution to the UHECRs., Comment: 5 pages, 3 figures, submitted to PRD

We present the first assessment, using hybrid PIC simulations, of the role of non-linear Landau damping in the process of self-generated scattering in a high $\beta$ plasma, conditions appropriate for CR scattering in the halo of the Galaxy. This damping process manifests itself in the form of heating of the background plasma and reduction of the drift speed of CRs that yet remains super-Alfvenic. We also show that the damping leads to an inverse cascade process, consisting of producing non-resonant large scale modes, a novel result with many potential phenomenological implications.

We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel non-relativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds $v_{\rm sh}\approx 0.067-0.267\,c$, Alfv\'{e}n Mach numbers $\mathcal{M}_{\rm A} = 5-40$, sonic Mach numbers $\mathcal{M}_{\rm s} = 5-160$, as well as the proton-to-electron mass ratios $m_{\rm i}/m_{\rm e}=16-1836$. We find that high Alfv\'{e}n Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is $\lesssim 0.5\%$ for electrons and $\approx 1\%$ for protons, and the corresponding energy efficiencies are $\lesssim 2\%$ and $\approx 10\%$, respectively. The extent of the nonthermal tail is sensitive to the Alfv\'{e}n Mach number; when $\mathcal{M}_{\rm A}\lesssim 10$, the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfv\'{e}n Mach number is large enough. We provide simulation-based parametrizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around $p_{\rm i,e}/m_{\rm i}v_{\rm sh} \approx 3\sqrt{m_{\rm i,e}/m_{\rm i}}$), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation., Comment: 19 pages, 11 figures, 1 table; Submitted to ApJ; Comments welcome!

The end of supernova remnant (SNR) evolution is characterized by a so-called "radiative" stage, in which efficient cooling of the hot bubble inside the forward shock slows expansion, leading to eventual shock breakup. Understanding SNR evolution at this stage is vital for predicting feedback in galaxies, since SNRs are expected to deposit their energy and momentum into the interstellar medium at the ends of their lives. A key prediction of SNR evolutionary models is the formation at the onset of the radiative stage of a cold, dense shell behind the forward shock. However, searches for these shells via their neutral hydrogen emission have had limited success. We instead introduce an independent observational signal of shell formation arising from the interaction between nonthermal particles accelerated by the SNR forward shock (cosmic rays) and the dense shell. Using a semi-analytic model of particle acceleration based on state-of-the-art simulations coupled with a high-resolution hydrodynamic model of SNR evolution, we predict the nonthermal emission that arises from this interaction. We demonstrate that the onset of the radiative stage leads to nonthermal signatures from radio to $\gamma$-rays, including radio and $\gamma$-ray brightening by nearly two orders of magnitude. Such a signature may be detectable with current instruments, and will be resolvable with the next generation of gamma-ray telescopes (namely, the Cherenkov Telescope Array)., Comment: 13 pages, 6 figures, accepted to ApJ

It has been long believed that oblique and quasi-perpendicular configurations in supernova remnants (SNRs) were inefficient at injecting ions into diffusive shock acceleration (DSA), and that the highest energy Galactic cosmic rays (CRs) must come from parallel or quasi-parallel shocks. However, recent 3D kinetic simulations have shown that high-obliquity shocks can successfully energize particles and produce amplified magnetic fields in the upstream. We aim to investigate the maximum energy particles it is possible to produce in oblique and quasi-perpendicular shocks and whether they are capable of triggering the non-resonant hybrid instability (NRHI). We present a novel setup for hybrid simulations of non-relativistic shocks that use a "faux shock" boundary condition instead of a real shock to significantly reduce the computational cost and that can be run for long enough to study the late-time behaviors of these systems. Our results show that it may be possible for oblique and quasi-perpendicular shocks to transition from early periods of shock drift acceleration (SDA) into DSA at later times, giving particles a brief period of rapid acceleration followed by a long-duration, self-sustaining period of slower energy growth. Furthermore, we find evidence that the NRHI is triggered in the upstream at late times. Oblique and quasi-perpendicular shocks may be an important contributor to high energy CRs, potentially even responsible for the knee in the CR energy spectrum.

Collisionless shocks tend to send charged particles into the upstream, driving electric currents through the plasma. Using kinetic particle-in-cell simulations, we investigate how the background thermal plasma neutralizes such currents in the upstream of quasi-parallel non-relativistic electron-proton shocks. We observe distinct processes in different regions: the far upstream, the shock precursor, and the shock foot. In the far upstream, the current is carried by nonthermal protons, which drive electrostatic modes and produce supra-thermal electrons that move towards upstream infinity. Closer to the shock (in the precursor), both the current density and the momentum flux of the beam increase, which leads to electromagnetic streaming instabilities that contribute to the thermalization of supra-thermal electrons. At the shock foot, these electrons are exposed to shock-reflected protons, resulting in a two-stream type instability. We analyze these processes and the resulting heating through particle tracking and controlled simulations. In particular, we show that the instability at the shock foot can make the effective thermal speed of electrons comparable to the drift speed of the reflected protons. These findings are important for understanding both the magnetic field amplification and the processes that may lead to the injection of supra-thermal electrons into diffusive shock acceleration., Comment: 12 pages, 10 figures, 1 table; Submitted to ApJ; Comments welcome!

