Divergent electric fields in downward current channels

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005ja011196, 2006 Divergent electric fields in downward current channels A. V. Streltsov 1,2 and G. T. Marklund 3 Received 17 April 2005; revised 27 January 2006; accepted 28 March 2006; published 26 July [1] The results from a numerical study on the formation and dynamics of the localized, diverging perpendicular electric fields found in the nightside auroral magnetosphere are presented. These fields are frequently observed inside the downward magnetic fieldaligned current (FAC) channels where the electrons flow upward from the ionosphere. The present study focuses on one particular example of the dynamics of such structures that was recorded by the Cluster spacecrafts on 14 January Simulations show that the localized, divergent electric fields observed by Cluster can be provided by the interactions between downward FACs and the ionosphere. Conditions promoting the formation of these fields include low ionospheric conductivities and solitary downward current channels. Numerical simulations are used to explain the dynamics of the currents and electric fields observed by the Cluster satellites during this event and also show that such electric fields are not normally detected in the upward current channels. Citation: Streltsov, A. V., and G. T. Marklund (2006), Divergent electric fields in downward current channels, J. Geophys. Res., 111,, doi: /2005ja Introduction [2] For years, observations performed on satellites and rockets above the auroral ionosphere have revealed electromagnetic structures with many different spatial and temporal scales. One particular class of these structures is localized, intense, bipolar electric fields measured in the downward current channels. These fields were reported by Weimer and Gurnett [1993] from data recorded on the DE-1 satellite, by Marklund et al. [1995], Marklund et al. [1997], and Karlsson et al. [1998] from the observations from the Freja satellite, and by Lotko et al. [1998] and Pashmann et al. [2002] from the FAST satellite observations. [3] A comprehensive statistical study of these fields [Marklund et al., 1997] have shown that they are mostly observed in the downward magnetic field-aligned current (FAC) channels where the electrons flow along the ambient magnetic field from the ionosphere. Sometimes these downward FACs were associated at high latitudes with a socalled black aurora. In addition, the strongest diverging E? occurred when the ionospheric conductivity was low. Thus the most intense fields are observed in the lower magnetosphere near the local magnetic midnight and during the winter season. [4] Numerous theoretical studies of the interactions between the FACs and the ionosphere [e.g., Glassmeier, 1983, 1984; Streltsov and Lotko, 2003b, 2004] reveal that the ionosphere plays a very important role in the formation, 1 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA. 2 Now at Plasma Physics Division, Naval Research Laboratory, Washington, D. C., USA. 3 Division of Plasma Physics, Alfvén Laboratory, Royal Institute of Technology, Stockholm, Sweden. Copyright 2006 by the American Geophysical Union /06/2005JA spatial structure, and temporal dynamics of small-scale electromagnetic structures in the low-altitude magnetosphere and that the low ionospheric conductivity is indeed one of the main conditions allowing them to exist. Both simulations and observations connect intense, localized perpendicular electric fields with low ionospheric conductivity and downward FACs. Unfortunately, the ambiguity of single spacecraft observations makes it hard to separate spatial and temporal properties of the localized electromagnetic structures and, as a result, it is difficult to provide a unique interpretation of the observed events. [5] The situation has changed with Cluster mission where the data from four identical satellites (Rumba, Samba, Salsa, and Tango) permit separation of spatial and temporal features for the localized electromagnetic structures and allow study their dynamics [Karlsson et al., 2004]. One example of such events was recorded by the Cluster satellites near 0430 UT on 14 January 2001 as shown in Figure 1 (reproduced from Marklund et al. [2001]). Four bottom panels in this figure show the north-south component of the electric field, E NS, measured by the Electric Field and Wave (EFW) instrument on four satellites. The four top panels show the density of FACs, derived from the eastwest variations of the magnetic field, measured by the Flux Gate Magnetometer (FGM) instrument. [6] During the event, the satellites were flying over the nightside auroral oval at the geocentric distance of 4.3 R E. The magnetic latitude of the satellites was 69.8, and the magnetic local time was 3.6 hours. The satellites traveled along almost the same trajectory one after another (as a string of pearls) with time intervals of about 100 s. The time axis in Figure 1 refers to the time on the Samba satellite. The spatial structure of E NS and j k measured by the different satellites is shown during the same temporal window by shifting the time on Rumba by 100 s, the time on Salsa by 90 s, and the time on Tango by 180 s. 1of7

