Fast Magnetic Reconnection and Spontaneous Stochasticity

Abstract

Magnetic field lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic-flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfvén flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic," so that infinitely many magnetic field lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive at the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity," but of the field lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian & Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth δ i is much smaller than the turbulent integral length or injection-scale L i .

Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere

“…Miller et al 1996;Larosa et al 1996;Cho & Lazarian 2006;Cargill & Vlahos 2009;. Turbulence results in field line stochasticity and fast reconnection in multiple smallscale current sheets (Lazarian & Vishniak 1999;Eyink et al 2011). Hence, the presence of small-scale turbulence, in principle, could drastically change characteristics of the electric field in the model and lead to a different picture of particle acceleration.…”

Mass entrainment and turbulence-driven acceleration of ultra-high energy cosmic rays in Centaurus A

“…Assuming fast (i.e. independent of resistivity) reconnection, the reconnection velocity υ rec is taken of the order of Alfvén speed (Lazarian & Vishniac 1999;Eyink et al 2011), υ rec ∼ υ A ∼ 0.081c. Under ideal circumstances, the fastest possible reconnection acceleration timescale is τ rec = r g /η υ A (de Gouveia dal Pino & Lazarian 2005), where η is the reconnection efficiency factor.…”

“…4.3.3. Lazarian & Vishniac (1999) have shown that most of the energy in the reconnection is transferred into turbulent motions, and in fact, the process of the reconnection is an intrinsic part of the MHD turbulent cascade (see also Eyink et al 2011). Given that the sizes of the reconnection regions are much 12 The injection energy depends on mass and charge: protons can be picked up by Alfvén waves at lower energies than electrons, and heavier particles have generally lower resonance thresholds than lighter ones in the (here adequate) weak scattering regime (e.g.…”

Simulations reveal fast mode shocks in magnetic reconnection outflows

“…The first occurs when the ion inertial length is larger than the magnetohydrodynamic (MHD) Sweet-Parker resistive length, facilitating current driven plasma instabilities that enhance dissipation near the X-point [3][4][5]. A second occurs in the context of turbulent MHD, where the global reconnection rate is enhanced by the contemporaneous action of many small scale sites [6][7][8]. A third path to fast reconnection occurs for a long enough laminar MHD current sheet that becomes tearing mode unstable and again multiple small scale reconnection sites acting together enhance the rate.…”