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1. An Unusual Energetic Particle Flux Enhancement Associated with Solar Wind Magnetic Island Dynamics

   Zhao, L.-L. ; Zank, G.P. ; Khabarova, O. ; Du, S. ; Chen, Y. ; Adhikari, L. ; Hu, Q. ( September 2018 , Astrophysical journal)

   The possibility that charged particles are accelerated statistically in a “sea” of small-scale interacting magnetic flux ropes in the supersonic solar wind is gaining credence. In this Letter, we extend the Zank et al. statistical transport theory for a nearly isotopic particle distribution by including an escape term corresponding to particle loss from a finite acceleration region. Steady-state 1D solutions for both the accelerated particle velocity distribution function and differential intensity are derived. We show Ulysses observations of an energetic particle flux enhancement event downstream of a shock near 5 au that is inconsistent with the predictions of classical diffusive shock acceleration (DSA) but may be explained by local acceleration associated with magnetic islands. An automated Grad-Shafranov reconstruction approach is employed to identify small-scale magnetic flux ropes behind the shock. For the first time, the observed energetic particle “time-intensity” profile and spectra are quantitatively compared with theoretical predictions. The results show that stochastic acceleration by interacting magnetic islands accounts successfully for the observed (i) peaking of particle intensities behind the shock instead of at the shock front as standard DSA predicts; (ii) increase in the particle flux amplification factor with increasing particle energy; (ii) increase in distance between the particlemore »intensity peak and the shock front with increasing energy; and (iv) hardening of particle power-law spectra with increasing distance downstream of the shock.« less
2. Interaction between Multiple Current Sheets and a Shock Wave: 2D Hybrid Kinetic Simulations

   https://doi.org/10.3847/1538-4357/ac2e06  

   Nakanotani, M. ; Zank, G. P. ; Zhao, L.-L. ( December 2021 , The Astrophysical Journal)

   Abstract Particle acceleration behind a shock wave due to interactions between magnetic islands in the heliosphere has attracted attention in recent years. The downstream acceleration may yield a continuous increase of particle flux downstream of the shock wave. Although it is not obvious how the downstream magnetic islands are produced, it has been suggested that current sheets are involved in the generation of magnetic islands due to their interaction with a shock wave. We perform 2D hybrid kinetic simulations to investigate the interaction between multiple current sheets and a shock wave. In the simulation, current sheets are compressed by the shock wave and a tearing instability develops at the compressed current sheets downstream of the shock. As the result of this instability, the electromagnetic fields become turbulent and magnetic islands form well downstream of the shock wave. We find a “post-cursor” region in which the downstream flow speed normal to the shock wave in the downstream rest frame is decelerated to ∼ 1 V A immediately behind the shock wave, where V A is the upstream Alfvén speed. The flow speed then gradually decelerates to 0 accompanied by the development of the tearing instability. We also observe an efficient productionmore »of energetic particles above 100 E 0 during the development of the instability some distance downstream of the shock wave, where E 0 = m p V A 2 and m p is the proton mass. This feature corresponds to Voyager observations showing that the anomalous cosmic-ray intensity increase begins some distance downstream of the heliospheric termination shock.« less
3. Particle Acceleration in Magnetic Reconnection with Ad Hoc Pitch-angle Scattering

   https://doi.org/10.3847/1538-4357/ac7143  

   Johnson, Grant ; Kilian, Patrick ; Guo, Fan ; Li, Xiaocan ( July 2022 , The Astrophysical Journal)

   Abstract Particle acceleration during magnetic reconnection is a long-standing topic in space, solar, and astrophysical plasmas. Recent 3D particle-in-cell simulations of magnetic reconnection show that particles can leave flux ropes due to 3D field-line chaos, allowing particles to access additional acceleration sites, gain more energy through Fermi acceleration, and develop a power-law energy distribution. This 3D effect does not exist in traditional 2D simulations, where particles are artificially confined to magnetic islands due to their restricted motions across field lines. Full 3D simulations, however, are prohibitively expensive for most studies. Here, we attempt to reproduce 3D results in 2D simulations by introducing ad hoc pitch-angle scattering to a small fraction of the particles. We show that scattered particles are able to transport out of 2D islands and achieve more efficient Fermi acceleration, leading to a significant increase of energetic particle flux. We also study how the scattering frequency influences the nonthermal particle spectra. This study helps achieve a complete picture of particle acceleration in magnetic reconnection.
4. Investigating Particle Acceleration by Dynamic Small-scale Flux Ropes behind Interplanetary Shocks in the Inner Heliosphere

   https://doi.org/10.3847/1538-4357/ac6d5e  

   Van Eck, Keaton ; le Roux, Jakobus ; Chen, Yu ; Zhao, Ling Ling ; Thompson, Noah ( July 2022 , The Astrophysical Journal)

   We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find thatmore »second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.

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5. 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)

   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 relationsmore »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.« less