2 current with the ionosphere when the ionospheric conductivity is low. The goal of this paper is to investigate this hypothesis with comprehensive numerical simulations. 2. Model [9] Analysis of the Cluster s 14 January 2001 event (shown in Figure 1) by Marklund et al. [2001] suggests that for this event, the Cluster satellites cross almost in the perpendicular direction a two-dimensional current sheet. (This structure is extended along the ambient magnetic field and the azimuthal (east-west) directions but localized in the meridional (north-south) direction.) Dynamics of such a current sheet and its interaction with the ionosphere can be modeled with a two-dimensional (2-D) set of reduced, two-fluid MHD equations that describe shear Alfvén waves in the cold, low-altitude-magnetosphere plasma [Streltsov and Lotko, 2003a, ke þ v ke r k v ke þ e E k þ 1 r k ðnt e Þ ¼ n e v ke ; m e m e þ nv ke^b ¼ 0; ð2þ j k^b þ 1 m 0 1 c 2 þ v 2 ¼ 0: ð3þ Figure 1. Parallel current density, j k, and north-south electric field, E NS, measured by four Cluster satellites above the nighttime, auroral ionosphere on 14 January 2001 near 0430 UT. (Reproduced from Marklund et al. [2001] with permission from Nature ( [7] The data related to the event discussed in this paper are emphasized in Figure 1 with thick, darker lines. The event represents an evolution of the localized downward FAC and the corresponding perpendicular (north-south) electric field. This study is focused on the three major features of the event. First, the amplitude of the current density of the downward FAC decreases with time. Second, the amplitude of E NS increases with time at least during the time when two first satellites crossed the structure. Third, the width of the FAC channel (and the size of the corresponding E NS ) increases with time. [8] Dynamics of the downward FAC seen in this event have a number of explanations related to the dynamics of the plasma and magnetic fields in the region of the magnetosphere where this FAC was generated. What makes this event particularly interesting for analysis is the behavior of the perpendicular electric field inside the current channel. Earlier, Marklund et al. [1997, 2001] suggested that such fields can be explained by the interaction of the downward Here the subscripts k and? denote vector components in the directions parallel and perpendicular to ^b = B 0 /B 0, v ke is the parallel component of the electron velocity, T e is the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi background electron temperature, v A = B 0 / m 0 n 0 m i is the Alfvén speed, and n e is the electron collision frequency. The electric field and the magnetic field-aligned current are expressed in terms of the scalar potential, f, and the parallel component of the vector potential, A k,ase? =?f, E k = r k k /@t, j k = env ke = r 2? A k /m 0. [10] The computational domain where the model is implemented numerically is formed by a dipolar flux tube, extending from the ionosphere to the equatorial plane and bounded in latitude by the L = 7.25 and the L = 8.25 magnetic shells. At the equatorial plane the dipole flux tube is spliced onto a cylindrical magnetic flux tube [see Streltsov and Lotko, 2003a, Figure 2]. The dipole part of the domain accurately represents the magnetic field geometry at low altitudes, whereas the cylindrical extension is used to provide a buffer zone where the wave can propagate after the reflection from the ionosphere. This buffer zone lets us eliminate effects of the artificial reflections from the magnetospheric end of the domain on the electrodynamics of the low-altitude region during some period of time. This time depends on the length of the cylindrical extension and parameters of the background plasma and the ambient magnetic field which are identical to those given by Streltsov and Lotko [2004]. In the simulations presented in this paper the length of the cylindrical extension is 35 R E and the Alfvén velocity in the cylinder is about 1704 km/s (the background magnetic field is nt and plasma density is 0.6 cm 3 ) which gives about 260 s of buffer time. 2of7

3 Here S P is the height-integrated Pedersen ionospheric conductivity (the Hall conductivity is not included in (1) because the model is limited to the two dimensions), n E is the hight-averaged plasma density inside the E-region, M P is the ion Pedersen mobility, e is the elementary charge, h is the effective thickness of the E-layer, q 11 is the angle between the dipole computational boundary and the ionosphere at 120 km altitude near the L = 7.75 magnetic shell, a is the coefficient of the recombination, and n E0 is an equilibrium density. We do not discuss in the paper physical mechanisms responsible for the density equilibrium because this task is far beyond the scope of this study. [12] Equation (6) represents the simplest form of the ionospheric density continuity equation considered in many classical studies of the magnetosphere-ionosphere (MI) interactions in the auroral zone [e.g., Sato, 1978; Miura and Sato, 1980; Lysak, 1990, 1991]. Some of these studies include an effect of the additional