Dynamo circuits for magnetopause reconnection

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A7, 1095, /2001JA000237, 2002 Dynamo circuits for magnetopause reconnection K. D. Siebert Mission Research Corporation, Nashua, New Hampshire, USA G. L. Siscoe Center for Space Physics, Department of Astronomy, Boston University, Boston, Massachusetts, USA Received 27 July 2001; revised 17 October 2001; accepted 17 October 2001; published 4 July [1] From the perspective of electric circuit theory a question regarding the existence of magnetopause reconnection arises because in circuit theory reconnection is a load and a load needs a dynamo to supply it. However, among current systems that have been identified that thread the presumed regions of magnetopause reconnection, none also treads a dynamo. Yet there is overwhelming observational evidence that magnetopause reconnection occurs. This paper attempts to reconcile the circuit theory viewpoint with observations of reconnection. The procedure is first to show that results of MHD simulation can be translated into circuit theory language. Then MHD simulation is applied to show that magnetopause reconnection is associated with current systems that close through the bow shock or the magnetosheath, which from the viewpoint of circuit theory are dynamos. Thus the reconciliation is simply that reconnection current systems are different from the standard set of current systems that have traditionally been associated with the magnetopause. INDEX TERMS: 2708 Magnetospheric Physics: Current systems (2409); 2712 Magnetospheric Physics: Electric fields (2411); 2740 Magnetospheric Physics: Magnetospheric configuration and dynamics; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; KEYWORDS: current systems, reconnection dynamo 1. Introduction [2] The classical paper in which Chapman and Ferraro [1931] disclosed a foreshadowing of the magnetosphere also presented a current system that now bears their names. Computing the shape of this current system was the Holy Grail of early magnetospheric modeling when the Chapman-Ferraro current system was identified with the magnetopause (see recent review by Siscoe [2001]). The discovery of the magnetotail with its current system that closes on the boundary between the tail and the solar wind complicated the one-current-magnetopause picture [e.g., Axford et al., 1965]. The new picture of a magnetopause comprising two current systems (Chapman-Ferraro and tail closure) has been modeled by means of global MHD simulations for the case of zero interplanetary magnetic field (IMF) [Siscoe et al., 2000]. This two-current-system picture of the magnetopause remained the standard picture for more than a decade until Atkinson [1978] suggested that the newly discovered region 1 current system in the ionosphere [Iijima and Potemra, 1976] closes on the magnetopause. Atkinson s conjecture has subsequently been confirmed by means of global MHD simulations [Janhunen et al., 1996; Tanaka, 1995, 2000; Siscoe et al., 2000]. Region 1 currents are especially evident on the magnetopause when the IMF is southward. When the IMF is northward, however, they are replaced as a boundary current by another current system that Wu [1983] discovered with a global MHD simulation. Copyright 2002 by the American Geophysical Union /02/2001JA Thus the current systems that have so far been described in the literature that flow fully or in part on the magnetopause are the Chapman-Ferraro, tail closure, region 1 for southward IMF, and the Wu current system for northward IMF. (We adopt Atkinson s definition that Chapman-Ferraro currents are those currents that close entirely on the magnetopause [Atkinson, 1978, p. 1090].) Here we note that there is one more magnetopause current system that should be added to this list, the low-latitude, subsolar reconnection current system. Moreover, we show that whereas the Chapman-Ferraro, tail closure, and region 1 current systems close either on or inside the magnetopause (see references cited above for figures), the Wu current system and subsolar reconnection current system close outside the magnetopause. They close in the dynamo regions of the magnetosheath and bow shock. [3] The results presented here were obtained with the Integrated Space Weather Prediction Model (ISM). Properties of the ISM code have been described elsewhere, most fully in the work of White et al. [2001]. Basically, the code integrates the standard MHD equations over a volume that extends from 40 R E upwind from Earth to 300 R E downwind from Earth, and 60 R E radially from an axis through Earth parallel to the solar wind flow direction. It handles connection to the ionosphere in a way that is unique among global MHD codes in that it uses the same set of equations from the base of the ionosphere to the outer boundaries of the grid, just described. The single set of equations that it uses segues continuously to the form of continuum mechanics equations appropriate to each domain from the ionosphere to the solar wind. SMP 6-1