Observations from past missions such as RXTE and Beppo-SAX suggested the presence of inverse Compton (IC) scattering at hard X-ray energies within the intracluster medium of some massive galaxy clusters. In subsequent years, observations by, e.g., Suzaku, and now NuSTAR, have not been able to confirm these detections. We report on NuSTAR hard X-ray searches for IC emission in two massive galaxy clusters, Abell 665 and Abell 2146. To constrain the global IC flux in these two clusters, we fit global NuSTAR spectra with three models: single (1T) and two-temperature (2T) models, and a 1T plus power law component (T$+$IC). The temperature components are meant to characterize the thermal ICM emission, while the power law represents the IC emission. We find that the 3-30 keV Abell 665 and 3-20 keV Abell 2146 spectra are best described by thermal emission alone, with average global temperatures of $kT = (9.15\pm 0.1)$ keV for Abell 665 and $kT = (8.29\pm 0.1)$ keV for Abell 2146. We constrain the IC flux to $F_{\rm NT} < 0.60 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ and $F_{\rm NT} < 0.85 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ (20-80 keV) for Abell 665 and Abell 2146, respectively both at the 90% confidence level. When we couple the IC flux limits with 1.4 GHz diffuse radio data from the VLA, we set lower limits on the average magnetic field strengths of $>$0.14 $\mu$G and $>$0.011 $\mu$G for Abell 665 and Abell 2146, respectively., Comment: 19 pages, 15 figures

Collisionless plasma shocks are a common feature of many space and astrophysical systems and are sources of high-energy particles and non-thermal emission, channeling as much as 20\% of the shock's energy into non-thermal particles. The generation and acceleration of these non-thermal particles have been extensively studied, however, how these particles feed back on the shock hydrodynamics has not been fully treated. This work presents the results of self-consistent hybrid particle-in-cell simulations that show the effect of self-generated non-thermal particle populations on the nature of collisionless, quasi-parallel shocks. They contribute to a significant heat flux density upstream of the shock. Non-thermal particles downstream of the shock leak into the upstream region, taking energy away from the shock. This increases the compression ratio, slows the shock down, and flattens the non-thermal population's spectral index for lower Mach number shocks. We incorporate this into a revised theory for the Rankine-Hugoniot jump conditions that include this effect and it shows excellent agreement with simulations. The results have the potential to explain discrepancies between predictions and observations in a wide range of systems, such as inaccuracies of predictions of arrival times of coronal mass ejections and the conflicting radio and x-ray observations of intracluster shocks. These effects will likely need to be included in fluid modeling to accurately predict shock evolution., Comment: 7 pages, 3 figures, a lot of appendix

These notes present the fundamentals of Fermi acceleration at shocks, with a special attention to the role that supernova remnants have in producing Galactic cosmic rays. Then, the recent discoveries in the theory of diffusive shock acceleration (DSA) that stem from first-principle kinetic plasma simulations are discussed. When ion acceleration is efficient, the back-reaction of non-thermal particles and self-generated magnetic fields becomes prominent and leads to both enhanced shock compression and particle spectra significantly softer than those predicted by the standard test-particle DSA theory. These results are discussed in the context of the non-thermal phenomenology of astrophysical shocks, with a special focus on the remnant of SN1006., Comment: 39 pages, 13 figures. Published in "Foundations of Cosmic Ray Astrophysics", Proceedings of the International School of Physics "Enrico Fermi", Course 208, Varenna, 24-29 June 2022, edited by F. Aharonian, E. Amato, and P. Blasi

HelioSwarm (HS) is a NASA Medium-Class Explorer mission of the Heliophysics Division designed to explore the dynamic three-dimensional mechanisms controlling the physics of plasma turbulence, a ubiquitous process occurring in the heliosphere and in plasmas throughout the universe. This will be accomplished by making simultaneous measurements at nine spacecraft with separations spanning magnetohydrodynamic and sub-ion spatial scales in a variety of near-Earth plasmas. In this paper, we describe the scientific background for the HS investigation, the mission goals and objectives, the observatory reference trajectory and instrumentation implementation before the start of Phase B. Through multipoint, multiscale measurements, HS promises to reveal how energy is transferred across scales and boundaries in plasmas throughout the universe., Comment: Submitted to Space Science Reviews, 60 pages, 15 figures, 2 videos

Understanding the conditions conducive to particle acceleration at collisionless, non-relativistic shocks is important for the origin of cosmic rays. We use hybrid (kinetic ions -- fluid electrons) kinetic simulations to investigate particle acceleration and magnetic field amplification at non-relativistic, weakly magnetized, quasi-perpendicular shocks. So far, no self-consistent kinetic simulation has reported non-thermal tails at quasi-perpendicular shocks. Unlike 2D simulations, 3D runs show that protons develop a non-thermal tail spontaneously (i.e., from the thermal bath and without pre-existing magnetic turbulence). They are rapidly accelerated via shock drift acceleration up to a maximum energy determined by their escape upstream. We discuss the implications of our results for the phenomenology of heliospheric shocks, supernova remnants and radio supernovae., Comment: 6 pages, 4 figures. Matches version published by PRL, Editors' Suggestion

Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions which reflect multiple times off the shock front through shock-drift acceleration, and how to distinguish these different reflected populations in phase space using the FPC technique. We further extend our analysis to simulations of three-dimensional shocks undergoing more complicated dynamics, such as shock ripple, to demonstrate the ability to recover the phase space signatures of this energization process in a more general system. This work thus extends previous applications of the FPC technique to more realistic collisionless shock environments, providing stronger evidence of the technique's utility for simulation, laboratory, and spacecraft analysis., Comment: 9 pages, 5 figures

In August of 2021, Fermi-LAT, H.E.S.S., and MAGIC detected GeV and TeV $\gamma$-ray emission from an outburst of recurrent nova RS Ophiuchi. This detection represents the first very high energy $\gamma$-rays observed from a nova, and opens a new window to study particle acceleration. Both H.E.S.S. and MAGIC described the observed $\gamma$-rays as arising from a single, external shock. In this paper, we perform detailed, multi-zone modeling of RS Ophiuchi's 2021 outburst including a self-consistent prescription for particle acceleration and magnetic field amplification. We demonstrate that, contrary to previous work, a single shock cannot simultaneously explain RS Ophiuchi's GeV and TeV emission, particularly the spectral shape and distinct light curve peaks. Instead, we put forward a model involving multiple shocks that reproduces the observed $\gamma$-ray spectrum and temporal evolution. The simultaneous appearance of multiple distinct velocity components in the nova optical spectrum over the first several days of the outburst supports the presence of distinct shocks, which may arise either from the strong latitudinal dependence of the density of the external circumbinary medium (e.g., in the binary equatorial plane versus the poles) or due to internal collisions within the white dwarf ejecta (as powers the $\gamma$-ray emission in classical novae)., Comment: 19 pages, 10 figures, published in ApJ

