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Energetic plasma is everywhere in the Universe. The terrestrial Magnetospheric System is a key case where direct measures of plasma energization and energy transport can be made in situ at high resolution. Despite the large amount of available observations, we still do not fully understand how plasma energization and energy transport work. Key physical processes driving much plasma energization and energy transport occur where plasma on fluid scales couple to the smaller ion kinetic scales. These scales (1 RE) are strongly related to the larger mesoscales (several RE) at which large-scale plasma energization and energy transport structures form. All these scales and processes need to be resolved experimentally, however existing multi-point in situ observations do not have a sufficient number of measurement points. New multiscale observations simultaneously covering scales from mesoscales to ion kinetic scales are needed. The implementation of these observations requires a strong international collaboration in the coming years between the major space agencies. The Plasma Observatory is a mission concept tailored to resolve scale coupling in plasma energization and energy transport at fluid and ion scales. It targets the two ESA-led Medium Mission themes Magnetospheric Systems and Plasma Cross-scale Coupling of the ESA Voyage 2050 report and is currently under evaluation as a candidate for the ESA M7 mission. MagCon (Magnetospheric Constellation) is a mission concept being studied by NASA aiming at studying the flow of mass, momentum, and energy through the Earth magnetosphere at mesoscales. Coordination between Plasma Observatory and MagCon missions would allow us for the first time to simultaneously cover from mesoscales to ion kinetic scales leading to a paradigm shift in the understanding of the Earth Magnetospheric System., Comment: A White Paper submitted for the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033

The non-resonant (Bell) streaming instability driven by energetic particles is crucial for producing amplified magnetic fields that are key to the acceleration of cosmic rays (CRs) in supernova remnants, around Galactic and extra-galactic CR sources, and for the CR transport. We present a covariant theory for the saturation of the Bell instability, substantiated by self-consistent kinetic simulations, that can be applied to arbitrary CR distributions and discuss its implications in several heliospheric and astrophysical contexts., Comment: 8 pages, 3 figures, Proceedings of the 38th International Cosmic Ray Conference (ICRC2023), 26 July - 3 August, 2023, Nagoya, Japan

GeV and TeV emission from the forward shocks of supernova remnants (SNRs) indicates that they are capable particle accelerators, making them promising sources of Galactic cosmic rays (CRs). However, it remains uncertain whether this $\gamma$-ray emission arises primarily from the decay of neutral pions produced by very high energy hadrons, or from inverse-Compton and/or bremsstrahlung emission from relativistic leptons. By applying a semi-analytic approach to non-linear diffusive shock acceleration (NLDSA) and calculating the particle and photon spectra produced in different astrophysical environments, we parametrize the relative strength of hadronic and leptonic emission. We show that, even if CR acceleration is likely to occur in all SNRs, the observed photon spectra may instead primarily reflect the environment surrounding the SNR, specifically the ambient density and radiation field. We find that the most hadronic-appearing spectra are young and found in environments of high density but low radiation energy density. This study aims to guide the interpretation of current $\gamma$-ray observations and single out the best targets of future campaigns., Comment: 9 pages, 6 figures, submitted to ApJ

Space plasmas are three-dimensional dynamic entities. Except under very special circumstances, their structure in space and their behavior in time are not related in any simple way. Therefore, single spacecraft in situ measurements cannot unambiguously unravel the full space-time structure of the heliospheric plasmas of interest in the inner heliosphere, in the Geospace environment, or the outer heliosphere. This shortcoming leaves numerous central questions incompletely answered. Deficiencies remain in at least two important subjects, Space Weather and fundamental plasma turbulence theory, due to a lack of a more complete understanding of the space-time structure of dynamic plasmas. Only with multispacecraft measurements over suitable spans of spatial separation and temporal duration can these ambiguities be resolved. We note that these characterizations apply to turbulence across a wide range of scales, and also equally well to shocks, flux ropes, magnetic clouds, current sheets, stream interactions, etc. In the following, we will describe the basic requirements for resolving space-time structure in general, using turbulence' as both an example and a principal target or study. Several types of missions are suggested to resolve space-time structure throughout the Heliosphere., Comment: White Paper submitted to: Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. arXiv admin note: substantial text overlap with arXiv:1903.06890