ionization of the ionosphere by energetic magnetospheric electrons in the upward current channels. This effect is described by additional source term in the right-hand side of (6) and it is not included in our study because we consider interaction of the ionosphere with downward FACs. [13] A single FAC propagating from the magnetosphere to the ionosphere is initiated in the simulations by specifying j k at the magnetospheric end of the cylindrical flux tube 8 < t=t r if t t r j k ¼ j * coshððl 7:75Þ= Þ 2 : ð7þ : 1 if t > t r Figure 2. Snapshots of j k and E NS taken every 45 s from the simulations of downward FAC interacting with the ionosphere. [11] The computations are performed on a grid with a parallel grid cell progressively decreasing by a factor of 100 in going from the equator to the ionosphere. Thus the grid with 75 cells along the ambient magnetic field over 10 R E distance in the dipole part of the domain provides a parallel spatial resolution of 28 km near the ionosphere. The ionospheric boundary of the computational domain is set at the altitude 120 km where the E-layer density is maximum. Here the boundary conditions describing the interactions between FACs and the ionosphere are implemented with three relations that connect the parallel current density, j k, the plasma density, n, and the perpendicular electric field, E?, in the ionosphere: ðs P E? Þ ¼ j k ; ð4þ S P ¼ n E M P he= cos ð5þ ¼ j k eh þ a n2 E0 n2 E : ð6þ Here parameters j * and define the amplitude and perpendicular scale length of the FAC, and t r = 19 s is a ramp time used to smooth out the front of the propagating wave. The sign of j * defines the direction of the current. In our simulations the positive current flows along the ambient magnetic field, which is pointed out from the ionosphere. Thus the negative j k corresponds to the downward current (electrons flow from the ionosphere) and positive j k corresponds to the upward current (electrons flow to the ionosphere). 3. Results and Discussion [14] To model the Cluster 14 January 2001 event, a number of model parameters describing FACs, plasma, and the magnetic field in the magnetosphere and the ionosphere should be adjusted. To reduce the amount of free parameters in the model, we chose plasma density and the ambient magnetic field in the magnetosphere according to Streltsov and Lotko [2004] and do not change them between the simulations. Thus in this study, only the parameters of the current driver and the ionosphere are varying to reproduce the main features of observations recorded by the Cluster satellites. [15] Figure 2 shows five consecutive snapshots of j k and E NS inside the dipolar part of the computational domain taken from the simulations after when the FAC reflected from the ionosphere. (This moment of time is marked as t 0 ) The time interval between the snapshots is 45 s, and the entire sequence covers 180 s of real time, which approximately corresponds to the time between crossings 3of7

4 of the 14 January 2001 event by Salsa and Rumba satellites. In these simulations parameters of the current driver are j * = ma/m 2 and = 16, and the parameters of the ionosphere are h = 20 km, M P = m 2 /sv, n E0 = (which correspond to S P0 = 1.5 mho), and a = cm 3 /s. All these values are in the range of parameters considered in many modeling studies of the ionospheremagnetosphere interactions at high latitudes [e.g., Sato, 1978; Miura and Sato, 1980; Lysak, 1999]. [16] Figure 3 shows profiles of j k and E NS taken from these two-dimensional simulations along the line corresponding to the trajectory of the Cluster satellites through the computational domain. These profiles are obtained instantly, so all the effects related to the evolution of the structure during the time of the satellite crossing are not presented in this figure. Figure 3 demonstrates that the model parameters used in these simulations provide electromagnetic structures with a perpendicular scale sizes and amplitudes quite close to the observational values. Thus magnitudes of j k in the simulations and in the observations varies in the Cluster location in the range ma/m 2, and magnitudes of simulated and observed E NS varies there in the range mv/m. [17] Figure 3 also show that the dynamics of simulated j k and E NS is similar to the dynamics of the observed fields and currents at least during the first 190 s of observations. In particular, they show that (1) the amplitude of j k decreases with time in the center of the current channel, (2) the amplitude of E NS increases at least during the first 45 s of the dynamics and a distinctive dipolar, localized, diverging field is formed, and (3) the width of the current channel increases with time. [18] Each of these three features can be explained by the interaction of the FACs with the ionosphere where the downward FAC decreases the Pedersen conductivity. Indeed, the downward current evacuates electrons from the ionosphere parallel to the ambient magnetic field and the ions are pushed in the direction across the ambient magnetic field by the perpendicular electric field driving a Pedersen current. As a result, the total plasma density decreases in this region of the