Magnetospheric currents during sawtooth events: Event-oriented magnetic field model analysis

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2007ja012983, 2008 Magnetospheric currents during sawtooth events: Event-oriented magnetic field model analysis M. Kubyshkina, 1 T. I. Pulkkinen, 2 N. Yu. Ganushkina, 2 and N. Partamies 2 Received 7 December 2007; revised 1 February 2008; accepted 10 March 2008; published 9 August [1] The behavior of inner magnetosphere current systems associated with a sawtooth sequence is examined using empirical magnetic field models during a sawtooth event on 18 April Three different empirical magnetic field models were developed for the same time period. In each case, the models were fitted using in situ magnetic field observations to minimize the differences between the model and observed field values. The results were compared with those previously obtained for a sawtooth event on 22 October The main features, namely, strong stretching of both nightside and dusk sector magnetic field prior to the injection, strong currents near geosynchronous distance, and strong dusk-sector magnetic field stretching, were all reproduced by all three models also for the April 2002 event. We conclude that these are repeatable and characteristic features of sawtooth events and discuss how the model details influence the minor differences between the models. Simple drift trajectory calculations are used to show that the models, which reproduce the magnetic field quite well, also accurately represent the energetic proton drift periods at geosynchronous orbit. Citation: Kubyshkina, M., T. I. Pulkkinen, N. Yu. Ganushkina, and N. Partamies (2008), Magnetospheric currents during sawtooth events: Event-oriented magnetic field model analysis, J. Geophys. Res., 113,, doi: /2007ja Introduction [2] Sawtooth events are a particular set of magnetospheric activations, most often observed during storms. They have been widely studied during the last few years [Henderson et al., 2006; Huang et al., 2003a, 2003b, 2005; Lee et al., 2004; Lui et al., 2004; Pulkkinen et al., 2006]. They are characterized by quasiperiodic injections at geosynchronous orbit expanding over the terminators within only a few minutes of the injection [Henderson, 2004]. Figure 1 shows two examples of sawtooth events. The top four panels show energetic proton fluxes from several spacecraft at geostationary orbit. In a timescale of several hours, the proton fluxes increase at each sawtooth onset almost simultaneously at widely different local times. The bottom panels of Figure 1 give the values of the solar wind velocity V X -component and the interplanetary magnetic field (IMF) B Z component. Both cases show driver values typical to sawtooth events (N. Partamies et al., What makes the difference between sawtooth events and steady magnetospheric convection period, submitted to Annales Geophysicae, 2008, hereinafter referred to as Partamies et al., submitted manuscript, 2008) moderate stormtime B Z around 10 nt and somewhat elevated solar wind speed around 500 km/s. For both events, solar wind data (from the ACE spacecraft for 18 April and from 1 Institute of Physics, University of St. Petersburg, St. Petersburg, Russia. 2 Earth s Observations, Finnish Meteorological Institute, Helsinki, Finland. Copyright 2008 by the American Geophysical Union /08/2007JA Wind for 22 October) have been shifted to a distance of 10 R E using the observed satellite position and solar wind speed. [3] Previous studies have paid special attention to several fundamental questions: how do the magnetospheric currents systems look like during sawtooth events, why are the substorm signatures so periodic, and what determines their period, what switches on sawtooth activity, or why do sawtooth events occur only under storm conditions. Most fundamentally, these studies have addressed the question of whether the sawtooth events form a new class of magnetospheric events or whether they are simply quasiperiodic stormtime substorms. [4] Most authors agree that sawtooth events are composed of substorms [Henderson et al., 2006; Huang et al., 2003a, 2003b; Pulkkinen et al., 2006, 2007], but have specific features such as a wide MLT extent of the injections, relatively poor correlation of the Dst response with the magnetic field dipolarization, and quasiperiodicity. In a recent paper, Henderson et al. [2006] showed that the energetic particle injections contain dispersion characteristics that can be explained in the framework of a Kp-dependent injection boundary model. They also suggested that the periodic structure of the sawtooth events is an analog to steady magnetospheric convection under much higher but steady solar wind energy input, when the magnetosphere is brought beyond a stability threshold and the energy dissipation can only be realized through periodic substorms. This point was further supported by Partamies et al. (submitted manuscript, 2008), who pointed out that in the case of similar driver conditions, the faster solar wind speed during sawtooth events results in stronger and periodic activity both in the magnetosphere and in the iono- 1of13

