ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: perpendicular to the reconnection plane, and 0 ε 1 the peakedness parameter of the current concentration in the magnetic islands. Subsequent numerical simulations have shown that, for a large range of S δ , the coalescence growth rate is much greater than the tearing growth rate (Pritchett Wu 1979 ) and that it depends critically on the value for ε (Bhattacharjee, Brunel Tajima 1983 ), linear tearing corresponding to ε = 0. The coalescence instability is characterized by two time-scales associated with its distinct phases (Kliem 1995 ). During the ideal phase, the current loops approach each other on a hydromagnetic time-scale, whereby the length-scale is given by the separation distance of paired current loops λ C , with δ ≲ λ C ≲ λ max . In general, , yet no magnetic energy is dissipated in the process. During the resistive phase, when the current loops merge, ‘anti-reconnection’ occurs in between the approaching islands. The reconnection rate is enhanced by the external driving forces of the converging current loops, such that in general . Moreover, for strongly peaked current concentrations (ε → 1), we have . For cm, the coalescence time-scale becomes comparable to the magnetospheric light crossing time, i.e. ms. Coalescence following tearing converts the bulk of the free magnetic energy in the current sheet, such that the island growth phase may act as mere prelude to the explosive energy release of merging current loops (Leboeuf, Tajima Dawson 1982 ). Its rapid development and ability to convert a significant fraction of magnetic energy argue in favour of coalescence, rather than tearing, as an explanation for the impulsive phase of flares (Tajima, Brunel Sakai 1982 ; Sakai Ohsawa 1987 ; Tajima et al. 1987 ; Kliem 1995 ; Schumacher Kliem 1997 ). The observed giant flare emission may therefore be a proxy of the non-linear, rather than the linear, tearing phase. Furthermore, for higher values of and σ m , a non-linear process known as ‘impulsive bursty reconnection’ may occur, whereby a cycle of slow tearing, rapid coalescence, current sheet thinning, and further secondary tearing (i.e. the plasmoid instability) at an increased rate repeats successively (Leboeuf et al. 1982 ; Priest 1985 ; Uzdensky, Loureiro Schekochihin 2010 ; Takamoto 2013 ). Consequently, energy is released during separate coalescence events in a fragmentary and quasi-periodic manner. This process is advanced to explain the periodic temporal fine structure of HXR emission and coherent drifting radio bursts associated with discrete (bidirectional) electron beams observed during the impulsive phase of solar flares (Aschwanden et al. 1995 ; Kliem, Karlicky Benz 2000 ; Karlicky 2004 ). QPOs of ν ∼ 10 2 Hz, which might be associated with separate energy injections, have also been detected during the initial phases of the magnetar giant flares: see Section 2.2 . These distinct energy surges may be interpreted as quasi-periodic peaks in coalescence rates, 13 resulting from