ionosphere while the plasma remains neutral. This mechanism follows directly from the density continuity equation in the ionosphere and is supported by the radar observations of the ionospheric cavities inside the downward FACs at the auroral latitudes reported by Doe et al. [1993] and Shepherd et al. [1998]. [19] The top panel in Figure 4 shows j k in the ionospheric E-layer taken from the simulation illustrated in Figure 2 at Figure 3. Profiles of j k and E NS taken every 45 s from the simulations shown in Figure 2 along the virtual satellite trajectory corresponding to the Cluster 14 January 2001 event. Figure 4. (a) Parallel current density above the auroral ionosphere for the simulations illustrated in Figure 3 at times t 0 and t s. (b) Perpendicular electric fields in the ionospheric E-region. (c) Height-integrated Pedersen conductivities. 4of7

5 Figure 5. Profiles of j k and E NS taken every 45 s from the simulations along the virtual Cluster trajectory. Thick curves show the case when j * = ma/m 2 (the same as shown in Figure 3). Thin curves show the case when j * = ma/m 2. the times t 0 and t s. The middle panel illustrates E? in the ionosphere at the same moments in time, and the bottom panel shows corresponding profiles of the Pedersen conductivity. [20] Decreasing of the ionospheric density/conductivity changes the character of the reflection of FACs from the ionosphere. Analytical and numerical studies of the reflection of shear Alfvén wave from the ionosphere [e.g., Scholer, 1970; Mallinckrodt and Carlson, 1978; Vogt and Haerendel, 1998; Streltsov and Lotko, 2003a] show that the magnitude of j k is larger when the ionospheric conductivity is high and smaller when the conductivity is low. Consequently, decreasing the ionospheric conductivity reduces amplitude of the parallel current density in the FAC interacting with the ionosphere. [21] The increase of E? inside the FAC channel is explained by the same reason: The localized reduction of the ionospheric conductivity requires a large perpendicular electric field to maintain closure of the FAC through the ionosphere. This follows directly from (1). The localized diverging E NS observed by the Cluster at a geocentrical distance of 4.3 R E is generated in the ionosphere and is mapped equipotentially to the magnetosphere. The electric field has an odd-symmetrical dipolar form because of the symmetry of the single, localized current. [22] The increase in the width of the downward current channel is explained by the E? in the ionosphere. This field pushes ions in the ionosphere away from the center of the channel and it is not localized inside the channel. So as time proceeds, E NS moves ions in the ionosphere from the region adjacent to the initial current channel. To maintain a quasineutrality, electrons also should be removed from the ionosphere at these locations. This is only accomplished by moving them along the ambient magnetic field to the magnetosphere. Thus the fact that the perpendicular electric field associated with a single FAC is not localized inside the current channel (e.g., see upper panels in Figure 3) leads to the generation of downward FACs outside the initial current channel. [23] Obviously, the interaction of the downward FAC with the ionosphere depends on the amplitude of the current itself. Figure 5 shows five profiles of E NS and j k taken from the simulations where the amplitude of the driver is larger by 20% than the amplitude of the driver used in the simulations illustrated in Figure 3. These results show that during the same period of time, larger-amplitude currents produces larger-amplitude electric fields and broader current channels. [24] What makes the numerical results different from the observations is the fact that the amplitude of the simulated electric field is not going to be equal to zero as far as there is a downward FAC interacting with the ionosphere. That means that a small amplitude of the electric field observed by the fourth Cluster satellite during its crossing of the event cannot be explained by the MI interactions considered in this study. This fact maybe a consequences of temporal and/ or spatial dynamics of the magnetospheric driver produced FACs itself or the result of interactions between the FACs and the current generator in the magnetosphere [Lysak, 1985; Vogt et al., 1999]. [25] The simulations show that the amplitude of E NS generated by the MI coupling considered here does not increase infinitely but saturates at some level. There are two major reasons for this saturation. The first reason is the fact that the magnitude of j k interacting with the ionosphere decreases with time due to the variation of the ionospheric conductivity as was discussed above. The second reason is the effect of the term proportional to the recombination in (6). Under the assumption that there is an equilibrium plasma density in the ionosphere, n E0, this term works as a source when the FACs deplete the ionosphere. In this paper we do not analyze what physical mechanisms are responsible for that, but we would like to demonstrate the influence of this term on the the dynamics of the diverging electric fields produced by the