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Abstract:

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Abstract:

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as$\tilde {t}^{-1}$, the number of islands decreases as$\tilde {t}^{-1}$and the averaged area of islands grows as$\tilde {t}$, where$\tilde {t}$is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Abstract:

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube (FT), full-flux-surface (FFS), and radially global (RG) domains. Two problems are studied: the linear relaxation of zonal flows (ZFs) and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The ZF relaxation properties obtained in different FTs are found to differ with each other and with the RG result, except for sufficiently long FTs, in general. The FT length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different FTs provide different results, but the discrepancy between them diminishes with increasing FT length. FFS and FT simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the FT and the FFS domains. RG simulations provide results close to the FFS ones. The radial scale of unstable ITG modes is studied in global and FT simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found.