2 SMP 6-2 SIEBERT AND SISCOE: BRIEF REPORT [4] Solar wind inflow boundary conditions for the simulation used typical values: speed, density, electron, and ion temperatures, IMF strength are 350 km/s, 5 protons/cm 3, 20 ev, and 5 nt, respectively. Earth s magnetic dipole axis is perpendicular to the solar wind flow direction (no dipole tilt). Results are presented in the geocentric solar ecliptic coordinate system (GSE), which in this case is the same as the geocentric magnetospheric coordinate system (GSM). In each case the ISM code was run for 2.5 hours of magnetosphere time; by then global-scale parameters related to magnetopause reconnection had become quasi-steady. 2. MHD and Circuit Analogs [5] As a first item of business, it is necessary in space physics when referring dynamo and other such terms borrowed from electrical engineering to address an issue of procedural correctness (PC). Parker [1996, 2000] has demonstrated, and his demonstration has not been refuted, that when currents are free to circulate in a magnetized conducting fluid like the magnetosphere, and are not confined to rigid wires, it is procedurally incorrect to use electrical circuit analogs to predict the behavior of the fluid. His argument is basically that in terms of macroscopic variables (current, electric field, magnetic field, velocity, density, and pressure) the equations of Newton and Maxwell can be written in prognostic form only for the magnetic field and the velocity and not for current and electric field. In a recent paper, Vasyliunas [2001] has explicitly demonstrated the same point. MHD formalism was invented to provide appropriate prognostic equations for the magnetic field and the velocity to predict the behavior of magnetized, conducting fluids. Parker notes, however, that, if desired, electrical circuit language could be adopted post hoc after a procedurally correct application of MHD has determined what, in fact, the currents and electric fields are. In this spirit, we here attempt to translate results of a procedurally correct MHD simulation into the language of dynamos and loads to describe energy flow associated with magnetic reconnection at the magnetopause. The reason that one might wish to do this is discussed below. [6] The Rosetta stone one needs to carry out the translation from MHD to circuit theory is a suitable electrical circuit defined in the variables of continuum mechanics. Poynting s theorem provides a means to obtain such a circuit. In steady state, which is valid for our application, Poynting s theorem can be expressed in the following simple though completely general form [Hill, 1983]. rj ¼ J E; where, J, and E are electrical potential, electric current density, and electric field strength, respectively. This seems to be nothing more than an identity by expanding the lefthand side, but since it is also Poynting s theorem, it has that theorem s usual meaning: J is the flux per unit area of electromagnetic energy, and J E is the rate per unit volume at which electromagnetic energy is converted into kinetic energy. Alternatively, one can view equation (1) as a conservation equation. Since J E is recognized as the volumetric creation rate of electromagnetic energy, by the usual structure of conservation equations, J can be ð1þ interpreted as the flux per unit area of electromagnetic energy. This is the form of Poynting s theorem that lets one most easily prove that the energy dissipated in a resistor is supplied by the battery to which it is connected. [7] To apply equation (1) to space plasmas where current is distributed throughout space, we replace the wires of circuit theory with tubular volumes the walls of which are current flow lines. Now, if these tubes of current close on themselves (as they do in the applications described below), we have something analogous to an electrical circuit, current flowing around a closed loop. If we then integrate equation (1) over the volume of a closed tube thus generated and apply Gauss s theorem, the left-hand side vanishes by virtue of the walls of the tube being parallel to J. Thus, referring to the right-hand side we find that the closed line integral around the tube of I E, where I is the total current flowing through the cross-sectional area of the tube, must also vanish. (As a check on the result, note that the closed line integral of I E is I EMF = I df/dt, where F is the total magnetic flux through the area enclosed by the tube and the equality follows from Faraday s induction law. By the assumption of steady state the time derivative, df/dt, is zero.) The result has the profound consequence that if there is a segment of a closed current tube in which magnetic energy is being dissipated (for example, in magnetic reconnection), and thus J E is positive, there must exist another segment of the tube in which J E is negative so as to exactly compensate for the dissipation segment in the closed line integral of I E. [8] We may now translate the result into the language of electrical circuit theory in which a segment of a current tube along which J E is positive is called a load and a segment along which J E is negative is called a dynamo. The translation reads: Magnetic energy dissipated by all loads along a closed current tube must be supplied by dynamos along that tube. This is the MHD equivalent of the rule from circuit theory (Kirchhoff