Fast Collisionless Reconnection Condition and Self-Organization of Solar Coronal Heating

Since the main heating process in the nanoflare model is magnetic reconnection, I first discuss what we have learned about reconnection in the past 20 years or so (see § 2). I argue that, even though we still do not have a complete picture of reconnection, there now appears to be some consensus in the magnetic reconnection community about some of its fundamental aspects. One of the main goals of this paper is to use this emerging knowledge to shed some new light on the old coronal heating problem. In this paper I purposefully adopt a rather conservative approach: I invoke only those very few results that seem to be relatively firmly established and try not to rely on those details of reconnection physics that are still under vigorous debate. Specifically, there is now strong evidence coming from numerous numerical simulations and some laborious laboratory experiments that there are two main modes of reconnection: slow Sweet-Parker reconnection taking place in collisional plasmas where classical resistive MHD applies; and fast Petscheklike reconnection in collisionless plasmas (in § 2.1). The transition between these two regimes seems to be rather sharp. An approximate condition for this transition can be formulated as a relationship between the global length L of the reconnecting system and the electron collisional mean-free path inside the layer, λ e,mfp (see § 2.2). Furthermore, this condition can be cast in terms of the plasma density n, the reconnecting magnetic field B 0 , and L; namely, one can define a critical density n c (L, B 0 ) below which reconnection switches to the fast regime. In the strong-guide field case, B z ≫ B 0 , the condition is modified; namely, the critical density for transition to fast reconnection is suppressed by a factor of order (B z ≫ B 0 ) 2/3 (see § 2.4). In § 2.5 I address various alternative ideas and caveats that may complicate the above simple picture.

I then apply these results to the active solar corona (in § 3), viewed withing the nanoflare model. My main point here is that the corona should be regarded as a selfregulating machine keeping itself (in a statistical sense) around marginal collisionality. This conclusion comes from the interplay between the way the plasma density controls reconnection via the above collisionless reconnection transition, and the way the coronal magnetic energy release due to reconnection in turn controls the ambient gas density via chromospheric evaporation. The coronal heating process is then highly intermittent and inhomogeneous; it can be thought of a sequence of characteristic energy-circulation cycles that occur simultaneously in a broad range of spatial, temporal, and energy scales. Each such elementary cycle consists of several phases: (1) a fast reconnection event (a nanoflare) causing (2) an evaporation episode filling the loop with hot dense plasma, followed by (3) a longer period during which the magnetic stresses build up and the plasma den-sity goes down due to slow radiative cooling (and thermal conduction). It is the collisionless reconnection condition that makes this scenario (in particular, the last phase) possible. Indeed, an important point here is that, even if a current sheet is formed, it will stay in the slow Sweet-Parker state if the density is large enough. This will continue for some time, until the reconnecting magnetic field becomes strong enough and/or the ambient plasma density becomes low enough for the system to transition to the fast collisionless reconnection regime. This enables a non-trivial amount of free magnetic energy to be accumulated before a sudden release. This energy amount, along with the characteristic time-scale between nanoflares and the characteristic coronal density, is determined, statistically, by the balance between the rate at which current sheets are created and amplified by the photospheric footpoint motions and the efficiency of radiative cooling. The collisionless reconnection condition plays a key role in this process as a mediator and ultimately governs the statistical distribution of the coronal reconnection events (flares).

In § 4, I discuss some of the open questions that, in my view, need to (and can) be addressed in the near future, in order to see whether the physical picture put forward in this paper is correct and what modifications should be made to improve it. This section is mostly targeted towards researchers doing numerical simulations of reconnection and also to experimentalists and observers. Finally, I present my conclusions in § 5.

I also would like to make a clarifying remark about the terms “collisional” and “collisionless” that will be used many times throu

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