downward FACs interacting with the ionosphere. [26] Figure 6 shows profiles of E NS and j k taken every 45 s along the virtual Cluster trajectory from the simulations with a = cm 3 /s (thick curves) and corresponding profiles of E NS and j k taken from the simulations with a = cm 3 /s (thin curves). These simulations demonstrate that during the same period of time smaller value of a leads to a larger depletion of the ionospheric density, larger perpendicular electric field in the ionosphere, and broader current channel than the larger value of a. [27] Another important parameter in equation (6) is the magnitude of the background ionospheric plasma density, n E0. Figure 7 shows snapshots of j k, E NS, and B EW inside the dipole part of the computational domain obtained from the simulations with n E0 = cm 3 (corresponds to S P0 = 4.5 mho). These particular snapshots are taken from the simulations at the moment of time t s, and they show that this value of n E0 is relatively large for the magnitude of FAC considered here, so all the simulated 5of7

6 observed features as (1) a decrease with time in the amplitude of j k, (2) an increase of the amplitude of E? inside the current channel, and (3) the broadening of the current channel itself. One of the main conditions necessary for the intensification and localization of E? inside the downward current channel is a low value for the background ionospheric conductivity. This computational result explains why such fields are usually observed near local magnetic midnight during winter time. [31] The main reason why the intense, diverging E? appears in the downward current channels is that the downward current reduces the ionospheric conductivity and more E? is required to close the magnetospheric FACs Figure 6. Profiles of j k and E NS taken every 45 s from the simulations along the virtual Cluster trajectory. Thick curves show the case when a = cm 3 /s (the same as shown in Figure 3). Thin curves show the case when a = cm 3 /s. quantities do not change significantly during the entire period of simulations (180 s). The single current channel in these simulations corresponds to a single gradient in the B? (and E? ) and no any localized E? appears inside the current channel. Because a and n E0 appear in the relation (6) together the same effect can be achieved for different value of n E0 by adjusting the magnitude of a [Streltsov and Lotko, 2005]. [28] To understand why the localized electric fields are not observed in the upward current channels, a simulation was performed for the interactions of upward FAC and the ionosphere with S P0 = 1.5 mho. All the parameters used in these simulations were identical to those of the simulations shown in Figure 2 except that the sign of the FAC was reversed. Two snapshots of E NS and j k are taken from this simulation 180 s apart (that corresponds to the first and the fifth sets of snapshots shown in Figure 2) are shown in Figure 8. No intensification of E NS inside the current channel, as well as a variation of the current amplitude and width of the current channel, was observed during this simulation. That happens because the upward current enhances the Pedersen conductivity by precipitating electrons into the ionosphere and no additional electric field is required in this location to maintain current closure. 4. Conclusions [29] Results from numerical simulations presented in this paper provide an explanation of the formation and the dynamics of localized, diverging perpendicular electric fields frequently observed on auroral magnetic field lines in association with the downward FACs and black aurora. [30] In particular, the simulations show that the interaction of downward FACs with the ionosphere explains such Figure 7. Snapshots of E NS, B EW, and j k at time t s in the simulations of the downward FAC interacting with the ionosphere with S P0 = 4.5 mho. 6of7

7 Figure 8. E NS and j k from the simulations of the upward FAC interacting with the ionosphere. through the ionosphere. Consistently, with this concept no intensification of E? was obtained in the simulations for the upward FACs, where the electrons precipitate into the ionosphere increasing the ionospheric conductivity. [32] In conclusion, the ionosphere plays an important role for the formation and dynamics of intense ULF electromagnetic structures observed in the nightside magnetosphere. These structures are generated in a result of strongly nonlinear MI interactions by means of FACs which depend on the parameters of the low-altitude magnetosphere, ionosphere, and FACs. [33] Acknowledgments. The authors would like to thank Paul A. Bernhardt for significant help with a preparation of this manuscript. The research was supported by ONR and by NASA grants NNG04GE22G and NNG05GJ70G. 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Gurnett (1993), Large-amplitude auroral electric fields measured with de-1, J. Geophys. Res., 98, 13. G. T. Marklund, Division of Plasma Physics, Alfvén Laboratory, Royal Institute of Technology, SE Stockholm, Sweden. (marklund@ plasma.kth.se) A. V. Streltsov, Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA. (anatoly.streltsov@nrl.navy.mil) 7of7