The nonresonant streaming instability (Bell instability) plays a pivotal role in the acceleration and confinement of cosmic rays (CRs); yet, the exact mechanism responsible for its saturation and the magnitude of the final amplified magnetic field have not been assessed from first-principles. Using a survey of hybrid simulations (with kinetic ions and fluid electrons), we study the evolution of the Bell instability as a function of the parameters of the CR population. We find that, at saturation, the magnetic pressure in the amplified field is comparable with the initial CR anisotropic pressure, rather than with the CR energy flux as previously argued. These results provide a predictive prescription for the total magnetic field amplification expected in the many astrophysical environments where the Bell instability is important., Comment: 12 pages, 8 figures. New final version, accepted for publication in ApJ

The origin of cosmic rays is a pivotal open issue of high-energy astrophysics. Supernova remnants are strong candidates to be the Galactic factory of cosmic rays, their blast waves being powerful particle accelerators. However, supernova remnants can power the observed flux of cosmic rays only if they transfer a significant fraction of their kinetic energy to the accelerated particles, but conclusive evidence for such efficient acceleration is still lacking. In this scenario, the shock energy channeled to cosmic rays should induce a higher post-shock density than that predicted by standard shock conditions. Here we show this effect, and probe its dependence on the orientation of the ambient magnetic field, by analyzing deep X-ray observations of the Galactic remnant of SN 1006. By comparing our results with state-of-the-art models, we conclude that SN 1006 is an efficient source of cosmic rays and obtain an observational support for the quasi-parallel acceleration mechanism., Comment: Published in Nature Communications. The published version of the paper, including supplementary material, is freely available online here https://doi.org/10.1038/s41467-022-32781-4 or as a PDF here https://www.nature.com/articles/s41467-022-32781-4.pdf

We present a bottom-up calculation of the flux of ultra-high energy cosmic rays (UHECRs) and high-energy neutrinos produced by powerful jets of active galactic nuclei (AGNs). By propagating test particles in 3D relativistic magnetohydrodynamic jet simulations, including a Monte Carlo treatment of sub-grid pitch-angle scattering and attenuation losses due to realistic photon fields, we study the spectrum and composition of the accelerated UHECRs and estimate the amount of neutrinos produced in such sources. We find that UHECRs may not be significantly affected by photodisintegration in AGN jets where the espresso mechanism efficiently accelerates particles, consistent with Auger's results that favor a heavy composition at the highest energies. Moreover, we present estimates and upper bounds for the flux of high-energy neutrinos expected from AGN jets. In particular, we find that: i) source neutrinos may account for a sizable fraction, or even dominate, the expected flux of cosmogenic neutrinos; ii) neutrinos from the beta-decay of secondary neutrons produced in nucleus photodisintegration end up in the TeV-PeV band observed by IceCube, but can hardly account for the observed flux; iii) UHECRs accelerated via the espresso mechanism lead to nearly isotropic neutrino emission, which suggests that nearby radio galaxies may be more promising as potential sources. We discuss our results in the light of multimessenger astronomy and current/future neutrino experiments., Comment: 16 pages, 7 figures, ApJ, Figure 5 and 6 amended

Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While the standard prediction for strong shocks is that the spectrum of accelerated particles is universal, $f(p)\propto p^{-4}$, numerous phenomena affect this simple conclusion. In general, the non-linear dynamical reaction of accelerated particles leads to a concave spectrum, steeper than $p^{-4}$ at momenta below a few tens of GeV/c and harder than the standard prediction at high energies. However, the non-linear effects become important in the presence of magnetic field amplification, which in turn leads to higher values of the maximum momentum $p_{max}$. It was recently discovered that the self-generated perturbations that enhance particle scattering, when advected downstream, move in the same direction as the background plasma, so that the effective compression factor at the shock decreases and the spectrum becomes steeper. We investigate the implications of the excitation of the non-resonant streaming instability on these spectral deformations, the dependence of the spectral steepening on the shock velocity and the role played by the injection momentum., Comment: 11 pages, 6 figures, accepted for publication in ApJ

The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CR) close to supernova remnants. Despite its importance, the exact mechanism responsible for the saturation of the instability has not been determined, and there is no first-principle prediction for the amplitude of the saturated magnetic field. Using a survey of self-consistent hybrid simulations (with kinetic ions and fluid electrons), we study the non-linear evolution of the Bell instability as a function of the parameters of the CR population. We find that saturation is achieved when the magnetic pressure in the amplified field is comparable to the initial CR momentum flux., Comment: 37th International Cosmic Ray Conference (ICRC2021), held 12-23 July, 2021 in Berlin, Germany - Online at $\href{https://pos.sissa.it/395/}{\rm this \; https \; URL}$, 8 pages, 3 figures

Cosmic rays are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated magnetic fluctuations induce particle diffusion in extended regions around the source, so that cosmic rays build up a large pressure gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid particle-in-cell simulations, we show that such a pressure gradient excavates a cavity around the source and leads to the formation of a cosmic-ray dominated bubble, inside which diffusivity is strongly suppressed. Based on the trends extracted from self-consistent simulations, we estimate that, in the absence of severe damping of the self-generated magnetic fields, the bubble should keep expanding until pressure balance with the surrounding medium is reached, corresponding to a radius of $\sim 10-50$ pc. The implications of the formation of these regions of low diffusivity for sources of Galactic cosmic rays are discussed. Special care is devoted to estimating the self-generated diffusion coefficient and the grammage that cosmic rays might accumulate in the bubbles before moving into the interstellar medium. Based on the results of 3D simulations, general considerations on the morphology of the $\gamma$-ray and synchrotron emission from these extended regions also are outlined., Comment: 12 pages, accepted for publication in MNRAS