We present a new 2 Ms Chandra observation of the cluster merger Abell 2146, which hosts two huge M~2 shock fronts each ~500 kpc across. For the first time, we resolve and measure the width of cluster merger shocks. The best-fit width for the bow shock is 17+/-1 kpc and for the upstream shock is 10.7+/-0.3 kpc. A narrow collisionless shock will appear broader in projection if its smooth shape is warped by local gas motions. We show that both shock widths are consistent with collisionless shocks blurred by local gas motions of 290+/-30 km/s. The upstream shock forms later on in the merger than the bow shock and is therefore expected to be significantly narrower. From the electron temperature profile behind the bow shock, we measure the timescale for the electrons and ions to come back into thermal equilibrium. We rule out rapid thermal equilibration of the electrons with the shock-heated ions at the 6 sigma level. The observed temperature profile instead favours collisional equilibration. For these cluster merger shocks, which have low sonic Mach numbers and propagate through a high $\beta$ plasma, we find no evidence for electron heating over that produced by adiabatic compression. Our findings are expected to be valid for collisionless shocks with similar parameters in other environments and support the existing picture from the solar wind and supernova remnants. The upstream shock is consistent with this result but has a more complex structure, including a ~2 keV increase in temperature ~50 kpc ahead of the shock., Comment: 18 pages, 17 figures, 1 table, accepted to MNRAS

Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth's bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the "foot" region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock's rest frame. That conversion allows for a unique study of the relative spatial scales of the shock's various features, including the shock's growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Results highlight the critical cross-scale coupling between electron-kinetic- and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks., Comment: In press and to be published in Astrophysical Journal Letters in 2021

The spectrum of cosmic ray protons and electrons released by supernova remnants throughout their evolution is poorly known, because of the difficulty in accounting for particle escape and confinement in the downstream of a shock front, where both adiabatic and radiative losses are present. Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from upstream and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons. The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to non--resonant and resonant streaming instability and their saturation. We find that when the field is the result of the growth of the cosmic-ray--driven non--resonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different, but such a difference becomes appreciable only at energies $\gtrsim 100-1000$ GeV, while observations of the electron spectrum require such a difference to be present at energies as low as $\sim 10$ GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of the supernova remnant evolution (shock velocity $\ll 1000$ km/s), perhaps not due to streaming instability but hydrodynamical processes. We comment on the feasibility of such conditions and speculate on the possibility that the difference in spectral shape between electrons and protons may reflect either some unknown acceleration effect, or additional energy losses in cocoons around the sources., Comment: 11 pages, 5 figures, Accepted for publication in Astronomy \& Astrophysics

We present X-ray and radio observations of the Fast Blue Optical Transient (FBOT) CRTS-CSS161010 J045834-081803 (CSS161010 hereafter) at t=69-531 days. CSS161010 shows luminous X-ray ($L_x\sim5\times 10^{39}\,\rm{erg\,s^{-1}}$) and radio ($L_{\nu}\sim10^{29}\,\rm{erg\,s^{-1}Hz^{-1}}$) emission. The radio emission peaked at ~100 days post transient explosion and rapidly decayed. We interpret these observations in the context of synchrotron emission from an expanding blastwave. CSS161010 launched a mildly relativistic outflow with velocity $\Gamma\beta c\ge0.55c$ at ~100 days. This is faster than the non-relativistic AT2018cow ($\Gamma\beta c\sim0.1c$) and closer to ZTF18abvkwla ($\Gamma\beta c\ge0.3c$ at 63 days). The inferred initial kinetic energy of CSS161010 ($E_k\gtrsim10^{51}$ erg) is comparable to that of long Gamma Ray Bursts (GRBs), but the ejecta mass that is coupled to the mildly relativistic outflow is significantly larger ($\sim0.01-0.1\,\rm{M_{\odot}}$). This is consistent with the lack of observed gamma-rays. The luminous X-rays were produced by a different emission component to the synchrotron radio emission. CSS161010 is located at ~150 Mpc in a dwarf galaxy with stellar mass $M_{*}\sim10^{7}\,\rm{M_{\odot}}$ and specific star formation rate $sSFR\sim 0.3\,\rm{Gyr^{-1}}$. This mass is among the lowest inferred for host-galaxies of explosive transients from massive stars. Our observations of CSS161010 are consistent with an engine-driven aspherical explosion from a rare evolutionary path of a H-rich stellar progenitor, but we cannot rule out a stellar tidal disruption event on a centrally-located intermediate mass black hole. Regardless of the physical mechanism, CSS161010 establishes the existence of a new class of rare (rate $<0.4\%$ of the local core-collapse supernova rate) H-rich transients that can launch mildly relativistic outflows., Comment: Accepted to ApJL

