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Register a new userStochastic acceleration by multi-island contraction during turbulent magnetic reconnection
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The acceleration of charged particles in magnetized plasmas is considered during turbulent multi-island magnetic reconnection. The particle acceleration model is constructed for an ensemble of islands which produce adiabatic compression of the particles. The model takes into account the statistical fluctuations in the compression rate experienced by the particles during their transport in the acceleration region. The evolution of the particle distribution function is described as a simultaneous first and second-order Fermi acceleration process. While the efficiency of the first-order process is controlled by the average rate of compression, the second order process involves the variance in the compression rate. Moreover, the acceleration efficiency associated with the second-order process involves both the Eulerian properties of the compression field and the Lagrangian properties of the particles. The stochastic contribution to the acceleration is non-resonant and can dominate the systematic part in the case of a large variance in the compression rate. The model addresses the role of the second-order process, how the latter can be related to the large-scale turbulent transport of particles and explains some features of the numerical simulations of particle acceleration by multi-island contraction during magnetic reconnection.
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The mechanism that accelerates particles to the energies required to produce the observed high-energy impulsive emission in solar flares is not well understood. Drake et al. (2006) proposed a mechanism for accelerating electrons in contracting magnetic islands formed by kinetic reconnection in multi-layered current sheets. We apply these ideas to sunward-moving flux ropes (2.5D magnetic islands) formed during fast reconnection in a simulated eruptive flare. A simple analytic model is used to calculate the energy gain of particles orbiting the field lines of the contracting magnetic islands in our ultrahigh-resolution 2.5D numerical simulation. We find that the estimated energy gains in a single island range up to a factor of five. This is higher than that found by Drake et al. for islands in the terrestrial magnetosphere and at the heliopause, due to strong plasma compression that occurs at the flare current sheet. In order to increase their energy by two orders of magnitude and plausibly account for the observed high-energy flare emission, the electrons must visit multiple contracting islands. This mechanism should produce sporadic emission because island formation is intermittent. Moreover, a large number of particles could be accelerated in each magnetohydrodynamic-scale island, which may explain the inferred rates of energetic-electron production in flares. We conclude that island contraction in the flare current sheet is a promising candidate for electron acceleration in solar eruptions.
A numerical study of magnetic reconnection in the large-Lundquist-number ($S$), plasmoid-dominated regime is carried out for $S$ up to $10^7$. The theoretical model of Uzdensky {it et al.} [Phys. Rev. Lett. {bf 105}, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is $ ormEeffsim 0.02$ independently of $S$ for $Sgg10^4$. The plasmoid flux ($Psi$) and half-width ($w_x$) distribution functions scale as $f(Psi)sim Psi^{-2}$ and $f(w_x)sim w_x^{-2}$. The joint distribution of $Psi$ and $w_x$ shows that plasmoids populate a triangular region $w_xgtrsimPsi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic monster plasmoids with $w_xsim 10$% of the system size are shown to emerge in just a few Alfven times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.
Plasmoids -- magnetized quasi-circular structures formed self-consistently in reconnecting current sheets -- were previously considered to be the graveyards of energetic particles. In this paper, we demonstrate the important role of plasmoids in shaping the particle energy spectrum in relativistic reconnection (i.e., with upstream magnetization $sigma_{rm up} gg 1$). Using two dimensional particle-in-cell simulations in pair plasmas with $sigma_{rm up}=10$ and $100$, we study a secondary particle energization process that takes place inside compressing plasmoids. We demonstrate that plasmoids grow in time, while their interiors compress, amplifying the internal magnetic field. The magnetic field felt by particles injected in an isolated plasmoid increases linearly with time, which leads to particle energization as a result of magnetic moment conservation. For particles injected with a power-law distribution function, this energization process acts in such a way that the shape of the injected power law is conserved, while producing an additional non-thermal tail $f(E)propto E^{-3}$ at higher energies followed by an exponential cutoff. The cutoff energy, which increases with time as $E_{rm cut}proptosqrt{t}$, can greatly exceed $sigma_{rm up} m_e c^2$. We analytically predict the secondary acceleration timescale and the shape of the emerging particle energy spectrum, which can be of major importance in certain astrophysical systems, such as blazar jets.
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.
The out-of-plane magnetic field, generated by fast magnetic reconnection, during collisionless, stressed $X$-point collapse, was studied with a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code, using both closed (flux conserving) and open boundary conditions on a square grid. It was discovered that the well known quadrupolar structure in the out-of-plane magnetic field gains four additional regions of opposite magnetic polarity, emerging near the corners of the simulation box, moving towards the $X$-point. The emerging, outer, magnetic field structure has opposite polarity to the inner quadrupolar structure, leading to an overall octupolar structure. Using Amperes law and integrating electron and ion currents, defined at grid cells, over the simulation domain, contributions to the out-of-plane magnetic field from electron and ion currents were determined. The emerging regions of opposite magnetic polarity were shown to be the result of ion currents. Magnetic octupolar structure is found to be a signature of $X$-point collapse, rather than tearing mode, and factors relating to potential discoveries in experimental scenarios or space-craft observations are discussed.
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