The recent discoveries in the theory of diffusive shock acceleration (DSA) that stem from first-principle kinetic plasma simulations are discussed. When ion acceleration is efficient, the back-reaction of non-thermal particles and self-generated magnetic fields becomes prominent and leads to both enhanced shock compression and particle spectra significantly softer than those predicted by the standard test-particle DSA theory. These results are discussed in the context of the non-thermal phenomenology of astrophysical shocks, with a special focus on the remnant of SN1006., Comment: 8 pages, 2 figures, Proceedings of 37th International Cosmic Ray Conference (ICRC2021) ; https://pos.sissa.it/395/482

Using fully-kinetic plasma simulations, we study the non-resonant (Bell) streaming instability driven by energetic leptons. We identify the necessary conditions to drive it and the differences from the standard proton-driven case in both linear and saturated stages. A simple analytic theory is presented to explain simulations. Our findings are crucial for understanding the phenomenology of astrophysical environments where only electrons may be accelerated (e.g., oblique shocks) or where relativistic pairs are produced (e.g., around pulsar wind nebulae)., Comment: 8 pages, 4 figures, Proceedings of Science: 37th International Cosmic Ray Conference (ICRC 2021). Comments welcome!

Shocks waves are a ubiquitous feature of many astrophysical plasma systems, and an important process for energy dissipation and transfer. The physics of these shock waves are frequently treated/modeled as a collisional, fluid MHD discontinuity, despite the fact that many shocks occur in the collisionless regime. In light of this, using fully kinetic, 3D simulations of non-relativistic, parallel propagating collisionless shocks comprised of electron-positron plasma, we detail the deviation of collisionless shocks form MHD predictions for varying magnetization/Alfv\'enic Mach numbers, with particular focus on systems with Alf\'enic Mach numbers much smaller than sonic Mach numbers. We show that the shock compression ratio decreases for sufficiently large upstream magnetic fields, in agreement with the predictions of Bret & Narayan (2018). Additionally, we examine the role of magnetic field strength on the shock front width. This work reinforces a growing body of work that suggest that modeling many astrophysical systems with only a fluid plasma description omits potentially important physics., Comment: 7 pages, 5 figures + a diagram, submitted to MNRAS

In Mbarek & Caprioli (2019), we laid the groundwork for studying the espresso paradigm Caprioli (2015), a reacceleration mechanism to boost galactic CRs to UHECR levels. Our bottom-up approach uses realistic 3D MHD simulations of relativistic AGN jets and accounts for all of the crucial ingredients of a universal acceleration theory: injection, acceleration, and escape in realistic environments. Our results are consistent with the main features of UHECR spectra, i.e., power-law slopes, chemical composition, and anisotropy. In Mbarek & Caprioli (2021), we refine our model by including sub-grid particle scattering to model small-scale magnetic turbulence that cannot be resolved by MHD simulations, constraining for the first time one crucial but hard-to-model ingredient, and allowing us to establish the relative importance of espresso and stochastic shear acceleration in relativistic jets. Our framework also enables us to analyze high-energy neutrinos produced from our accelerated UHECRs considering the effects of external photon fields, and to incorporate nucleus photodisintegration. The spectra we obtain are consistent with the picture drawn by observations with Auger, Telescope Array, and IceCube observatory., Comment: 8 pages, 4 figures, Proceedings of 37th International Cosmic Ray Conference (ICRC2021)

We derive basic scaling equations for relativistic magnetic reconnection in the general case of asymmetric inflow conditions and obtain predictions for the outflow Lorentz factor and the reconnection rate. Kinetic Particle-in-Cell simulations show that the outflow speeds as well as the nonthermal spectral index are constrained by the inflowing plasma with the weaker magnetic energy per particle, in agreement with the scaling predictions. These results are significant for understanding non-thermal emission from reconnection in magnetically-dominated, astrophysical systems, many of which may be asymmetric in nature. The results provide a quantitative approach for including asymmetry on reconnection in the relativistic regime., Comment: 6 pages, 4 Figures, published in PRL, Supplemental Material content included for clarity

Galactic cosmic rays (CRs) are accelerated by astrophysical shocks, primarily supernova remnants (SNRs), via diffusive shock acceleration (DSA), an efficient mechanism that predicts power-law energy distributions of CRs. However, observations of both nonthermal SNR emission and Galactic CRs imply CR spectra that are steeper than the standard DSA prediction, $\propto E^{-2}$. Recent kinetic hybrid simulations suggest that such steep spectra may be the result of a "postcursor", or drift of CRs and magnetic structures with respect to the thermal plasma behind the shock. Using a semi-analytic model of non-linear DSA, we generalize this result to a wide range of astrophysical shocks. By accounting for the presence of a postcursor, we produce CR energy distributions that are substantially steeper than $E^{-2}$ and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs ($\propto E^{-2.2}$) and the very steep spectra of young radio supernovae ($\propto E^{-3}$)., Comment: 16 pages, 5 figures, proceedings of the 37th International Cosmic Ray Conference (ICRC 2021). arXiv admin note: substantial text overlap with arXiv:2107.08520

Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than $E^{-2}$, the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of non-linear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than $E^{-2}$ and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic supernova remnants ($\propto E^{-2.2}$) and the very steep spectra of young radio supernovae ($\propto E^{-3}$)., Comment: 15 pages, 9 figures, accepted to ApJ

A strong super-Alfv\'{e}nic drift of energetic particles (or cosmic rays, CRs) in a magnetized plasma can amplify the magnetic field significantly through non-resonant streaming instability (NRSI). While the traditional analysis is done for an ion current, here we use kinetic particle-in-cell simulations to study how the NRSI behaves when it is driven by electrons or by a mixture of electrons and positrons. In particular, we characterize growth rate, spectrum, and helicity of the unstable modes, as well the level of magnetic field at saturation. Our results are potentially relevant for several space/astrophysical environments (e.g, electron strahl in the solar wind, at oblique non-relativistic shocks, around pulsar wind nebulae) and also in laboratory experiments., Comment: 16 pages, 9 figures, 1 table; Submitted to ApJ; Comments welcome!