We present comprehensive observations and analysis of the energetic H-stripped SN 2016coi (a.k.a. ASASSN-16fp), spanning the $\gamma$-ray through optical and radio wavelengths, acquired within the first hours to $\sim$420 days post explosion. Our campaign confirms the identification of He in the SN ejecta, which we interpret to be caused by a larger mixing of Ni into the outer ejecta layers. From the modeling of the broad bolometric light curve we derive a large ejecta mass to kinetic energy ratio ($M_{\rm{ej}}\sim 4-7\,\rm{M_{\odot}}$, $E_{\rm{k}}\sim 7-8\times 10^{51}\,\rm{erg}$). The small [\ion{Ca}{ii}] \lam\lam7291,7324 to [\ion{O}{i}] \lam\lam6300,6364 ratio ($\sim$0.2) observed in our late-time optical spectra is suggestive of a large progenitor core mass at the time of collapse. We find that SN 2016coi is a luminous source of X-rays ($L_{X}>10^{39}\,\rm{erg\,s^{-1}}$ in the first $\sim100$ days post explosion) and radio emission ($L_{8.5\,GHz}\sim7\times 10^{27}\,\rm{erg\,s^{-1}Hz^{-1}}$ at peak). These values are in line with those of relativistic SNe (2009bb, 2012ap). However, for SN 2016coi we infer substantial pre-explosion progenitor mass-loss with rate $\dot M \sim (1-2)\times 10^{-4}\,\rm{M_{\odot}yr^{-1}}$ and a sub-relativistic shock velocity $v_{sh}\sim0.15c$, in stark contrast with relativistic SNe and similar to normal SNe. Finally, we find no evidence for a SN-associated shock breakout $\gamma$-ray pulse with energy $E_{\gamma}>2\times 10^{46}\,\rm{erg}$. While we cannot exclude the presence of a companion in a binary system, taken together, our findings are consistent with a massive single star progenitor that experienced large mass loss in the years leading up to core-collapse, but was unable to achieve complete stripping of its outer layers before explosion., Comment: Submitted to ApJ. Main text: 21 pages; Appendix: 15 pages; 12 figures

This paper briefly reviews a number of fundamental measurements that need to be made in order to characterize turbulence in space plasmas such as the solar wind. It has long been known that many of these quantities require simultaneous multipoint measurements to attain a proper characterization that would reveal the fundamental physics of plasma turbulence. The solar wind is an ideal plasma for such an investigation, and it now appears to be technologically feasible to carry out such an investigation, following the pioneering Cluster and MMS missions. Quantities that need to be measured using multipoint measurements include the two-point, two-time second correlation function of velocity, magnetic field and density, and higher order statistical objects such as third and fourth order structure functions. Some details of these requirements are given here, with a eye towards achieving closure on fundamental questions regarding the cascade rate, spectral anisotropy, characteristic coherent structures, intermittency, and dissipation mechanisms that describe plasma turbuelence, as well as its variability with plasma parameters in the solar wind. The motivation for this discussion is the current planning for a proposed Helioswarm mission that would be designed to make these measurements,leading to breakthrough understanding of the physics of space and astrophysical turbulence., Comment: White paper submitted to the PLASMA 2020 Decadal Survey Committee