2 Figure 1. Left: Sawtooth event on 22 October Right: Sawtooth event on 18 April Upper: LANL proton fluxes in the energy range kev; kev; kev, kev, and kev. Bottom: Solar wind velocity V X component (thin line) and the interplanetary magnetic field B Z component (thick line). Scale for the solar wind velocity is given on the right. sphere. On the other hand, there still exists a point of view that sawtooth events are directly driven by solar wind dynamic pressure enhancements [Lee et al., 2004]. [5] In order to determine the changes in magnetospheric current systems during sawtooth events, Pulkkinen et al. [2006] developed an empirical magnetic field model for a sawtooth event on 22 October Their main findings concerning the current system structure and dynamics were: (1) sawtooth injections are associated with strong stretching of both nightside and dusk sector magnetic field prior to the injection, (2) the magnetospheric currents are strongest near geosynchronous distance and in the premidnight sector, (3) the strong dusk-sector field stretching produces very fast proton drift times, which allows rapid expansion of the injection front, and (4) the drifting protons are mostly on open drift paths, which leads to lesser enhancement of the symmetric ring current and larger variations in the asymmetric ring current. [6] The results above are reasonably consistent with observations. However, with a single model and single event it is impossible to say to what extent the results are dependent on the details of the event or model in question. In order to answer this question, in this paper we use three independent ways to model a sawtooth event on 18 April 2002 and compare the results with those by Pulkkinen et al. [2006]. Details of the modeling procedure are given in section 2, model results are presented in sections 3 and 4, and section 5 compares our findings with previous studies. Section 6 concludes with discussion. 2. Models and Modeling Procedures [7] It is important to realize that when a model is used to describe a set of observations, it is always some approximation of the real current distribution. Even the best of models can thus include some artifacts resulting from differences between the model currents and the true current configuration. In order to isolate the repetitive, characteristic features of a particular observational structure, it is necessary to examine several events and preferably several independent models. To that end, in this paper we use three models to describe a sawtooth event on 18 April [8] The empirical modeling method is similar for all three models: each model contains a set of free parameters (different for each model). In situ magnetic field observations from the inner magnetosphere are fitted to minimize 2of13

3 the error between the model and observations. Observations used are the same for all three models: Magnetic field components at GOES-8, GOES-10, Geotail, and Polar, and magnetic field inclination derived from energetic electron measurements on two LANL spacecraft and Observed Dst-values were used in fitting model 1; models 2 and 3 contain Dst as an input parameter. The resulting configurations are compared in section 4 to discuss the differences and similarities in current systems and magnetic field configurations Model 1 [9] Model 1 has been used to analyze a number of stormtime events and has been discussed in detail by Ganushkina et al. [2004] and Pulkkinen et al. [2006]. It is based on the T89 model [Tsyganenko, 1989], with the original ring current replaced by a storm-time ring current module [Ganushkina et al., 2002]. This ring current module contains two symmetric currents, one flowing eastward closer to the Earth and one flowing westward further from the Earth. Both symmetric ring current intensities are given by J r; B ¼ J 0 exp r 2! eq r 0 B A=2 B 0 2s 2 ð1þ B 0 where B 0 is the magnetic field at the equator, J 0 is the maximum current density, r 0 is the location of the maximum current density, s is the current distribution width in the radial direction, and A is the anisotropy index determining how concentrated the current is close to the equatorial plane. Similarly, the asymmetric partial ring current J PART is modeled by a function similar to the symmetric ring current, but with an additional asymmetry factor given by (1 cos(f d)), where f is the azimuth angle and d is the duskward shift angle giving the azimuthal location of the current maximum. The asymmetry factor gives rise to fieldaligned currents in the region 2 sense. [10] With this formulation, the ring current module includes eight free parameters: The distances of maximum current densities of the eastward and westward symmetric ring currents and the asymmetric partial ring current (R 0,EAST, R 0,WEST, R 0,PART ), maximum current densities (J 0,EAST, J 0,WEST, J 0,PART ), current distribution width (s), and anisotropy index (A), both of which are the same for all three current systems. As the duskward shift d of the partial ring current is known to depend on the level of magnetic activity, it is evaluated from the Dst index [see Tsyganenko, 2002b] from d ¼ p 2 tanh jdstj 40 : ð2þ [11] Additionally we modify the intensity of the T89 model tail current by a factor of ATC (Amplitude of Tail Current) and add a new thin current sheet with its intensity (ANTC) and thickness (dntc) as free parameters. We also intensify the magnetopause currents by a factor AMP, whose value is determined from the solar wind dynamic pressure. The values of these free parameters are then obtained from finding the best fit to the observations for each time step separately Model 2 [12] Tsyganenko [2002a, 2002b] developed a magnetic field model (T01) for