Resistive scales for collisionless reconnection in space plasma

We derive restrictions on collisional reconnection under the conditions in near-Earth space. The arguments are based on the precise definition and estimates of the resistive scale Lη at the ion inertial site in collisionless reconnection, i.e. in the so-called ‘ion diffusion region’ which is the region of Hall-current flow. Introduction. – Collisional magnetic reconnection is fast only in insulators. In vacuum, for instance, magnetic fields can reorder arbitrarily. Reconnection in a plasma of finite conductivity is a slow process, in contrast. In ideally conducting media, reconnection should be inhibited according to the frozen-in condition E = −v ×B which is imposed on the medium by Lorentz-invariance and acts on the particles of charge q, velocity v and kinetic energy W in magnetic B and electric E fields. The frozen-in condition implies conservation of the magnetic moments μ = W⊥/|B| of the charged particles tying them to the magnetic field. Undisputable observations in situ the collisionless (and therefore highly if not ideally conducting) space plasma have, on the other hand, proven for long time that reconnection is going on not only here as well but in addition at a very fast rate, indicating that reconnection is a kinetic process. Such observations refer to the magnetopause [1], Earth’s magnetotail [2–4] and most recently the solar wind [5]. Being fast means that reconnection proceeds on the ion or electron plasma spatial and time scales. Such observations have lead to attribute reconnection to various processes believed of having the potential to break the frozen-in condition by referring to the various different terms in the generalized Ohm’s law [6–8] in plasma: generation of anomalous resistivity [8–10], extra-diagonal electron pressure terms [11], large-amplitude whistlers [12–14], the Hall-effect [2,15–18], chaotic motions of ions and electrons [19] in the current sheet separating oppositely directed magnetic fields, hard driving [20], magnetic-field (a)Visiting the International Space Science Institute, Bern, Switzerland aligned electric fields, ponderomotive forces [8], plasma composition etc. None of these processes has so far provided a satisfactory explanation of the occurrence of fast reconnection in ideally conducting plasma. Numerical simulations in two and three dimensions have, on the other hand, shown that reconnection indeed occurs under many different initial conditions. In particular, it also occurs in the complete absence of the Hall effect [21] in pair plasma. However, in all these simulations reconnection is ignited externally in some particular way and is thus imposed on the plasma. For correctly chosen settings it then evolves and keeps itself going, allowing for the study of many secondary processes like magnetic topologies, generation of electric fields, current breakdown, wave excitation, anomalous diffusion [9], plasmoids, electron hole production [22, 23], plasma jetting, and particle acceleration [24–26]. In this way numerical simulations in fluid, hybrid, kinetic Vlasov and full-particle codes as well as in two and three spatial dimensions have contributed substantially to understanding the properties of ongoing reconnection. They have not explained, however, the fundamental problem of why reconnection occurs under collisionless conditions. Fast reconnection in collisionless plasma indeed requires breaking the frozen-in condition. Here, on discussing the role of the so-called resistive scale, we investigate the conditions under which collisional reconnection in a warm dilute space plasma can be expected to occur, i.e. the conditions when it alone is capable of breaking the frozen-in condition. The resistive scale. – On the scales of reconnection space plamas are (almost or nearly) collisionless. These p-1 ar X iv :0 90 2. 01 23 v1 [ ph ys ic s. sp ac eph ] 1 F eb 2 00 9