A multi-institutional, multi-national science team will soon submit a NASA proposal to build a constellation of spacecraft to fly into the near-Earth solar wind in a swarm spanning a multitude of scales in order to obtain critically needed measurements that will reveal the underlying dynamics of magnetized turbulence. This white paper, submitted to the Plasma 2020 Decadal Survey Committee, provides a brief overview of turbulent systems that constitute an area of compelling plasma physics research, including why this mission is needed, and how this mission will achieve the goal of revealing how energy is transferred across scales and boundaries in plasmas throughout the universe., Comment: 6 pages, submitted to the Plasma 2020 Decadal Survey Committee; version 2 includes movie of proposed orbit

Foreshock disturbances -- large-scale (~1000 km to >30,000 km), transient (~5-10 per day - lasting ~10s of seconds to several minutes) structures [1,2] - generated by suprathermal (>100 eV to 100s of keV) ions [3,4] arise upstream of Earth's bow shock formed by the solar wind colliding with the Earth's magnetosphere. They have recently been found to accelerate ions to energies of several keV [5,6]. Although electrons in Saturn's high Mach number (M > 40) bow shock can be accelerated to relativistic energies (nearly 1000 keV) [7], it has hitherto been thought impossible to accelerate electrons at the much weaker (M < 20) Earth's bow shock beyond a few 10s of keV [8]. Here we report observations of electrons energized by foreshock disturbances to energies up to at least ~300 keV. Although such energetic electrons have been previously reported, their presence has been attributed to escaping magnetospheric particles [9,10] or solar events [11]. These relativistic electrons are not associated with any solar activity nor are they of magnetospheric origin. Further, current theories of ion acceleration in foreshock disturbances cannot account for electrons accelerated to the observed relativistic energies [12-17]. These electrons are clearly coming from the disturbances, leaving us with no explanation as to their origin., Comment: 14 pages, 8 figures, rejected from Nature, intend to submit to Phys. Rev. Lett

We used unprecedentedly large 2D and 3D hybrid (kinetic ions - fluid electrons) simulations of non-relativistic collisionless strong shocks in order to investigate the effects of self-consistently accelerated ions on the overall shock dynamics. The current driven by suprathermal particles streaming ahead of the shock excites modes transverse to the background magnetic field. The Lorentz force induced by these self-amplified fields tends to excavate tubular, underdense, magnetic-field-depleted cavities that are advected with the fluid and perturb the shock surface, triggering downstream turbulent motions. These motions further amplify the magnetic field, up to factors of 50-100 in knot-like structures. Once downstream, the cavities tend to be filled by hot plasma plumes that compress and stretch the magnetic fields in elongated filaments; this effect is particularly evident if the shock propagates parallel to the background field. Highly-magnetized knots and filaments may provide explanations for the rapid X-ray variability observed in RX J1713.7-3946 and for the regular pattern of X-ray bright stripes detected in Tycho's supernova remnant., Comment: 8 pages, 5 figures (larger than in v1). Minor changes reflecting the version accepted in ApJL