storm periods. This model gives the magnetospheric field configuration as a function of several solar wind and magnetospheric activity parameters. However, the magnetic field predicted by the T01 model does not give the repetitive activity structure observed during saw tooth events because the solar wind driving during saw tooth events often remains rather steady. This problem can be overcome by considering the input parameters to T01, the solar wind P dyn, B Z, IMF, B Y, IMF, and the Dst-index, free parameters of the model. Thus instead of using the observed solar wind and Dst values, we find those values for these parameters that for each time step separately gives a best fit to the in situ field observations Model 3 [13] Model 3 is based on the T96 model [Tsyganenko, 1995], which has been modified in a way similar to that in Model 1. We have added three free parameters that define amplification of the ring current, the long tail current, and the short tail current (ARC, ATC2, ATC3, see Tsyganenko [1995] for definition of the currents). We also include an additional short tail current with its thickness and intensity as free parameters (dntc2 and ANTC2). 3. Model 1: Comparison of Two Events [14] The above models give three independent representations of the magnetic field and currents during the sawtooth sequence. We use them all to model the sawtooth event on 18 April 2002 (see Figure 1). This event has been discussed in a number of earlier papers [Henderson et al., 2006; Huang et al., 2005; Lee et al., 2004; Lui et al., 2004; Pulkkinen et al., 2006]. Furthermore, we compare the results obtained from model 1 with results from the same model during a sawtooth event of 22 October 2001 [see Pulkkinen et al., 2006]. [15] Magnetic field measurements from four spacecraft were used for fitting the 18 April 2002 sawtooth event. Figure 2 gives the orbits of GOES-8, GOES-10, Polar, and Geotail spacecraft during the modeling period from 0000 to 1400 UT. In this event, the spacecraft configuration was favorable for empirical event-oriented magnetic field modeling: GOES-8 and GOES-10 monitored the nightside magnetic field at geosynchronous distance, Polar measured the dayside near-geosynchronous field thus providing an estimate for the symmetric ring current, and Geotail was in the magnetotail lobe, thus following the nightside magnetic flux variations. Two additional geosynchronous LANL spacecraft were used to monitor the magnetic field inclination. [16] The red curves in the top three rows of Figure 3 show the model results for the B X, B Y, and B Z components in GSM coordinates for the 18 April 2002 sawtooth event; observed values are shown in black. The values show only the external field induced by magnetospheric currents, i.e., the internal dipole field has been subtracted both from the measurements and from the model results. Each column shows results for one spacecraft, from left to right from GOES-8, GOES-10, Polar, and Geotail. The sawtooth dipolarizations are especially evident in the B Z components. 3of13

4 Figure 2. Spacecraft orbits during 18 April 2002, 0 14 UT. The top shows the GSM X-Y plane, the bottom shows the midnight meridian (X-Z) plane. In the inner magnetosphere the model does a good job in representing the stretching and dipolarization of the field, while in the midmagnetotail lobe the model is unable to reproduce the strong variations observed at the Geotail location. [17] The green and blue curves in the top three rows of Figure 3 show the model results for the standard Tsyganenko models T96 and T01s for comparison. One could probably note that T01 model is considered to be limited to within 15 Re, since most of the data comes from inside this distance and thus the model accuracy rapidly decreases outside of that distance. At the same time being the global model T01s is determined everywhere inside the magnetosphere. Thus we show the model results and compare them with the observations at the Geotail location (around 25 Re for 18 April 2002) assuming that the T01s model still gives reasonable results for the purpose of the comparisons. This is justified by comparison with the T96 model, whose validity extends to more distant magnetotail, and which gives quite comparable results (see Figure 3 for example). From our modeling experience we can conclude that for the storm-time conditions the T01s model gives better correlation with observations at distant spacecraft than any other standard model. Comparison of the different models leads to the following conclusions: (1) All models (including the nonstorm time T96 model) give an average representation of the observed field variations. (2) Comparison of T96 (green) and T01s (blue) shows that T01s gives much more accurate values for the B Y component and for the lobe field at Geotail. (3) Event-oriented model 1 is otherwise close to T01s, but is the only one to capture the sawtooth structure, especially the dipolarizations seen in the B Z components in the inner magnetosphere. (4) B Z variations at Geotail are poorly reproduced by all models, but the scale of these variations is notably lower than that near geostationary orbit at the GOES position. That is why, when constructing a model, measurements at GOES spacecraft give more input to the error function, which is minimized during finding the model parameters. As a result, the fine structure of magnetic field variations is better represented at spacecraft