In the espresso scenario, ultra-high-energy (UHE) cosmic rays (CRs) are produced via a one-shot reacceleration of galactic-like CRs in the relativistic jets of active galactic nuclei, independently of the scattering rate dictated by magnetic fluctuations. In Mbarek & Caprioli (2019), we traced test-particle CRs in high-resolution magnetohyrodynamic (MHD) jet simulations and found that the associated spectral slope, chemical composition, and anisotropy are consistent with UHECR phenomenology. In this work, we extend such an analysis by including sub-grid pitch-angle scattering to model small-scale magnetic turbulence that cannot be resolved by MHD simulations. We find that a large scattering rate unlocks stochastic acceleration and fosters the energization of lower-energy CRs, which eventually leads to harder UHECR spectra. Yet, the particles that achieve the highest energies (up to the Hillas limit) are invariably produced by espresso acceleration and their spectrum is independent of the assumed sub-grid scattering rate., Comment: 12 pages, 9 figures; Accepted to ApJ

Observations of the $\gamma$-ray emission around star clusters, isolated supernova remnants, and pulsar wind nebulae indicate that the cosmic-ray (CR) diffusion coefficient near acceleration sites can be suppressed by a large factor compared to the Galaxy average. We explore the effects of such local suppression of CR diffusion on galaxy evolution using simulations of isolated disk galaxies with regular and high gas fractions. Our results show that while CR propagation with constant diffusivity can make gaseous disks more stable by increasing the midplane pressure, large-scale CR pressure gradients cannot prevent local fragmentation when the disk is unstable. In contrast, when CR diffusivity is suppressed in star-forming regions, the accumulation of CRs in these regions results in strong local pressure gradients that prevent the formation of massive gaseous clumps. As a result, the distribution of dense gas and star formation changes qualitatively: a globally unstable gaseous disk does not violently fragment into massive star-forming clumps but maintains a regular grand-design spiral structure. This effect regulates star formation and disk structure and is qualitatively different from and complementary to the global role of CRs in vertical hydrostatic support of the gaseous disk and in driving galactic winds., Comment: 18 pages + appendix, 15 figures; accepted for publication in ApJ

Using the field-particle correlation technique, we examine the particle energization in a 1D-2V continuum Vlasov--Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field-particle correlation technique with the high fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons due to the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov-Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field-particle correlation technique to spacecraft measurements of collisionless shocks., Comment: 49 pages, 20 figures

Collisionless shocks play an important role in space and astrophysical plasmas by irreversibly converting the energy of the incoming supersonic plasma flows into other forms, including plasma heat, particle acceleration, and electromagnetic field energy. Here we present the application of the field-particle correlation technique to an idealized perpendicular magnetized collisionless shock to understand the transfer of energy from the incoming flow into ion and electron energy through the structure of the shock. The connection between a Lagrangian perspective following particle trajectories, and an Eulerian perspective observing the net energization of the distribution of particles, illuminates the energy transfer mechanisms. Using the field-particle correlation analysis, we identify the velocity-space signature of shock-drift acceleration of the ions in the shock foot, as well as the velocity-space signature of adiabatic electron heating through the shock ramp., Comment: During the review process, it was requested that 2011.13841 be merged with 2011.13829. I have replaced 2011.13829 with the new merged paper and would thus like to withdraw this original paper

Cosmic rays (CRs) leave their sources mainly along the local magnetic field; in doing so they excite both resonant and nonresonant modes through streaming instabilities. The excitation of these modes leads to enhanced scattering and in turn to a large pressure gradient that causes the formation of bubbles of gas, CRs, and self-generated magnetic fields expanding into the interstellar medium. By means of hybrid Particle-In-Cell simulations, we show that, by exciting the nonresonant instability, CRs excavate a cavity around their source where the diffusivity is strongly suppressed. This finding invalidates the so far largely adopted flux-tube assumption, under which particles move along magnetic lines even in the nonlinear regime. This phenomenon is general and is expected to occur around any sufficiently powerful CR source in the Galaxy. Our results might provide a physical explanation of the numerous claims of suppressed CR diffusion around Galactic sources such as supernova remnants, pulsar wind nebulae, and stellar clusters., Comment: 7 pages, 3 figures, Accepted for publication on The Astrophysical Journal Letters

Diffusive shock acceleration is a prominent mechanism for producing energetic particles in space and in astrophysical systems. Such energetic particles have long been predicted to affect the hydrodynamic structure of the shock, in turn leading to CR spectra flatter than the test-particle prediction. However, in this work along with a companion paper, C. C. Haggerty and D. Caprioli, 2020, arXiv:2008.12308 [astro-ph.HE], we use self-consistent hybrid (kinetic ions-fluid electrons) simulations to show for the first time how CR-modified shocks actually produce steeper spectra. The steepening is driven by the enhanced advection of CRs embedded in magnetic turbulence downstream of the shock, in what we call the "postcursor". These results are consistent with multi-wavelength observations of supernovae and supernova remnants and have significant phenomenological implications for space/astrophysical shocks in general., Comment: 10 pages, 5 figures, submitted to ApJ, Paper II of a series of 2 (Paper I: Kinetic Simulations of Cosmic-Ray-Modified Shocks II: Hydrodynamics, arXiv:2008.12308 [astro-ph], arXiv:2008.12308)