In this paper we present the first formulation of the theory of non-linear particle acceleration in collisionless shocks in the presence of neutral hydrogen in the acceleration region. The dynamical reaction of the accelerated particles, the magnetic field amplification and the magnetic dynamical effects on the shock are also included. The main new aspect consists however in accounting for charge exchange and ionization of neutral hydrogen, which profoundly change the structure of the shock, as discussed in our previous work. This important dynamical effect of neutrals is mainly associated to the so-called neutral return flux, namely the return of hot neutrals from the downstream region to the upstream, where they deposit energy and momentum through charge exchange and ionization. We also present the self-consistent calculation of Balmer line emission from the shock region and discuss how to use measurements of the anomalous width of the different components of the Balmer line to infer the cosmic ray acceleration efficiency in supernova remnants showing Balmer emission: the broad Balmer line, which is due to charge exchange of hydrogen atoms with hot ions downstream of the shock, is shown to become narrower as a result of the energy drainage into cosmic rays, while the narrow Balmer line, due to charge exchange in the cosmic-ray--induced precursor, is shown to become broader. In addition to these two well-known components, the neutral return flux leads to the formation of a third component with intermediate width: this too contains information on ongoing processes at the shock., Comment: 14 pages, 10 figures. Version accepted for publication in the Astrophysical Journal

We apply the non-linear diffusive shock acceleration theory in order to describe the properties of two supernova remnants, SN 1572 (Tycho) and SN 1604 (Kepler). By analyzing the multi-wavelength spectra, we infer that both Tycho's and Kepler's forward shocks are accelerating protons up to ~500 TeV, channeling into cosmic rays more than 10 per cent of their kinetic energy. We find that the streaming instability induced by cosmic rays is consistent with the X-ray morphology of the remnants, indicating a very efficient magnetic field amplification (up to ~300 microG). In the case of Tycho we explain the gamma-ray spectrum from the GeV up to the TeV band as due to pion decay produced in nuclear collisions by accelerated nuclei scattering against the background gas. On the other hand, due to the larger distance, the gamma-ray emission from Kepler is not detected, being below the sensitivity of the present detectors, but it should be detectable by the Cerenkov Telescope Array., Comment: 4 pages, 2 figures. Proceeding of the "High Energy Gamma-Ray Astronomy", July 9-13 2012, Heidelberg (Germany)

A collisionless shock may be strongly modified by the presence of neutral atoms through the processes of charge exchange between ions and neutrals and ionization of the latter. These two processes lead to exchange of energy and momentum between charged and neutral particles both upstream and downstream of the shock. In particular, neutrals that suffer a charge exchange downstream with shock-heated ions generate high velocity neutrals that have a finite probability of returning upstream. These neutrals might then deposit heat in the upstream plasma through ionization and charge exchange, thereby reducing the fluid Mach number. A consequence of this phenomenon, that we refer to as the "neutral return flux", is a reduction of the shock compression factor and the formation of a shock precursor upstream. The scale length of the precursor is determined by the ionization and charge exchange interaction lengths of fast neutrals moving towards upstream infinity. In the case of a shock propagating in the interstellar medium, the effects of ion-neutral interactions are especially important for shock velocities < 3000 km/s. Such propagation velocities are common among shocks associated with supernova remnants, the primary candidate sources for the acceleration of Galactic cosmic rays. We then investigate the effects of the return flux of neutrals on the spectrum of test-particles accelerated at the shock. We find that, for shocks slower than ~3000 km/s, the particle energy spectrum steepens appreciably with respect to the naive expectation for a strong shock, namely E^-2., Comment: 13 pages, 8 figures. Paper accepted for publication in the Astrophysical Journal

Very recent gamma-ray observations of G120.1+1.4 (Tycho's) supernova remnant (SNR) by Fermi-LAT and VERITAS provided new fundamental pieces of information for understanding particle acceleration and non-thermal emission in SNRs. We want to outline a coherent description of Tycho's properties in terms of SNR evolution, shock hydrodynamics and multi-wavelength emission by accounting for particle acceleration at the forward shock via first order Fermi mechanism. We adopt here a quick and reliable semi-analytical approach to non-linear diffusive shock acceleration which includes magnetic field amplification due to resonant streaming instability and the dynamical backreaction on the shock of both cosmic rays (CRs) and self-generated magnetic turbulence. We find that Tycho's forward shock is accelerating protons up to at least 500 TeV, channelling into CRs about the 10 per cent of its kinetic energy. Moreover, the CR-induced streaming instability is consistent with all the observational evidences indicating a very efficient magnetic field amplification (up to ~300 micro Gauss). In such a strong magnetic field the velocity of the Alfv\'en waves scattering CRs in the upstream is expected to be enhanced and to make accelerated particles feel an effective compression factor lower than 4, in turn leading to an energy spectrum steeper than the standard prediction {\propto} E^-2. This latter effect is crucial to explain the GeV-to-TeV gamma-ray spectrum as due to the decay of neutral pions produced in nuclear collisions between accelerated nuclei and the background gas. The self-consistency of such an hadronic scenario, along with the fact that the concurrent leptonic mechanism cannot reproduce both the shape and the normalization of the detected the gamma-ray emission, represents the first clear and direct radiative evidence that hadron acceleration occurs efficiently in young Galactic SNRs., Comment: Minor changes. Accepted for publication in Astronomy & Astrophysics

