Exact solutions for reconnective annihilation in magnetic configurations with three sources

Abstract

Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and in general they describe a process of reconnective annihilation in a curved current layer with non vanishing magnetic field. In the derivation of the solutions the ideal case with vanishing resistivity and electric field is considered first and then generalized to include the effects of finite electric field and resistivity. Particular attention is devoted to the analysis how the latter ones influence the presence of singularities in the solutions. In this respect comparisons with the purely two-dimensional case are made and the resulting important differences are highlighted. Finally, applications of the solutions for modeling an important class of solar flares are discussed.PACS numbers: 52.30, 96.60.R

Dynamic Three‐dimensional Reconnection in a Separator Geometry with Two Null Points

“…It has been shown that the system can be analyzed in terms of the superposition of transient disturbances onto a background field defining the two nulls. This result generalizes the previous Cartesian description of transient reconnecting disturbances in a three-dimensional single null geometry (Craig & Fabling 1998), as well as steady state cylindrical merging solutions (Watson & Craig 2002;Tassi et al 2003).…”

“…In what follows we develop a resistive, time-dependent model for reconnection occurring in a magnetic field in cylindrical geometry, where either one or two three-dimensional null points are present. This extends and generalizes the work of Watson & Craig (2002), who made a preliminary investigation of similar configurations in a steady state regime (see also Tassi et al 2003), and it provides the possibility of reconnection at curved current sheets and also separator current sheets. Although we consider here only resistive nonideal effects, we do not expect that the introduction of further nonideal effects would alter the qualitative results significantly.…”

The plasmoid instability in a confined solar flare

“…For example, in models of EFs (MacTaggart & Haynes 2014), in studies of reconnection at null points (Wyper & Pontin 2014a), in fly-by experiments (Parnell & Galsgaard 2004;, in magnetospheric studies (Dorelli et al 2007; and in an early model of flaring in Sweet (1958) (see also Longcope 2005, and references therein for a detailed topological description of this last work). Interestingly, 2.5D resistive MHD equilibria (Watson & Craig 2002;Tassi et al 2003) in cylindrical coordinates have been found with a similar structure, including the presence of a separator. The existence of such solutions, combined with the frequency with which this magnetic structure occurs in different situations, suggests that the model representation (in Figure 1) of this pre-flare active region described in Simões et al (2015a,b) is a general magnetic structure.…”

New classes of exact solutions for magnetic reconnective annihilation

“…A fundamental difference between the cases λ = 0 and λ = 0 is that for the former the ideal solutions for A 1 and ψ 1 provided by (11) and ( 13) are also exact solutions of the complete resistive equations ( 7) and (10). For λ = 0, however, this is not the case.…”

“…After the early works of Parker [3], Sweet [4] and Petschek [5] considerable effort has been made to improve the theory of magnetic reconnection with the help of exact analytical models for reconnective annihilation in Cartesian coordinates [6,7,8]. More recently exact solutions for magnetic reconnection in curvilinear coordinates have been presented [9,10,11]. Some features of these solutions make them particularly interesting for modeling a large class of solar flares.…”