Collisionless plasma shocks are efficient sources of non-thermal particle acceleration in space and astrophysical systems. We use hybrid (kinetic ions -- fluid electrons) simulations to examine the non-linear feedback of the self-generated energetic particles (cosmic rays, CRs) on the shock hydrodynamics. When CR acceleration is efficient, we find evidence of both an upstream precursor, where the inflowing plasma is compressed and heated, and a downstream postcursor, where the energy flux in CRs and amplified magnetic fields play a dynamical role. For the first time, we assess how non-linear magnetic fluctuations in the postcursor preferentially travel away from the shock at roughly the local Alfv\'en speed with respect to the downstream plasma. The drift of both magnetic and CR energy with respect to the thermal plasma substantially increases the shock compression ratio with respect to the standard prediction, in particular exceeding 4 for strong shocks. Such modifications also have implications for the spectrum of the particles accelerated via diffusive shock acceleration, a significant result detailed in a companion paper, Caprioli, Haggerty & Blasi 2020, arXiv:2009.00007 [astro-ph.HE]., Comment: Paper 1 of 2, 15 pages, 11 figures, companion paper to arXiv:2009.00007 [astro-ph.HE], arXiv:2009.00007

We present the results of a detailed investigation into the physical conditions in interstellar material interacting with the supernova remnant IC 443. Our analysis is based on a comprehensive examination of high-resolution far-ultraviolet spectra obtained with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope of two stars behind IC 443. One of our targets (HD 43582) probes gas along the entire line of sight through the supernova remnant, while the other (HD 254755) samples material located ahead of the primary supernova shock front. We identify low velocity quiescent gas in both directions and find that the densities and temperatures in these components are typical of diffuse atomic and molecular clouds. Numerous high velocity components are observed in the absorption profiles of neutral and singly-ionized atomic species toward HD 43582. These components exhibit a combination of greatly enhanced thermal pressures and significantly reduced dust-grain depletions. We interpret this material as cooling gas in a recombination zone far downstream from shocks driven into neutral gas clumps. The pressures derived for a group of ionized gas components at high positive velocity toward HD 43582 are lower than those of the other shocked components, pointing to pressure inhomogeneities across the remnant. A strong very high velocity component near -620 km/s is seen in the absorption profiles of highly-ionized species toward HD 43582. The velocity of this material is consistent with the range of shock velocities implied by observations of soft thermal X-ray emission from IC 443. Moderately high-velocity gas toward HD 254755 may represent shocked material from a separate foreground supernova remnant., Comment: 88 pages, 27 figures, accepted for publication in ApJ

Analysis of model fit results of 15,210 electron velocity distribution functions (VDFs), observed within $\pm$2 hours of 52 interplanetary (IP) shocks by the Wind spacecraft near 1 AU, is presented as the third and final part on electron VDFs near IP shocks. The core electrons and protons dominate in the magnitude and change in the partial-to-total thermal pressure ratio, with the core electrons often gaining as much or more than the protons. Only a moderate positive correlation is observed between the electron temperature and the kinetic energy change across the shock, while weaker, if any, correlations were found with any other macroscopic shock parameter. No VDF parameter correlated with the shock normal angle. The electron VDF evolves from a narrowly peaked core with flaring suprathermal tails in the upstream to either a slightly hotter core with steeper tails or much hotter flattop core with even steeper tails downstream of the weaker and strongest shocks, respectively. Both quasi-static and fluctuating fields are examined as possible mechanisms modifying the VDF but neither is sufficient alone. For instance, flattop VDFs can be generated by nonlinear ion acoustic wave stochastic acceleration (i.e., inelastic collisions) while other work suggested they result from the combination of quasi-static and fluctuating fields. This three-part study shows that not only are these systems not thermodynamic in nature, even kinetic models may require modification to include things like inelastic collision operators to properly model electron VDF evolution across shocks or in the solar wind., Comment: 30 pages, 10 figures, 3 tables, to be submitted to Astrophys. J

We investigate the possibility of secondary production as the source of cosmic ray (CR) positrons, taking into account observed electron and antiproton spectra and allowing that the reported steepening in the AMS-02 positron spectrum may be due to radiative losses. Using a simple argument based on the antiproton spectrum, we show that positrons cannot be purely secondary. Namely, the antiproton to positron ratio requires that positrons be uncooled up to a few hundred GeV. This requirement implies that CR protons escape from the Galaxy too quickly to reproduce the observed antiproton flux. We further show that this result rules out also more complex secondary production scenarios such as reacceleration and the Nested Leaky Box. Thus, we conclude that while antiprotons can be produced exclusively in secondary interactions, a primary source of CR positrons -- be it dark matter or pulsars -- is required to explain their spectrum., Comment: 7 pages, 2 figures, accepted for publication in PRD

A statistical analysis of 15,210 electron velocity distribution function (VDF) fits, observed within $\pm$2 hours of 52 interplanetary (IP) shocks by the $Wind$ spacecraft near 1 AU, is presented. This is the second in a three-part series on electron VDFs near IP shocks. The electron velocity moment statistics for the dense, low energy core, tenuous, hot halo, and field-aligned beam/strahl are a statistically significant list of values illustrated with both histograms and tabular lists for reference and baselines in future work. The beam/strahl fit results in the upstream are currently the closest thing to a proper parameterization of the beam/strahl electron velocity moments in the ambient solar wind. This work will also serve as a 1 AU baseline and reference for missions like $Parker \ Solar \ Probe$ and $Solar \ Orbiter$. The median density, temperature, beta, and temperature anisotropy values for the core(halo)[beam/strahl] components, with subscripts $ec$($eh$)[$eb$], of all fit results respectively are $n{\scriptstyle_{ec(h)[b]}}$ $\sim$ 11.3(0.36)[0.17] $cm^{-3}$, $T{\scriptstyle_{ec(h)[b], tot}}$ $\sim$ 14.6(48.4)[40.2] $eV$, $\beta{\scriptstyle_{ec(h)[b], tot}}$ $\sim$ 0.93(0.11)[0.05], and $\mathcal{A}{\scriptstyle_{ec(h)[b]}}$ $\sim$ 0.98(1.03)[0.93]. The nuanced details of the fitting method and data product description were published in Paper I and the detailed analysis of the results will be shown in Paper III., Comment: 40 pages, 11 figures, 18 tables, to be submitted to Astrophys. J. Suppl

