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-Comparison between models of different resolution: B2, B2l, and B2h (Table 1). It presents the same quantities as in Figure 3.

-Comparison between models of different resolution: B2, B2l, and B2h (Table 1). It presents the same quantities as in Figure 3.

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The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence is reassuring that the magnetic field behavior in comput...

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... The wandering of the magnetic field lines in the turbulent flow allows for many simultaneous events of reconnection and the enlargement of the outflow regions, removing the reconnected flux more efficiently. These two factors result in the reconnection rate being a substantial fraction of the Alfvén speed and independent of the microscopic magnetic resistivity (i.e., independent of the Lundquist number and depending only on the parameters of the turbulence; Lazarian & Vishniac 1999;Kowal et al. 2009;Santos-Lima et al. 2010Eyink et al. 2013;Takamoto et al. 2015;Lazarian et al. 2020). The intrinsic 3D nature of the turbulent reconnection and the particle acceleration that it entails makes the process more efficient than the acceleration in the 2D shrinking plasmoids and X-points that are usually excited by tearing mode instability in PIC (Drake et al. 2006;Hoshino & Lyubarsky 2012;Sironi & Spitkovsky 2014) and in resistive MHD (e.g., Kowal et al. 2011;Puzzoni et al. 2022) simulations. ...
... One may still inquire how the results of the present study would change if we had included an explicit resistivity in the flow. As remarked above, this would affect only the very small scales of the flow, of the order of a few grid cells size (e.g.,Santos-Lima et al. 2010). In the integration of the particles' equation of motion, we accounted only for the ideal electric fields of the magnetic fluctuations that persist in the entire range of the turbulence. ...
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... The application of reconnection diffusion allows us to solve the long-standing problem of magnetic flux removal from accretion disks, the so-called "magnetic braking catastrophe". The essence of the problem is that during circumstellar disk formation, the magnetic fields of molecular clouds are able to transfer the matter momentum from the forming disk on a time scale shorter than the disk formation time. Figure 10, from numerical studies in [81], shows that the problem can be solved if reconnection diffusion is accounted for. The authors plot the results of the simulations of disk formation in a magnetized interstellar medium. ...
... Right: The disk produced via reconnection diffusion in 30,000 years. From[81]. ...
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... The application of reconnection diffusion allows for solving the long-standing problem of magnetic flux removal from accretion disks, the so-called "magnetic braking catastrophe." The essence of the problem is that during circumstellar disk formation, the magnetic field of molecular clouds magnetic field is strong to transfer the matter momentum from the forming disk on a time scale shorter than the disk formation time. Figure 8 from numerical studies in Santos-Lima et al. (2010) show that the problem can be solved if reconnection diffusion is accounted for. ...
... The disk produced via reconnection diffusion in 30 000 years. FromSantos-Lima et al. (2010). ...
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... It is generally believed that the macroscopic transport properties of turbulence are independent of microscopic diffusivities (Spiegel 1971). This is also found to be true for the diffusion of magnetic fields in the presence of turbulence (Lazarian et al. 2004;Santos-Lima et al. 2010;Lazarian 2014). Efficient reconnection acceleration requires a sufficiently high reconnection rate. ...
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... It has been recognized that the magnetic fields in galaxies significantly affect the interstellar medium (ISM). Magnetic fields play a fundamental role in how stars form (Spitzer 1978;Kulsrud & Zweibel 2008;Elmegreen & Scalo 2004;Santos-Lima et al. 2010;Federrath & Klessen 2012). The magnetic field controls the origin and the confinement of cosmic rays in galaxies, high energy particles that play important roles themselves in the galactic environment (Skilling 1971;Casse et al. 2001;Schlickeiser 2002). ...
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... It is generally believed that the macroscopic transport properties of turbulence are independent of microscopic diffusivities (Spiegel 1971). This is also found to be true for diffusion of magnetic fields in the presence of turbulence (Lazarian et al. 2004;Santos-Lima et al. 2010;Lazarian 2014). Efficient reconnection acceleration requires a sufficiently high reconnection rate. ...
