Numerical simulations of highly nonlinear magnetic reconnection provide evidence of ultrathin current microsheets. These small-scale sheets are formed by strong exhaust jets from a primary large-scale current layer. The overall size of the secondary microsheet is determined by the thickness of the primary sheet. Preliminary scalings show that the thickness of the microsheet varies linearly with the plasma resistivity. This scaling suggests that microsheets may provide fast reconnection sites in magnetically complex plasmas such as the solar corona and planetary magnetospheres

Craig, Ian J.D.

Watson, P.G.

English

Name not available

Fast magnetic reconnection via jets and current microsheets

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L57The Astrophysical Journal, 590:L57–L60, 2003 June 10 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.FAST MAGNETIC RECONNECTION VIA JETS AND CURRENT MICROSHEETSP. G. WatsonCenter for Magnetic Reconnection Studies, Institute for Fusion Studies, Department of Physics, University of Texas at Austin,1 University Station C1600, Austin, Texas 78712; pgwatson@kato.ph.utexas.eduandI. J. D. CraigDepartment of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand; math0097@waikato.ac.nzReceived 2003 March 28; accepted 2003 April 29; published 2003 May 7ABSTRACTNumerical simulations of highly nonlinear magnetic reconnection provide evidence of ultrathin current mi-crosheets. These small-scale sheets are formed by strong exhaust jets from a primary large-scale current layer.The overall size of the secondary microsheet is determined by the thickness of the primary sheet. Preliminaryscalings show that the thickness of the microsheet varies linearly with the plasma resistivity. This scaling suggeststhat microsheets may provide fast reconnection sites in magnetically complex plasmas such as the solar coronaand planetary magnetospheres.Subject headings: galaxies: jets — MHD — plasmas — Sun: flares — Sun: X-rays, gamma rays1. INTRODUCTIONMagnetic reconnection is believed to play an important rolein a variety of explosive energy-release mechanisms observedin astrophysical and laboratory plasmas, for example, solarflares, geomagnetic substorms, and tokamak disruptions. Inmost studies of magnetic reconnection, the merging is poweredby a large-scale velocity field that washes magnetic plasmatoward a localized diffusion region (see Priest & Forbes 2000).A critical feature of the mechanism is the collapse of the mag-netic field to small length-scales. This collapse is halted by theplasma resistivity h, and although h is very small for typicalastrophysical plasmas, it is thought to determine both the speedand strength of the magnetic energy release. Accordingly, re-connection theory has focused on the dependence of the merg-ing rate on the plasma resistivity. It is commonly believed thatthe energy release in many space and laboratory plasmas re-quires a “fast” reconnection mechanism in which the recon-nection rate is independent of resistivity.The purpose of this Letter is to point out that the exhaustregion of a large-scale current layer can provide the externalsource for small-scale secondary reconnection events. Numer-ical simulations show that ejecta from the primary sheet actrather like a turbo mechanism, enhancing dissipation by sup-plying high-pressure collimated jets to sustain the microsheet.Although the primary sheet has an overall length comparableto the size of the computational domain, the microsheet is verymuch smaller, its length being controlled by the narrow exhaustjet of the primary current layer. Such microsheets have thepotential to act as extremely short-lived localized sites of en-ergy release (e.g., X-ray–bright points) in magnetically com-plex plasmas such as the solar corona.The exhaust jets themselves are also of some interest. In oursimulations, the jets emerge from an initially global flow viathe action of the magnetic field. The mechanism involves theformation of a magnetic slingshot that accelerates fluid fromthe end of a reconnecting current sheet into a strongly colli-mated flow. This mechanism could have an important role toplay in the formation of astrophysical jets observed in activegalactic nuclei and protostellar objects, and it contrasts some-what with