The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CRs) close to supernova remnants. Despite its importance, the exact mechanism responsible for the saturation of the instability has not been determined, and there is no first-principle prediction for the amplitude of the saturated magnetic field. Using a survey of self-consistent kinetic hybrid simulations (with kinetic ions and fluid electrons), we study the saturation of the non-resonant streaming instability as a function of the parameters of both the thermal background plasma and the CR population. The strength of the saturated magnetic field has important implications for both CR acceleration in supernova remnants and CR diffusion in the Galaxy., Comment: 36th International Cosmic Ray Conference (ICRC2019), held July 24th-August 1st, 2019 in Madison, WI, U.S.A. Online at https://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=358, id.483, 7 pages, 3 figures

Espresso is a novel acceleration model for Ultra-High-Energy Cosmic Rays (UHECRs), where lower-energy CRs produced in supernova remnants experience a one-shot reacceleration in the relativistic jets of powerful Active Galactic Nuclei (AGNs) to reach energies up to $10^{20}$ eV. To test the espresso framework, we follow UHECR acceleration bottom-up from injection to the highest energies by propagating 100,000 particles in realistic 3D magneto-hydrodynamic (MHD) simulations of ultra-relativistic jets. We find that simulations agree well with analytical expectations in terms of trajectories of individual particles. We also quantify that $\sim 10\%$ of CR seeds gain a factor of $\sim\Gamma^2$ in energy, where $\Gamma$ is the jet's effective Lorentz factor; moreover, about $0.1\%$ of the particles undergo two or more shots to achieve gains in excess of $\Gamma^2$. Particles are generally accelerated up to the jet's Hillas limit, indicating that the espresso mechanism should boost galactic CRs to UHECRs in typical AGN jets. Finally, we discuss how espresso acceleration in AGN jets is consistent with UHECR spectra and chemical composition, and also with the UHECR arrival directions measured by Auger and Telescope Array., Comment: 36th International Cosmic Ray Conference (ICRC2019), held July 24th-August 1st, 2019 in Madison, WI, U.S.A. Online at https://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=358, id.348

Using hybrid simulations (kinetic ions--fluid electrons), we test the linear theory predictions of the cosmic ray (CR) streaming instability. We consider two types of CR distribution functions: a "hot" distribution where CRs are represented by a drifting power law in momentum and an anisotropic "beam" of monochromatic particles. Additionally, for each CR distribution we scan over different CR densities to transition from triggering the resonant to the non-resonant (Bell) streaming instability. We determine the growth rates of these instabilities in simulations by fitting an exponential curve during the linear stage, and we show that they agree well with the theoretical predictions as a function of wave number agree. We also examine the magnetic helicity as a function of time and wave number, finding a general good agreement with the predictions, as well as some unexpected non-linear features to the instability development., Comment: 8 Pages, 3 figures. Accepted conference proceeding in Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect

We discuss the recent developments in the theory of diffusive shock acceleration (DSA) by using both first-principle kinetic plasma simulations and analytical theory based on the solution of the convection/diffusion equation. In particular, we show how simulations reveal that the spectra of accelerated particles are significantly steeper than the $E^{-2}$ predicted by the standard theory of DSA for strong shocks, in agreement with several observational pieces of evidence. We single out which standard assumptions of test-particle and non-linear DSA are violated in the presence of strong (self-generated) magnetic turbulence and put forward a novel theory in better agreement with the particle spectra inferred with multi-wavelength observations of young SN remnants, radio-supernovae, and Galactic cosmic rays., Comment: 8 pages, 2 figures, 36th International Cosmic Ray Conference (ICRC2019), held July 24th-August 1st, 2019 in Madison, WI, U.S.A

We present the first plasma simulations obtained with the code dHybridR, a hybrid particle-in-cell code with fluid electrons and both thermal and energetic ions that retain relativistic dynamics. dHybridR is constructed to study astrophysical and space-physics problems where a few energetic non-thermal particles (i.e., cosmic rays, CRs) affect the overall dynamics of a non-relativistic plasma, such as CR-driven instabilities, collisionless shocks, magnetic reconnection, turbulence, etc.In this method paper we provide some applications to linear (resonant/non-resonant CR streaming instability) and strongly non-linear (parallel shocks) problems that show the capabilities of the code. In particular, we provide the first self-consistent hybrid runs that show the acceleration of relativistic ions at non-relativistic shocks; CRs develop a power-law in momentum, which translates to a broken power law in energy that exhibits a steepening around the ion rest mass, as predicted by the theory of diffusive shock acceleration. We present examples of 2D dHybridR runs relevant for fast shocks in radio supernovae, whose evolution can be followed in real time, and 3D runs of low-Mach-number heliospheric shocks, which can be compared with in-situ spacecraft observations., Comment: 14 pages, 12 figures, 1 table

We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfv\'{e}nic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and undergo multiple cycles of shock drift acceleration before the injection into DSA. Strong current-driven waves also temporarily change the shock obliquity and cause mild proton pre-acceleration even in quasi-perpendicular shocks, which otherwise do not accelerate protons. These results can be used to understand nonthermal emission in supernova remnants and intracluster medium in galaxy clusters., Comment: 5 pages, 4 figures, accepted by ApJL