s second law) that says the sum of voltages across all circuit elements around a closed circuit must vanish. [9] Why would one wish to translate from MHD to circuit theory anyway? For one thing, to be able to use results of an MHD calculation to answer a question posed in the language of electric circuit theory that challenges the concept of reconnection at the magnetopause. The question is this: Since reconnection is a load, where is the dynamo to supply it? Although reconnection is a local process, it has, from a circuit theory perspective, the nonlocal need for an energy source. Heikkila [1984] was the first to raise the question. The translation just performed gives us a means to use MHD simulation to answer the question in its own terms. [10] However, first, we need to say why the question appears to challenge the concept of reconnection at the magnetopause in the first place. It is because among the repertoire of magnetopause currents that one can consider answering the question, the Chapman-Ferraro current seems to be the one that passes through the subsolar part of the magnetopause where reconnection is presumed to occur. However, as Heikkila perceived, the role of the Chapman- Ferraro current is to confine the dipole field. It is basically a passive shielding current, which does not thread a dynamo where J E is negative. If therefore the current responsible

3 SIEBERT AND SISCOE: BRIEF REPORT SMP 6-3 Figure 1. Subsolar reconnection and Chapman-Ferraro current systems. Color contours on the equatorial and noon-midnight meridian planes give values of J E. See color version of this figure at back of this issue. for reconnection is part of the Chapman-Ferraro current, reconnection would seem to be energetically precluded. However, as reconnection advocates have emphasized, there is strong observational evidence indicating that reconnection occurs at the magnetopause. Moreover, magnetopause reconnection certainly happens in global MHD simulations [e.g., Siscoe et al., 2001]. It seems that from the circuit theory perspective reconnection should not happen, whereas from an MHD perspective, it does anyway. [11] Fedder et al. [1997], in a comparison between satellite data and results of global MHD simulation, opened a door to a possible reconciliation between the circuit theory and MHD perspectives. In the cited paper and in previous talks, Fedder has noted that in MHD simulations, magnetopause currents sometimes close on the bow shock, which is a dynamo in the sense that J E is negative. If therefore in an MHD simulation, current associated with magnetopause reconnection forms tubes that close on themselves via the bow shock, then by the translation discussed above, the question about an energy supply is answered in its own terms. The energy comes from magnetic compression at the bow shock. We need not worry about whether there is enough energy to supply reconnection, since the simulation satisfies Poynting s theorem to the precision of the numerical computation. It is only necessary to verify that the circuit geometry is satisfied. The following sections pursue the possible resolution opened by Fedder s suggestion. 3. Dynamo Circuit for Subsolar Reconnection [12] To maximize the intensity of subsolar reconnection and thus also to maximize its demand for energy, we employ the output from a strictly southward IMF run of the ISM code. By using one of four quadrants (NE, SE, SW, and NW) of the solution domain as seen from the Sun to generate the other three, we create bilateral symmetry, Figure 2. Same as Figure 1 for the polar reconnection current system except for a factor of 5 decrease in the dynamic range of the color scale. See color version of this figure at back of this issue.

4 SMP 6-4 SIEBERT AND SISCOE: BRIEF REPORT which forces current tubes to close on themselves. This is a legitimate procedure since the MHD equations are satisfied across the junctures of the four quadrants. [13] Figure 1 shows a three-dimensional (3-D), dawnside view of a set of current flow lines initiated slightly above the equatorial plane of the magnetopause (red) and a set initiated on the magnetopause at higher latitudes (blue). The flow lines close on themselves symmetrically on the dusk side of the magnetosphere. Color contours on the equatorial plane and the noon-midnight meridian plane denote values of J E. Negative values (blue) indicate a dynamo in the sense that kinetic energy is being converted into magnetic energy, and positive values (tan) indicate a load in the sense that magnetic energy is being converted into kinetic (either thermal or flow) energy. The relevant point that Figure 1 brings out is that whereas flow lines at higher latitudes remain on the magnetopause in the manner of Chapman-Ferraro currents, the equatorial flow lines form closed loops that connect the magnetopause with the bow shock in the manner that Fedder described. On the magnetopause they pass through a region where J E is tan (the load color), which corresponds to reconnection dissipation. In the magnetosheath and on the bow shock they pass through regions where J E is blue (the dynamo color), corresponding to the source of the energy that is dissipated by