other proposed MHD acceleration scenarios (e.g.,Blandford & Payne 1982), where the magnetic slingshot effectis generated by rotation.In § 2, we describe planar simulations that lead to the for-mation of current microsheets. We also discuss the scalingswith resistivity of the primary and secondary current layers.Section 3 summarizes our findings.2. THE RECONNECTION SIMULATION2.1. The Numerical ExperimentWe use the planar incompressible code of Craig & Watson(1999), which includes the effects of resistivity h and viscosity, to perform the numerical experiments on the doubly periodicndomain . The code employs stream and flux(1, 1)# (1, 1)function representations for the velocity and magnetic fields,, , and has been checkedˆ ˆv(x, y, t)p f z B(x, y, t)p w zby Heerikhuisen, Craig, & Watson (2000) and Watson & Craig(2001) against a family of analytic reconnection models (Craig &Henton 1995; Craig & Fabling 1996; Craig & Watson 2000). Thepresent results, obtained using a fourth-order accurate version ofthe program, have also been reproduced using a spectral code andthe compressible FLASH code (Fryxell et al. 2000).Simulations involving microsheets begin with the initialconditionfp a sin (px) sin (py)/p, a 1 0, (1)wp e cos (px)/p. (2)This system comprises four counterrotating flow cells and aninitially one-dimensional vertical magnetic field. Given the pe-riodic boundary conditions and the nature of the flow, a two-dimensional field structure soon develops and magnetic recon-nection ensues at a periodic array of X-type magnetic nullslocated at (x, y)p (0,1) , . The reconnection(x, y)p (1, 0)proceeds via an initial implosion phase, during which the mag-netic field is swept toward the nulls and amplified formingquasi–one-dimensional current sheets.L58 JETS AND CURRENT MICROSHEETS Vol. 590Fig. 1.—Velocity streamlines and fieldlines at the time of maximum current in the microsheet. The top row of plots shows the flow and field over the entiredomain, while the bottom row shows a blow-up of these same profiles in the vicinity of the microsheet located at the origin.Fig. 2.—Surface plot of the current of the run shown in Fig. 1. The primarysheet is still evident, running down the middle of the domain (and along theedges of the box). The secondary microsheet appears as a sharp spike at thecenter of the box (and at the four corners).2.2. The Primary and Secondary Current SheetsThe properties of the primary current sheet follow the theorydescribed by Craig & Watson (1999). There are two regimesto consider. In the presaturation regime, the magnetic pressurein the sheet is relatively weak, and so it can be intensified bysystematically reducing the plasma resistivity h. In this phase,the reconnection rate is fast (Sonnerup & Priest 1975; Craig& Henton 1995) and the properties of the solution scale inaccordance with analytic predictions (Craig & Watson 1999).A value of h is reached, however, when the back pressure ofthe field in the current sheet is sufficient to stall the backgroundflow. The sheet “saturates,” and the solution appears to entera slow reconnection phase, superficially resembling Sweet-Parker. In reality the saturated regime is very complicated, andthere is some evidence for the emergence of disparate spatialscales and temporal chaos (Craig & Watson 1999).It is the exhaust of reconnected flux from the primaries thatpowers the secondary microsheets. The ejected horizontal field,advected by strong exhaust jets, generates secondary sheets atand at the four corners of the box. In the pre-(x, y)p (0, 0)saturation regime, the secondary sheets resemble scaled downversions of the primaries. The secondary sheets convert thehorizontal field back into vertical field and in doing so generatetertiary current layers at the location of the old primaries. Thewhole process then repeats itself and reconnection proceeds ina regular periodic cycle, with energy and flux being liberatedat each reconnection event.This picture changes dramatically once the primaries enterthe saturation phase. The secondary sheets now change theircharacter in response to the increasingly narrow collimated jetsthat emerge from the primary, becoming current “microsheets.”The periodic nature of the reconnection also disappears, andthe temporal behavior becomes increasingly