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1. A Kinetic Study of the Saturation of the Bell Instability

   https://doi.org/10.22323/1.395.0483  

   Zacharegkas, Georgios; Caprioli, Damiano; Haggerty, Colby; Gupta, Siddhartha (July 2021, 37th International Cosmic Ray Conference (ICRC2021))

   null (Ed.)

   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. 

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2. Modeling the Saturation of the Bell Instability Using Hybrid Simulations

   https://doi.org/10.3847/1538-4357/ad3960  

   Zacharegkas, Georgios; Caprioli, Damiano; Haggerty, Colby; Gupta, Siddhartha; Schroer, Benedikt (May 2024, The Astrophysical Journal)

   Abstract 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. 

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3. Cosmic ray protons and electrons from supernova remnants

   https://doi.org/10.1051/0004-6361/202140448  

   Cristofari, P.; Blasi, P.; Caprioli, D. (June 2021, Astronomy & Astrophysics)

   null (Ed.)

   Context. 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 downstream of a shock front, where both adiabatic and radiative losses are present. Since electrons lose energy mainly through synchrotron losses, it is natural to ask whether the spectrum released into the interstellar medium may be different from that of their hadronic counterpart. Independent studies of cosmic ray transport through the Galaxy require that the source spectrum of electrons and protons be very different. Therefore, the above question acquires a phenomenological relevance. Aims. Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from the upstream region and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons, where in addition to adiabatic losses we take the radiative losses suffered behind the shock into account. These electrons are dominated by synchrotron losses in the magnetic field, which most likely is self-generated by cosmic rays accelerated at the shock. Methods. We use standard temporal evolution relations for supernova shocks expanding in different types of interstellar media together with an analytic description of particle acceleration and magnetic field amplification to determine the density and spectrum of cosmic ray particles. Their evolution in time is derived by numerically solving the equation describing advection with adiabatic and radiative losses for electrons and protons. The flux from particles continuously escaping the supernova remnants is also accounted for. Results. The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to nonresonant and resonant streaming instability and their saturation. The resulting field is compared with the available set of observational results concerning the dependence of the magnetic field strength upon shock velocity. We find that when the field is the result of the growth of the cosmic-ray-driven nonresonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different; however, such a difference becomes appreciable only at energies ≳100−1000 GeV, while observations of the electron spectrum require such a difference to be present at energies as low as ∼10 GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of supernova remnant evolution (shock velocity ≪1000 km s −1 ); this may not be due to streaming instability but rather 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. 

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4. The supernova remnant SN 1006 as a Galactic particle accelerator

   https://doi.org/10.1038/s41467-022-32781-4  

   Giuffrida, Roberta; Miceli, Marco; Caprioli, Damiano; Decourchelle, Anne; Vink, Jacco; Orlando, Salvatore; Bocchino, Fabrizio; Greco, Emanuele; Peres, Giovanni (December 2022, Nature Communications)

   Abstract 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. 

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5. Understanding Streaming Instabilities in the Limit of High Cosmic-Ray Current Density

   https://doi.org/10.3847/1538-4357/adadf5  

   Lichko, Emily; Caprioli, Damiano; Schroer, Benedikt; Gupta, Siddhartha (February 2025, The Astrophysical Journal)

   Abstract A critical component of particle acceleration in astrophysical shocks is the nonresonant (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-cell 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 than in low-current cases, an effect due to the anisotropic heating that occurs in this regime. We also find that electron-scale modes, despite being the fastest growing, mostly lead to moderate electron heating and do not affect the late evolution or saturation of the instability. 

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