closer to the Earth. At Geotail distance, the sawtooth variations appear to be of the scale of the error, especially for the Bz component (see the axis scale). Larger variations of Bx on Geotail are well reproduced by Model 1 and Model 2. Note that while this is a feature of the modeling method, it is on purpose so: Because the dipole makes the magnetic field more rigid in the inner magnetosphere, changes near geostationary orbit are more likely to be caused by dynamic processes we are trying to describe (changes in the current intensities). On the other hand, at larger distances, tail flapping that is mere motion of the location of the current sheet can cause significant variations in the field. From single-point measurements it is impossible to separate current intensity variations and current location variations in a unique way. Thus the modeling in principle always gives better results in the inner magnetosphere where (1) the background field is larger and (2) there are more data points to be used in the fitting. [18] The 22 October 2001 event has been discussed in detail by Pulkkinen et al. [2006]. Their Figure 5 show similar results for the 22 October 2001 sawtooth event and is not repeated here. [19] Figure 4 contains observations (shown black) together with results from model 1 for two sawtooth events on 22 October 2001 (left) and 18 April 2002 (right). The top panel shows the magnetotail B Z variations. The periodic structure is typical of sawtooth events. The red curves show the field values given by model 1. Observations shown come from the Polar spacecraft at about 8 R E distance in the magnetotail during the 22 October event and from the geostationary GOES-10 satellite during the 18 April event. [20] The second panel of Figure 4 shows the Dst-index together with model values of symmetric ring current intensity (red) and total ring current intensity (symmetric ring current and maximum of the partial ring current, magenta). The Dst index variations for both events clearly show typical substorm behavior with a reduction of magnitude during each dipolarization and intensification during the growth phase. [21] The third panel of Figure 4 shows the solar wind dynamic pressure and the variations of the magnetopause current amplitude computed using the measured pressure values. The dynamic pressure is different during the two events: In the 22 October event, the pressure is large and variable throughout the whole period of interest, while in the 18 April event, after the first short intensification the pressure decreases to values lower than 1 npa and remains low until the end of the period. (Note the different scales for the dynamic pressure for the two events.) This difference in pressure values may give rise to the larger total tail current values seen in the 22 October event as compared to those obtained in the 18 April event. Pressure enhancements during the 22 October event are numerous and do not 4of13

5 Figure April 2002 sawtooth event. Top: Observed external magnetic field (dipole field subtracted, black) components at GOES-8, GOES-10, Polar, and Geotail spacecraft (columns from left to right) and GSM B X, B Y, and B Z components (rows from top). The model results are shown with color: Model 1 (red), T96 model using observed solar wind parameters as input (green) and T01s model using observed solar wind parameters as input (blue). Bottom: Similar to top, but only for B X and B Z components. The colors indicate observations (black), model 1 (red), model 2 (blue) and model 3 (green). necessarily coincide with the large energetic ion flux injections at geostationary orbit. Similar variations may be observed in the Bz IMF behavior: many of the existing northward excursions occur close to the injection times. However, as their amplitude is small and numerous similar Bz variations occur at times not associated with injections, we cannot reliably identify them as triggers. [22] The fourth panel of Figure 4 shows the AE-index (black) together with the amplification factor for the total tail current intensification (red) and for the additional thin current intensity (magenta). The behavior of both curves seems similar. There is a general tendency that the tail current is high when the AE is high. This is naturally so, as the AE-index includes both the driven system and the substorm-associated currents, and intensifies strongly as the driving increases. Similarly, the driving increases the tail currents. The correlation in finer timescales is disrupted by the substorm-associated current systems, which cause strong peaks in the AE index while they are associated with disruption of the inner tail currents and hence weakening of the ATS parameter. 5of13