chaotic.A typical simulation is shown in Figure 1. The parametervalues for this run are , , and .ap 1 ep 0.3 hp np 0.0001The top two plots show the flow streamlines and magneticfieldlines over the entire box at the time of maximum currentin the secondary. In these plots, the primary sheets are stillclearly visible as accumulations of field around the nulls at thetop, bottom, and sides of the domain. That saturation has oc-curred is evidenced by the fact that the flow has stagnated inthe vicinity of the primary sheets. The small secondary sheetis just visible at the center of the domain in the magnetic fieldplot. The bottom two plots show close-ups of the flow andfield in the vicinity of the microsheet. Of particular note hereare the strong collimated vertical jets evident in the flow profile.Figure 2 shows the corresponding surface plot of the currentdensity. While the large-scale primary sheets are still visible,No. 1, 2003 WATSON & CRAIG L59Fig. 3.—Plot of the maximum current vs. time. The current in the primarypeaks around , while the sharp feature near relates to thetp 1.2 tp 1.4extremely intense and short-lived microsheet.Fig. 4.—Scalings of various sheet characteristics vs. resistivity for both the primary (left) and secondary (right) sheets. The top row of diagrams shows thescaling of the maximum current in the sheet with h. The bottom row shows the scaling of the sheet widths.they are overshadowed by the sharp, almost spikelike currentfeatures associated with the microsheets.Figure 3 shows the evolution of the maximum current overthe domain with time. The initial implosion, which occurs overa timescale of 1.2 Alfve´n times, results in the primary sheet,while a second, much faster localization results in the strongsecondary current spike near . The timescales involvedtp 1.4in the development and lifetime of the secondary sheet aremuch shorter than those of the primary.2.3. Resistive ScalingsIn Figure 4, we show key diagnostics for the primary andsecondary sheets. The top row of diagrams shows how the max-imum current in the two sheets scales with resistivity. The firstplot (for the primary) can be explained by the scaling argumentspresented in Craig & Watson (1999). In the presaturation regime( ), the reconnection is fast and the maximum currenth  0.002scales as h1. Once the field in the sheet saturates ( ),h  0.002the reconnection slows and the solution enters a slow Sweet-Parker regime in which the maximum current scales as h1/2.The maximum current in the secondary sheet (Fig. 4, top right)also undergoes changes when the primary sheet saturates. Ofparticular note is the fact that after saturation, the maximumcurrent in the secondary grows significantly faster than h1.The bottom row shows the scaling of the primary and sec-ondary sheet widths with h. The width of the primary sheet(Fig. 4, bottom left) scales as h1/2 in the presaturation phase,as expected. It is a remarkable fact that this scaling carries overinto the saturation regime. In contrast, the secondary sheetundergoes a change near , where the primary sheeth  0.002saturates. After saturation, the width appears to obey an h1scaling law, indicating that the secondary sheet is very muchthinner than the primary.The scalings of the secondary sheet are enticing. In the sat-uration regime (of the primary), the reconnection rate Ep, where J is the current density at the null, is superfast (i.e.,hJit scales as a weak inverse power of h). Since the sheet fieldand the exhaust velocity in the secondary are still increasingwith reductions in h, we cannot expect this behavior to continueL60 JETS AND CURRENT MICROSHEETS Vol. 590indefinitely. However, given that the width of the secondarysheet scales as h, the current can still behave as h1 even aftersaturation of the secondary field. The implication is that thereconnection rate will eventually switch from superfast to fast(i.e., hJ will become independent of h). The reconnection ratein the microsheet is then fast for arbitrarily small values of theplasma resistivity.These scalings are reminiscent of Petschek’s reconnectionmechanism (Petschek 1964). Although there may be some ev-idence that MHD shocks are forming (see the blow-up regionsin Fig. 1), the microsheets display several differences to thesimple Petschek