reconnection at the magnetopause. Although Figure 1 shows only equatorial flow lines, current flow lines close on or near the bow shock in a latitudinally wide band that reaches up to the outer Chapman-Ferraro flow line in Figure 1. [14] Thus the resolution between circuit theory and MHD perspectives on magnetopause reconnection turns out to be simple. It entails no revolution on either side. However, it does entail a minor revolution in what might be called magnetospheric anatomy; we must add a subsolar reconnection current system to the standard set. [15] We have used subsolar reconnection to describe the resolution the magnetopause reconnection question, but there is also a polar form of magnetopause reconnection. Section 4 shows that it, too, receives its energy (to speak in the language of circuit theory) from magnetic compression upstream from the magnetopause. 4. Dynamo Circuit for Polar Reconnection [16] In the northward IMF case a current system first recognized by Wu, as mentioned in the introduction, is associated with magnetic reconnection that occurs tailward of the plasma entry cusps [Berchem et al., 1995; Song et al., 1999; Raeder, 1999; Guzdar et al., 2001], although, to keep historical details straight, Wu thought that the current system was not associated with magnetic reconnection. Therefore, for the purpose of this section we refer to it as the polar reconnection current system. [17] Figure 2 shows a 3-D view of the polar reconnection current system (red) and the Chapman-Ferraro system (blue) for the northward IMF case. (Here the Chapman-Ferraro current system has its normal equatorial reach.) Color contours are as in Figure 1. As in the subsolar case, current flow lines of the polar reconnection current system form closed loops that connect the magnetopause with the magnetosheath and bow shock. Also, as in the subsolar case, they pass through a region on the magnetopause where J E is tan (the load color), which corresponds to reconnection dissipation. In the magnetosheath and on the bow shock they pass through regions where J E is blue (the dynamo color), corresponding to the compression source of the energy that is dissipated by reconnection at the magnetopause. The Chapman-Ferraro current system grades continuously into the polar reconnection current system and lies on a region of the magnetopause where J E is weak or zero. [18] The size of the reconnection load here is less than in the southward IMF case as indicated by a factor of 5 decrease in the dynamic range on the color bars between Figures 1 and 2. The strength of the magnetosheath dynamo is stronger in this case, however. This reflects an increase of compression of the magnetic field in the magnetosheath between the bow shock and the magnetopause as a result of absence of subsolar reconnection at the magnetopause. (That is, the pre-reconnection magnetosheath field strength just upwind from the stagnation point is stronger in this case than in the southward IMF case [Anderson et al., 1997].) 5. Summary [19] The main point of this report is to resolve a question concerning the existence of magnetopause reconnection that arises because the process can be described from two perspectives (circuit theory and MHD) that give apparently conflicting answers. The resolution is achieved by devising a way to translate between the two perspectives that maintains validity in both. The resolution is that, from the circuit theory perspective, the reconnection circuit is not related to the passive, dynamoless Chapman-Ferraro current system. Instead, it is a distinct and separate reconnection current system, which closes through the bow shock and magnetosheath where, from a circuit theory perspective, it picks up the energy it spends on reconnection dissipation. [20] The result is reasonable in retrospect. Reconnection is a process by which magnetic energy that has been created through compression at the bow shock and magnetosheath is partially consumed. The bow shock and the magnetosheath are, from a circuit theory perspective, energy sources. The ultimate energy source is, of course, solar wind flow energy, which gets tapped to compress the field. The subsolar and polar reconnection current systems have the geometry needed to deliver energy from the source to the sink. [21] Acknowledgments. The authors are supported by grants from NSF s Upper Atmospheric Section of the Atmospheric Sciences Division (AM ) and NASA s Sun-Earth Connections Theory Program (NAG5-8135) and NASW The Integrated Space Weather Model was developed by Mission Research Corporation under contract from the Defense Threat Reduction Agency, Willard White principal investigator. Daniel Weimer developed the graphics package (ISM_VIEW) used to generate the images. [22] Janet G. Luhmann thanks the referees for their assistance in evaluating this paper. References Anderson, B. J., T.-D. Phan, and S. A. Fuselier, Relation between plasma depletion and subsolar reconnection, J. Geophys. Res., 102, , Atkinson, G., Energy flow and closure of current systems in the magnetosphere, J. Geophys. Res., 83, , Axford, W. I., H. E. Petschek, and G. L. Siscoe, Tail of the magnetosphere, J. Geophys. Res., 65, 1231, 1965.