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The ubiquitous turbulence in astrophysical plasmas is important for both magnetic reconnection and reconnection acceleration. We study the particle acceleration during fast 3D turbulent reconnection with reconnection-driven turbulence. Particles bounce back and forth between the reconnection-driven inflows due to the mirror reflection and convergence of strong magnetic fields. Via successive head-on collisions, the kinetic energy of the inflows is converted into the accelerated particles. Turbulence not only regulates the inflow speed but also introduces various inflow obliquities with respect to the local turbulent magnetic fields. As both the energy gain and escape probability of particles depend on the inflow speed, the spectral index of particle energy spectrum is not universal. We find it in the range from $\approx 2.5$ to $4$, with the steepest spectrum expected at a strong guide field, i.e. a small angle between the total incoming magnetic field and the guide field. Without scattering diffusion needed for confining particles, the reconnection acceleration can be very efficient at a large inflow speed and a weak guide field.
... The gas and dust that comprise the interstellar medium (ISM) of galaxies is known to be magnetized and in a highly turbulent dynamical state (Goldreich & Sridhar 1995;Elmegreen & Scalo 2004;Lazarian 2007;Krumholz 2014). Magnetohydrodynamic (MHD) turbulence in the ISM plays an important role in the evolution of galaxies, including regulating the motion of cosmic rays (Schlickeiser 2002;Lazarian & Yan 2014;Xu et al. 2016), mediating the destruction and creation of magnetic fields (Lazarian & Vishniac 1999;Santos-Lima et al. 2010), and playing a role in star formation (Larson 1981;Elmegreen & Scalo 2004;Mac Low & Klessen 2004;McKee & Ostriker 2007;Collins et al. 2012;Burkhart et al. 2015Burkhart et al. , 2017Padoan & Haugbølle 2017;Burkhart & Mocz 2019). ...
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... With the exception of very few works (see, e.g., Kowal et al. 2009;Santos-Lima et al. 2010), however, the vast majority of these studies largely overlooks the impact of the numerical method on the simulation results, it scarcely addresses the problem of convergence with respect to grid resolution and it often neglects the effect of a physical resistivity on the evolution of the instabilities. ...
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We present 2D MHD numerical simulations of tearing-unstable current sheets coupled to a population of non-thermal test-particles, in order to address the problem of numerical convergence with respect to grid resolution, numerical method and physical resistivity. Numerical simulations are performed with the PLUTO code for astrophysical fluid dynamics through different combinations of Riemann solvers, reconstruction methods, grid resolutions at various Lundquist numbers. The constrained transport method is employed to control the divergence-free condition of magnetic field. Our results indicate that the reconnection rate of the background tearing-unstable plasma converges only for finite values of the Lundquist number and for sufficiently large grid resolutions. In general, it is found that (for a 2nd-order scheme) the minimum threshold for numerical convergence during the linear phases requires the number of computational zones covering the initial current sheet width to scale roughly as $\sim \sqrt{\bar{S}}$, where $\bar{S}$ is the Lundquist number defined on the current sheet width. On the other hand, the process of particle acceleration is found to be nearly independent of the underlying numerical details inasmuch as the system becomes tearing-unstable and enters in its nonlinear stages. In the limit of large $\bar{S}$, the ensuing power-law index quickly converge to $p \approx 1.7$, consistently with the fast reconnection regime.
... Diffusion of magnetic fields relative to plasma as a result of turbulent reconnection is termed as "reconnection diffusion (RD)" [29,30,31]. It has been applied in the context of star formation and well explains observations (e.g., [42,43,44]). Despite its importance, RD was disregarded in earlier studies of nonlinear turbulent dynamo. ...
... By contrast, when the reconnection diffusion of magnetic field is taken into account, E has a much weaker dependence on ρ. The removal of magnetic flux during compression has been numerically demonstrated by, e.g, [42]. ...
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Small-scale turbulent dynamo is responsible for the amplification of magnetic fields on scales smaller than the driving scale of turbulence in diverse astrophysical media. Most earlier dynamo theories concern the kinematic regime and small-scale magnetic field amplification. Here we review our recent progress in developing the theories for the nonlinear dynamo and the dynamo regime in a partially ionized plasma. The importance of reconnection diffusion of magnetic fields is identified for both the nonlinear dynamo and magnetic field amplification during gravitational contraction. For the dynamo in a partially ionized plasma, the coupling state between neutrals and ions and the ion-neutral collisional damping can significantly affect the dynamo behavior and the resulting magnetic field structure. We present both our analytical predictions and numerical tests with a two-fluid dynamo simulation on the dynamo features in this regime. In addition, to illustrate the astrophysical implications, we discuss several examples for the applications of the dynamo theory to studying magnetic field evolution in both preshock and postshock regions of supernova remnants, in weakly magnetized molecular clouds, during the (primordial) star formation, and during the first galaxy formation.