We present the non-linear theory of shock acceleration applied to SNRs expanding into partially neutral plasma. Using this theory we show how the Balmer lines detected from young SNRs can be used to test the efficiency of shocks in the production of cosmic rays. In particular we investigate the effect of charge-exchange between protons and neutral hydrogen occurring in the precursor formed ahead of the shock. In this precursor the CR pressure accelerate the ionized component of the plasma and a relative velocity between protons and neutral hydrogen is established. On the other hand the charge-exchange process tends to equilibrate ions and neutrals resulting in the heating of both components. We show that even when the shock converts only a few per cent of the total bulk kinetic energy into CRs, the heating is efficient enough to produce a detectable broadening of the narrow Balmer lines emitted by the neutral hydrogen., Comment: To appear on the proceedings of the 12th ICATPP Conference, Villa Olmo, Como, Italy, 7-8 October 2010

We investigate the theoretical and observational implications of the acceleration of protons and heavier nuclei in supernova remnants (SNRs). By adopting a semi-analytical technique, we study the non-linear interplay among particle acceleration, magnetic field generation and shock dynamics, outlining a self-consistent scenario for the origin of the spectrum of Galactic cosmic rays as produced in this class of sources. Moreover, the inferred chemical abundances suggest nuclei heavier than Hydrogen to be relevant not only in the shock dynamics but also in the calculation of the gamma-ray emission from SNRs due to the decay of neutral pions produced in nuclear interactions., Comment: To appear on the proceedings of ICATPP Conference on Cosmic Rays for Particle and Astroparticle Physics, Villa Olmo, Como 7-8 October 2010

We describe a semi-analytical approach to non-linear diffusive shock acceleration in the case in which nuclei other than protons are also accelerated. The structure of the shock is determined by the complex interplay of all nuclei, and in turn this shock structure determines the spectra of all components. The magnetic field amplification upstream is described as due to streaming instability of all nuclear species. The amplified magnetic field is then taken into account for its dynamical feedback on the shock structure as well as in terms of the induced modification of the velocity of the scattering centers that enters the particle transport equation. The spectra of accelerated particles are steep enough to be compared with observed cosmic ray spectra only if the magnetic field is sufficiently amplified and the scattering centers have high speed in the frame of the background plasma. We discuss the implications of this generalized approach on the structure of the knee in the all-particle cosmic ray spectrum, which we interpret as due to an increasingly heavier chemical composition above $10^{15}$eV. The effects of a non trivial chemical composition at the sources on the gamma ray emission from a supernova remnant when gamma rays are of hadronic origin are also discussed., Comment: 23 pages, 5 figures, minor changes to reflect the published version

We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical, Monte Carlo and semi-analytical), even if based on different physical assumptions and implementations, for typical environmental parameters lead to very consistent results in terms of shock hydrodynamics, cosmic ray spectrum and also escaping flux spectrum and anisotropy. Strong points and limits of each approach are also discussed, as a function of the problem one wants to study., Comment: 26 pages, 4 figures, published version (references updated)