5 SIEBERT AND SISCOE: BRIEF REPORT SMP 6-5 Berchem, J., J. Reader, and M. Ashour-Abdalla, Reconnection at the magnetospheric boundary: Results from global magnetohydrodynamic simulations, in Physics of the Magnetopause, Geophys. Monogr. Ser. vol. 90, edited by P. Song, B. U. Ö. Sonnerup, and M. F. Thomsen, pp , AGU, Washington, D.C., Chapman, S., and V. C. A. Ferraro, A new theory of magnetic storms, J. Geophys. Res., 36, , Fedder, J. A., S. P. Slinker, J. G. Lyon, C. T. Russell, F. R. Fenrich, and J. G. Luhmann, A first comparison of POLAR magnetic field measurements and magnetohydrodynamic simulation results for field aligned currents, Geophys. Res. Lett., 24, , Guzdar, P. N., X. Shao, C. C. Goodrich, K. Papadopoulos, M. J. Wiltberger, and J. G. Lyon, Three-dimensional MHD simulations of the steady state magnetosphere with northward interplanetary magnetic field, J. Geophys. Res., 106, , Heikkila, W. J., Magnetospheric topology of fields and currents, in Magnetospheric Currents, Geophys. Monogr. Ser. vol. 28, edited by T. A. Potemra, pp , AGU, Washington, D.C., Hill, T. W., Solar-wind magnetosphere coupling, in Solar-Terrestrial Physics, edited by R. L. Carovillano and J. M. Forbes, pp , Reidel, D., Hingham, Mass., Iijima, T., and T. A. Potemra, Field-aligned currents in the dayside cusp observed by Triad, J. Geophys. Res., 81, , Janhunen, P., H. E. J. Koskinen, andt. I. Pulkkinen, A new global ionosphere-magnetosphere coupling simulation utilizing locally varying time step, Proceedings of the Third International Conference on Substorms (ICS-3), Eur. Space Agency, Spec. Publ., SP-389, , Oct Parker, E. N., The alternative paradigm for magnetospheric physics, J. Geophys. Res., 101, 10,587 10,625, Parker, E. N., Newton, Maxwell, and magnetospheric physics, in Magnetospheric Current Systems, Geophys. Monogr. Ser., vol. 118, edited by S.-I. Ohtani et al., pp. 1 10, AGU, Washington, D.C., Raeder, J., Modeling the magnetosphere for northward interplanetary magnetic field: Effects of electrical resistivity, J. Geophys. Res., 104, 17,357 17,367, Siscoe, G. L., N. U. Crooker, G. M. Erickson, B. U. Ö Sonnerup, K. D. Siebert, D. R. Weimer, W. W. White, and N. C. Maynard, Global geometry of magnetospheric currents, in Magnetospheric Current Systems, Geophys. Monogr. Ser., vol. 118, edited by S.-I. Ohtani et al., pp , AGU, Washington, D.C., Siscoe, G., 70 years of magnetospheric modeling, Space Weather, Geophys. Monogr. Ser., vol. 125, edited by P. Song, H. J. Singer, and G. L. Siscoe, pp , AGU, Washington, DC, Siscoe, G. L., G. M. Erickson, B. U. Ö. Sonnerup, N. C. Maynard, K. D. Siebert, D. R. Weimer, and W. W. White, Global role of E-parallel in magnetopause reconnection: An explicit demonstration, J. Geophys. Res., 106, 13,015 13,022, Song, P., D. L. DeZeeuw, T. I. Gombosi, C. P. T. Groth, and K. G. Powell, A numerical study of solar wind-magnetosphere interaction for northward interplanetary magnetic field, J. Geophys. Res., 104, 28,361 28,378, Tanaka, T., Generation mechanisms for magnetosphere-ionosphere current systems deduced from a three-dimensional MHD simulation of the solar wind-magnetosphere-ionosphere coupling process, J. Geophys. Res., 100, 12,057 12,074, Tanaka, T., Field-aligned-current systems in the numerically simulated magnetosphere, in Magnetospheric Current Systems, Geophys. Monogr. Ser., vol. 118, edited by S.-I. Ohtani et al., pp , AGU, Washington, D.C., Vasyliunas, V. M., Electric field and plasma flow: What drives what?, Geophys. Res. Lett., 28, , White, W. W., J. A. Schoendorf, K. D. Siebert, N. C. Maynard, D. R. Weimer, G. L. Wilson, B. U. Ö Sonnerup, G. L. Siscoe, and G. M. Erickson, MHD simulation of magnetospheric transport at the mesoscale, Space Weather, Geophys. Monogr. Ser., vol. 125, edited by P. Song, H. J. Singer, and G. L. Siscoe, pp , Washington, D.C., Wu, C. C., Shape of the magnetosphere, Geophys. Res. Lett., 10, , K. D. Siebert, Mission Research Corporation, 589 West Hollis Street, Suite 201, Nashua, NH 03062, USA. G. L. Siscoe, Center for Space Physics, Department of Astronomy, Boston University, 68 Dutton Road, Sudbury, MA USA. (siscoe@bu.edu)

6 SIEBERT AND SISCOE: BRIEF REPORT Figure 1. Subsolar reconnection and Chapman-Ferraro current systems. Color contours on the equatorial and noon-midnight meridian planes give values of J E. Figure 2. Same as Figure 1 for the polar reconnection current system except for a factor of 5 decrease in the dynamic range of the color scale. SMP 6-3