We have become heavily reliant on electrical technologies, from power grids to GPS to wireless communication. Any disruption of these systems will have severe global consequences. A major natural hazard for such electrical disruption is caused by solar wind disturbances that have dramatic geospace impact.Estimates are that a solar storm of the magnitude of the 1859 Carrington Solar Superstorm would cause over $2 trillion in damage today. In July 23, 2012, we had a near miss of a solar Superstorm that could have broken the record of largest such storms at Earth. To enable pre-emptive measures, developing accurate space weather forecasts is urgent. At the core of space weather forecasts is plasma physics, and kinetic turbulence, in particular. For example, the intense turbulence stirred up at the bow shock and foreshock have been shown to open up pathways for high velocity solar wind parcels to bypass the protective shield of the terrestrial magnetosphere and create disturbances in the ionosphere and lower atmosphere. A primary challenge in understanding kinetic turbulence and its global implications is its multi-scale nature, spanning from electron scales to macro scales of the magnetosphere. Current four-spacecraft missions with 3D formations, the Magnetospheric Multiscale (MMS) and Cluster, have made progress in our understanding of such turbulence. Yet the limitation of a fixed spacecraft formation size at a given time prohibits probing the multi-scale nature as well as the dynamical evolution of the phenomena. A transformative leap in our understanding of turbulence is expected with in-situ probes populating a 3D volume and forming multiple 'n-hedrons (n > 4)' in MHD to kinetic scales., Comment: White Paper for Plasma 2020 Decadal Survey

Using a semi-analytic model of non-linear diffusive shock acceleration, we model the spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic of SNRs, they exhibit substantially steeper spectra than protons. In particular, we find that the difference between the electron and proton spectral index (power law slope) ranges from 0.1 to 0.4. Our findings must be reckoned with theories of Galactic CR transport, which often assume that electrons and protons are injected with the same slope, and may especially have implications for the observed "positron excess.", Comment: 6 pages, 4 figures, accepted to PRL

It has been proposed that Ultra-High-Energy Cosmic Rays (UHECRs) up to $10^{20}$eV could be produced in the relativistic jets of powerful Active Galactic Nuclei (AGNs) via a one-shot reacceleration of lower-energy CRs produced in supernova remnants (the $\textit{espresso}$ mechanism). We test this theory by propagating particles in realistic 3D magneto-hydrodynamic simulations of ultra-relativistic jets and find that about $10\%$ of the CRs entering the jet are boosted by at least a factor of $\sim\Gamma^2$ in energy, where $\Gamma$ is the jet's effective Lorentz factor, in agreement with the analytical expectations. Furthermore, about $0.1\%$ of the CRs undergo two or more shots and achieve boosts well in excess of $\Gamma^2$. Particles are typically accelerated up to the Hillas limit, suggesting that the $\textit{espresso}$ mechanism may promote galactic-like CRs to UHECRs even in AGN jets with moderate Lorentz factors, and not in powerful blazars only. Finally, we find that the sign of the toroidal magnetic field in the jet and in the cocoon controls the angular distribution of the reaccelerated particles, leading to a UHECR emission that may be either quasi-isotropic or beamed along the jet axis. These findings strongly support the idea that $\textit{espresso}$ acceleration in AGN jets can account for the UHECR spectra, chemical composition, and arrival directions measured by Auger and Telescope Array., Comment: 15 pages, 11 figures

Galaxy clusters are the largest and most massive bound objects resulting from cosmic hierarchical structure formation. Baryons account for somewhat more than 10% of that mass, with roughly 90% of the baryonic matter distributed throughout the clusters as hot ($T>1$ keV), high-$\beta$, very weakly collisional plasma; the so-called "intracluster medium" (ICM). Cluster mergers, close gravitational encounters and accretion, along with violent feedback from galaxies and relativistic jets from active galactic nuclei, drive winds, gravity waves, turbulence and shocks within the ICM. Those dynamics, in turn, generate cluster-scale magnetic fields and accelerate and mediate the transport of high-energy charged particles. Kinetic-scale, collective plasma processes define the basic character and fundamental signatures of these ICM phenomena, which are observed primarily by X-ray and radio astronomers., Comment: 5 pages, 2 figures, submitted for the 2020 Decadal Assessment of Plasma Science

Analysis of 15314 electron velocity distribution functions (VDFs) within $\pm$2 hours of 52 interplanetary (IP) shocks observed by the \emph{Wind} spacecraft near 1 AU are introduced. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The best results were found by modeling the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar velocity distribution function, while both the halo and beam/strahl components were best fit to bi-kappa velocity distribution function. This is the first statistical study to show that the core electron distribution is better fit to a self-similar velocity distribution function than a bi-Maxwellian under all conditions. The self-similar distribution deviation from a Maxwellian is a measure of inelasticity in particle scattering from waves and/or turbulence. The range of values defined by the lower and upper quartiles for the kappa exponents are $\kappa{\scriptstyle_{ec}}$ $\sim$ 5.40--10.2 for the core, $\kappa{\scriptstyle_{eh}}$ $\sim$ 3.58--5.34 for the halo, and $\kappa{\scriptstyle_{eb}}$ $\sim$ 3.40--5.16 for the beam/strahl. The lower-to-upper quartile range of symmetric bi-self-similar core exponents are $s{\scriptstyle_{ec}}$ $\sim$ 2.00--2.04, and asymmetric bi-self-similar core exponents are $p{\scriptstyle_{ec}}$ $\sim$ 2.20--4.00 for the parallel exponent, and $q{\scriptstyle_{ec}}$ $\sim$ 2.00--2.46 for the perpendicular exponent. The nuanced details of the fit procedure and description of resulting data product are also presented. The statistics and detailed analysis of the results are presented in Paper II and Paper III of this three-part study., Comment: 35 pages, 10 figures, 3 tables, under review in Astrophys. J. Suppl [updated in response to 2nd round of referee comments]