model: the angle of the field separatrices isvery small; the sheet aspect ratio increases with reductions inresistivity (there are indications that the aspect ratio is becomingfixed, but we have not been able to investigate small enoughvalues of h to confirm this); and there is no appreciable ac-cumulation of current along the field separatrices. However, itis possible that we are observing the first stages of a transitionfrom Sweet-Parker to Petschek reconnection.Finally, we should emphasize that the results presented hereare robust to the addition of small-scale turbulent disturbancesand insensitive to whether the reconnection is head-on (as de-scribed in this Letter) or appreciably sheared. This robustness tothe breaking of the fourfold symmetry of the simulations pre-sented here suggests that microsheets may occur in quite generalsettings. Indeed, here we have relied on the collision of two jetsto generate a microsheet, but it seems likely that even the highlyasymmetric configuration of one jet colliding with a stationarymagnetic field might give rise to a microsheet. The emergenceof microsheets, however, is sensitive to tuning the relative mag-nitudes of the initial flow and field strengths a and e.3. DISCUSSION AND CONCLUSIONSThe simulations presented here suggest that magneticallycomplex regions such as the corona and the magnetospheremay, at least potentially, possess a hierarchy of current-sheetstructures. The primary current layers produce narrow Alfve´nicexhaust jets that feed the secondary current microsheets andso on. Although the bulk of the energy release probably occursin the primary structures, microsheets powered by primaryejecta could well account for localized hot spots within theplasma (e.g., X-ray–bright points associated with solar flares).This idea of a hierarchy of small-scale secondary sheet struc-tures is not new. Biskamp (1993), in a series of steady statesimulations, also observed the formation of secondary sheets.However, as his secondary sheets are self-similar copies of themain sheet, and given that they are also aligned parallel to it,their generation mechanism must be somewhat different fromthe current microsheets found in our simulations.Perhaps the key observation is the very small time and length-scales associated with the microsheets. The present results implythat transient magnetic reconnection may occur over a smallfraction of an Alfve´n time in a small-scale sheet whose thicknessscales as h1, characteristic of fast reconnection solutions.Finally, our results suggest that under certain circumstances,magnetic reconnection events may act as sources of stronglycollimated jets. Other MHD jet formation models have beenproposed that rely on rotation as a global acceleration mechanism(Blandford & Payne 1982), but reconnection-driven jets mayprovide an attractive alternative for small-scale jet generation.We are grateful to Sean Oughton for confirming these resultsusing a spectral code. This work was supported by the USDepartment of Energy Contract DE-FC02-01ER-54652 underthe auspices of the program for Scientific Discovery throughAdvanced Computing.REFERENCESBiskamp, D. 1993, Nonlinear Magnetohydrodynamics (Cambridge: CambridgeUniv. Press)Blandford, R. D., & Payne, D. G. 1982, MNRAS, 199, 883Craig, I. J. D., & Fabling, R. B. 1996, ApJ, 462, 969Craig, I. J. D., & Henton, S. M. 1995, ApJ, 450, 280Craig, I. J. D., & Watson, P. G. 1999, ApJ, 516, 924———. 2000, Sol. Phys., 194, 251Fryxell, B., et al. 2000, ApJS, 131, 273Heerikhuisen, J., Craig, I. J. D., & Watson, P. G. 2000, Geophys. Astrophys.Fluid Dyn., 93, 115Petschek, H. E. 1964, in AAS/NASA Symp. on Physics of Solar Flares, ed.W. N. Hess (NASA SP-50; Washington, DC: NASA), 425Priest, E. R., & Forbes, T. G. 2000, Magnetic Reconnection MHD Theory andApplications (Cambridge: Cambridge Univ. Press)Sonnerup, B. U. O¨ ., & Priest, E. R. 1975, J. Plasma Phys., 14, 283Watson, P. G., & Craig, I. J. D. 2001, J. Geophys. Res., 106, 15,735

Magnetic Reconnection MHD Theory and Applications (Cambridge: Cambridge Univ.

Nonlinear Magnetohydrodynamics (Cambridge:Cambridge Univ.

http://www.journals.uchicago.edu/doi/abs/10.1086/376566

Fast magnetic reconnection via jets and current microsheets

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