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Register a new userScaling of Magnetic Dissipation and Particle Acceleration in ABC Fields
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Using particle-in-cell (PIC) numerical simulations with electron-positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length $lambda_0$ in relation to the system size $L$ of the two-dimensional (2D) `Arnold-Beltrami-Childress (ABC) magnetic field configurations. Topological constraints on the distribution of magnetic helicity in 2D systems, identified earlier in relativistic force-free (FF) simulations, that prevent the high-$(L/lambda_0)$ configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about $epsilon_{rm diss} simeq 60%$. We find that the peak growth time scale of the electric energy $tau_{rm E,peak}$ scales with the characteristic value of initial Alfven velocity $beta_{rm A,ini}$ like $tau_{rm E,peak} propto (lambda_0/L)beta_{rm A,ini}^{-3}$. The particle energy change is decomposed into non-thermal and thermal parts, with non-thermal energy gain dominant only for high initial magnetisation. The most robust description of the non-thermal high-energy part of the particle distribution is that the power-law index is a linear function of the initial magnetic energy fraction.
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Using analytical and numerical methods (fluid and particle-in-cell simulations) we study a number of model problems involving merger of magnetic flux tubes in relativistic magnetically-dominated plasma. Mergers of current-carrying flux tubes (exemplified by the two dimensional `ABC structures) and zero total current magnetic flux tubes are considered. In all cases regimes of spontaneous and driven evolution are investigated. We identify two stages of particle acceleration during flux mergers: (i) fast explosive prompt X-point collapse and (ii) ensuing island merger. The fastest acceleration occurs during the initial catastrophic X-point collapse, with the reconnection electric field of the order of the magnetic field. During the X-point collapse particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $sigma$. For plasma magnetization $sigma leq 10^2$ the spectrum power law index is $p> 2$; in this case the maximal energy depends linearly on the size of the reconnecting islands. For higher magnetization, $sigma geq 10^2$, the spectra are hard, $p< 2$, yet the maximal energy $gamma_{max}$ can still exceed the average magnetic energy per particle, $ sim sigma$, by orders of magnitude (if $p$ is not too close to unity). The X-point collapse stage is followed by magnetic island merger that dissipates a large fraction of the initial magnetic energy in a regime of forced magnetic reconnection, further accelerating the particles, but proceeds at a slower reconnection rate.
We review here some magnetic phenomena in astrophysical particle accelerators associated with collisionless shocks in supernova remnants, radio galaxies and clusters of galaxies. A specific feature is that the accelerated particles can play an important role in magnetic field evolution in the objects. We discuss a number of CR-driven, magnetic field amplification processes that are likely to operate when diffusive shock acceleration (DSA) becomes efficient and nonlinear. The turbulent magnetic fields produced by these processes determine the maximum energies of accelerated particles and result in specific features in the observed photon radiation of the sources. Equally important, magnetic field amplification by the CR currents and pressure anisotropies may affect the shocked gas temperatures and compression, both in the shock precursor and in the downstream flow, if the shock is an efficient CR accelerator. Strong fluctuations of the magnetic field on scales above the radiation formation length in the shock vicinity result in intermittent structures observable in synchrotron emission images. Resonant and non-resonant CR streaming instabilities in the shock precursor can generate mesoscale magnetic fields with scale-sizes comparable to supernova remnants and even superbubbles. This opens the possibility that magnetic fields in the earliest galaxies were produced by the first generation Population III supernova remnants and by clustered supernovae in star forming regions.
Magnetic reconnection, especially in the relativistic regime, provides an efficient mechanism for accelerating relativistic particles and thus offers an attractive physical explanation for nonthermal high-energy emission from various astrophysical sources. I present a simple analytical model that elucidates key physical processes responsible for reconnection-driven relativistic nonthermal particle acceleration (NTPA) in the large-system, plasmoid-dominated regime in two dimensions. The model aims to explain the numerically-observed dependencies of the power-law index $p$ and high-energy cutoff $gamma_c$ of the resulting nonthermal particle energy spectrum $f(gamma)$ on the ambient plasma magnetization $sigma$, and (for $gamma_c$) on the system size $L$. In this self-similar model, energetic particles are continuously accelerated by the out-of-plane reconnection electric field $E_{rm rec}$ until they become magnetized by the reconnected magnetic field and eventually trapped in plasmoids large enough to confine them. The model also includes diffusive Fermi acceleration by particle bouncing off rapidly moving plasmoids. I argue that the balance between electric acceleration and magnetization controls the power-law index, while trapping in plasmoids governs the cutoff, thus tying the particle energy spectrum to the plasmoid distribution.
In this chapter, we review some features of particle acceleration in astrophysical jets. We begin by describing four observational results relating to the topic, with particular emphasis on jets in active galactic nuclei and parallels between different sources. We then discuss the ways in which particles can be accelerated to high energies in magnetised plasmas, focusing mainly on shock acceleration, second-order Fermi and magnetic reconnection; in the process, we attempt to shed some light on the basic conditions that must be met by any mechanism for the various observational constraints to be satisfied. We describe the limiting factors for the maximum particle energy and briefly discuss multimessenger signals from neutrinos and ultrahigh energy cosmic rays, before describing the journey of jet plasma from jet launch to cocoon with reference to the different acceleration mechanisms. We conclude with some general comments on the future outlook.
Hot accretion flows contain collisionless plasmas that are believed to be capable of accelerating particles to very high energies, as a result of turbulence generated by the magnetorotational instability (MRI). We conduct unstratified shearing-box simulations of the MRI turbulence in ideal magnetohydrodynamic (MHD), and inject energetic (relativistic) test particles in simulation snapshots to conduct a detailed investigation on particle diffusion and stochastic acceleration. We consider different amount of net vertical magnetic flux to achieve different disk magnetizations levels at saturated states, with sufficiently high resolution to resolve the gyro-radii ($R_g$) of most particles. Particles with large $R_g$ ($gtrsim0.03$ disk scale height $H$) show spatial diffusion coefficients of $sim30$ and $sim5$ times Bohm values in the azimuthal and poloidal directions, respectively. We further measure particle momentum diffusion coefficient $D(p)$ by applying the Fokker-Planck equation to particle momentum evolution. For these particles, contribution from turbulent fluctuations scales as $D(p)propto p$, and shear acceleration takes over when $R_ggtrsim0.1H$, characterized by $D(p)propto p^3$. For particles with smaller $R_g$ ($lesssim0.03H$), their spatial diffusion coefficients roughly scale as $sim p^{-1}$, and show evidence of $D(p)propto p^2$ scaling in momentum diffusion but with large uncertainties. We find that multiple effects contribute to stochastic acceleration/deceleration, and the process is also likely affected by intermittency in the MRI turbulence. We also discuss the potential of accelerating PeV cosmic-rays in hot accretion flows around supermassive black holes.
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