The supernova paradigm for the origin of galactic cosmic rays has been deeply affected by the development of the non-linear theory of particle acceleration at shock waves. Here we discuss the implications of applying such theory to the calculation of the spectrum of cosmic rays at Earth as accelerated in supernova remnants and propagating in the Galaxy. The spectrum is calculated taking into account the dynamical reaction of the accelerated particles on the shock, the generation of magnetic turbulence which enhances the scattering near the shock, and the dynamical reaction of the amplified field on the plasma. Most important, the spectrum of cosmic rays at Earth is calculated taking into account the flux of particles escaping from upstream during the Sedov-Taylor phase and the adiabatically decompressed particles confined in the expanding shell and escaping at later times. We show how the spectrum obtained in this way is well described by a power law in momentum with spectral index close to -4, despite the concave shape of the instantaneous spectra of accelerated particles. On the other hand we also show how the shape of the spectrum is sensible to details of the acceleration process and environment which are and will probably remain very poorly known., Comment: 19 pages, 8 figures, published version (references updated)

The theory of Non-Linear Diffusive Shock Acceleration (NLDSA) predicts the formation of a precursor upstream of the shock, where accelerated particles diffuse and induce magnetic field amplification through streaming instability. The non detection of this precursor in X-rays in {\it Chandra} observations of the north-eastern region of SN 1006 (G329.6+14.6) led to impose an upper limit to the X-ray emission generated by accelerated electrons diffusing in this precursor, at an emissivity level of <1.5 per cent of the emission from the downstream region (Long et al. 2003). This has been used as an argument against Fermi acceleration at this shock. Here we calculate the spectrum and spatial distribution of accelerated particles in SN 1006 and show that Chandra results (including more recent data) are in perfect agreement with the predictions of NLDSA suggesting efficient particle acceleration and magnetic field amplification upstream of the shock by a factor ~10., Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter

We present here a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream. This solution, besides allowing us to determine the spectrum of particles accelerated at the shock front, including the shape of the cutoff at some maximum momentum, also allows us to determine the spectrum of particles escaping the system from upstream. This latter aspect of the problem is crucial for establishing a connection between the accelerated particles in astrophysical sources, such as supernova remnants, and the cosmic rays observed at the Earth. An excellent approximate solution, which leads to a computationally fast calculation of the structure of shocks with an arbitrary level of cosmic ray modification, is also obtained., Comment: 11 pages, 2 figures, Accepted for publication in APh.

We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes the magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. The approach is specialized to parallel shock waves and the parameters we chose are the ones appropriate to forward shocks in Supernova Remnants. Our calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which noticeably reduces the modification of the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are $R_{tot}\sim 7-10$, in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims are interpreted as due to severe synchrotron losses of high energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in driving the reduction of the precursor modification., Comment: Accepted for publication in MNRAS

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles, $p_{max}$, decreases with time, as is the case for the Sedov-Taylor phase of expansion of a shell Supernova Remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time $t$, particles with momenta larger than $p_{max}(t)$ leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at Earth. In this paper we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov-Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at Earth., Comment: Version accepted for publication in MNRAS

The Universe is permeated by hot, turbulent, magnetized plasmas. Turbulent plasma is a major constituent of active galactic nuclei, supernova remnants, the intergalactic and interstellar medium, the solar corona, the solar wind and the Earths magnetosphere, just to mention a few examples. Energy dissipation of turbulent fluctuations plays a key role in plasma heating and energization, yet we still do not understand the underlying physical mechanisms involved. THOR is a mission designed to answer the questions of how turbulent plasma is heated and particles accelerated, how the dissipated energy is partitioned and how dissipation operates in different regimes of turbulence. THOR is a single-spacecraft mission with an orbit tuned to maximize data return from regions in near-Earth space magnetosheath, shock, foreshock and pristine solar wind featuring different kinds of turbulence. Here we summarize the THOR proposal submitted on 15 January 2015 to the Call for a Medium-size mission opportunity in ESAs Science Programme for a launch in 2025 (M4). THOR has been selected by European Space Agency (ESA) for the study phase.