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Register a new userOblique tearing mode instability: guide field and Hall effect
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The tearing mode instability is one important mechanism that may explain the triggering of fast magnetic reconnection in astrophysical plasmas such as the solar corona and the Earths magnetosphere. In this paper, the linear stability analysis of the tearing mode is carried out for a current sheet in the presence of a guide field, including the Hall effect. We show that the presence of a strong guide field does not modify the most unstable mode in the two-dimensional wave vector space orthogonal to the current gradient direction, which remains the fastest growing parallel mode. With the Hall effect, the inclusion of a guide field turns the non-dispersive propagation along the guide field direction to a dispersive one. The oblique modes have a wave-like structure along the normal direction of the current sheet and a strong guide field suppresses this structure while making the eigen-functions asymmetric.
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Magnetic reconnection occurs when two plasmas having co-planar but anti-parallel magnetic fields meet. At the contact point, the field is locally annihilated and the magnetic energy can be released into the surrounding plasma. Theory and numerical modelling still face many challenges in handling this complex process, the predictability of which remains elusive. Here we test, through a laboratory experiment conducted in a controlled geometry, the effect of changing the field topology from two-dimensional to three-dimensional. This is done by imposing an out-of-plane (guide) magnetic field of adjustable strength. A strong slowing down or even halting of symmetric reconnection is observed, even for a weak guide-field. Concomitantly, we observe a delayed heating of the plasma in the reconnection region and modified particle acceleration, with super-Alfvenic outflows ejected along the reconnection layer. These observations highlight the importance of taking into account three-dimensional effects in the many reconnection events taking place in natural and laboratory environments.
Results of the first validation of large guide field, $B_g / delta B_0 gg 1$, gyrokinetic simulations of magnetic reconnection at a fusion and solar corona relevant $beta_i = 0.01$ and solar wind relevant $beta_i = 1$ are presented, where $delta B_0$ is the reconnecting field. Particle-in-cell (PIC) simulations scan a wide range of guide magnetic field strength to test for convergence to the gyrokinetic limit. The gyrokinetic simulations display a high degree of morphological symmetry, to which the PIC simulations converge when $beta_i B_g / delta B_0 gtrsim 1$ and $B_g / delta B_0 gg 1$. In the regime of convergence, the reconnection rate, relative energy conversion, and overall magnitudes are found to match well between the PIC and gyrokinetic simulations, implying that gyrokinetics is capable of making accurate predictions well outside its regime of formal applicability. These results imply that in the large guide field limit many quantities resulting from the nonlinear evolution of reconnection scale linearly with the guide field.
Magnetic reconnection may be the fundamental process allowing energy stored in magnetic fields to be released abruptly, solar flares and coronal mass ejection (CME) being archetypal natural plasma examples. Magnetic reconnection is much too slow a process to be efficient on the large scales, but accelerates once small enough scales are formed in the system. For this reason, the fractal reconnection scenario was introduced (Shibata and Tanuma 2001) to explain explosive events in the solar atmosphere: it was based on the recursive triggering and collapse via tearing instability of a current sheet originally thinned during the rise of a filament in the solar corona. Here we compare the different fractal reconnection scenarios that have been proposed, and derive generalized scaling relations for the recursive triggering of fast, `ideal - i.e. Lundquist number independent - tearing in collapsing current sheet configurations with arbitrary current profile shapes. An important result is that the Sweet-Parker scaling with Lundquist number, if interpreted as the aspect ratio of the singular layer in an ideally unstable sheet, is universal and does not depend on the details of the current profile in the sheet. Such a scaling however must not be interpreted in terms of stationary reconnection, rather it defines a step in the accelerating sequence of events of the ideal tearing mediated fractal cascade. We calculate scalings for the expected number of plasmoids for such generic profiles and realistic Lundquist numbers.
In this paper we study the scaling relations for the triggering of the fast, or ideal, tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio scalings at which the growth rates become independent of the Lundquist number $S$, in terms of the dependence of the $Delta$ parameter on the wavenumber $k$ of unstable modes. The scaling $Delta(k)$ with $k$ at small $k$ is found to categorize different equilibria broadly: the critical aspect ratios may be even smaller than $L/a sim S^{alpha}$ with $alpha=1/3$ originally found for the Harris current sheet, but there exists a general lower bound $alphage1/4$.
Linear gyrokinetic simulations covering the collisional -- collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures, and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta.
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