6 Figure 4. Observations and model parameters for 22 October 2001 and 18 April From top to bottom: (1) external magnetic field Bz variations observed (black) and modeled (red); (2) Dst variations(black line) together with symmetric (red line) and total - symmetric and partial ring current values (magenta line); (3) solar wind dynamic pressure(black) and amplification factor for magnetopause currents (red); (4) AE magnetospheric index(black) and amplification factors for overall tail current ATS(red) and for additional thin current Antc (magenta); (5) ASY-H index (black) and sum of partial and tail currents. [23] The variations of the tail current resemble those of the AE-index. The bottom panels of Figure 4 plot the ASY-H index together with the sum of the partial ring current and the tail current, which both bring asymmetry to the magnetic field structure. Together Figures 4 and 1 reveal that no solar wind parameter contains any distinct periodic structure consistent with the observed sawtooth periodicity. This strongly suggests that the periodic substorms during constant loading are mostly triggered by internal magnetospheric processes. [24] In addition to the inner magnetosphere particle injections and magnetic field dipolarizations, the periodic structures are seen in the Dst index and in the ASY-H index. The ASY-H variations are especially clear, but the periodicity and the amplitude of the variations are less regular and do not exactly reproduce the size and period of the particle injections. The Dst and ASY-H values as well as variations are rather similar during both events, which points to the direction that the current systems structure had similar configurations during both events April 2002: Three Models Compared [25] Empirical magnetic field models are based on some predescribed mathematical representations of the current systems in the magnetosphere. Therefore even if in the fitting procedure the current systems are reshaped, intensified, and weakened, the global features of the models remain tied to the original mathematical representation. Because of the complexity of the true magnetospheric current system, every model is always only an approximation of the real one. Thus the success of a model to represent a particular phenomenon and/or event depends crucially on how well the predescribed currents describe the situation at hand. A typical problem with many of the models is that they do not contain field-aligned currents. Therefore the large variations in the azimuthal field components sometimes observed during substorms or strongly asymmetric ring currents are difficult to capture with such models Magnetic Field Values [26] In order to evaluate the model result dependence on the background mathematical model, we use models 1, 2, and 3 to describe the same event. Each model has a unique set of current systems in the background field model, and is then fitted using the same set of observations. The two bottom rows of Figure 3 show the B X and B Z components of the observed and model fields. The observations are given in black, model 1 in red, T01s-based model 2 in blue, and T96-based model in blue. Three main conclusions can be drawn based on these results. [27] 1. All three models give values very close to those observed at geostationary orbit (at the GOES-8 and GOES- 10 locations). Furthermore, all models overestimate the field stretching (underestimate B Z ) at GOES-8 during UT when the spacecraft crosses the midnight sector (GOES-8 is at midnight at 0500 UT). At the same time, the timing and relative change (difference from maximum stretching to maximum dipolarization) are close to those observed. The B Z variations at GOES-10, which has its local midnight at 0900 UT, are almost exactly reproduced by all models, giving values close to 80 nt near local midnight, 6of13

7 Figure 5. Magnetic field lines for model 1 (left), model 2 (middle), and model 3 (right) at the midnight meridian during times given on the right. Field lines start from Earth s surface at midnight meridian from 57 corrected geomagnetic latitude and follow in 1 intervals. The field line plotted in red starts at 63. similar to those at GOES-8 near midnight. This would indicate that there is an azimuthally localized current system around UT, which leads to an increase of B Z and strong intensification of B X at Polar location. [28] 2. Variations at the Polar location are much less clear, but on average all three models give a good representation of the field, and all models are rather close together. This indicates that the dayside magnetic field is dominated by the symmetric part of ring current, which is well determined in all three models. [29] 3. Magnetic field at Geotail, which gives us an estimation of the lobe field and tail magnetic flux variations, is better reproduced by models 1 and 2 (especially the B X component giving the lobe field). The normal component of the field (B Z, giving tail flaring and dipolarization) is more accurately reproduced in models 1 and 3. The differences between the models are relatively larger in the more distant tail, although the absolute values of the differences between the models and observations is about the same as in the inner magnetotail and geostationary orbit Magnetic Field Lines [30] Perhaps the most illustrative comparison of the various models comes from comparing the magnetic field 7of13

8 Figure 6. Current density distribution in the equatorial plane at 05:30 (maximal stretching configuration) for model 1 (left), model 2 (middle), and model 3 (right). line structure and topology. Figure 5 gives a series of field lines for all three models at several time instants. Field lines start from the Earth s surface at the midnight meridian. The innermost field line originates from 57 corrected geomagnetic latitude, the subsequent ones are plotted at 1 intervals. The times are chosen to show the moments of maximal field line stretching and the following maximal dipolarization. The field line plotted in red starts at 63 in each model, to illustrate the varying amounts of stretching and dipolarization in the models. [31] It is evident that the sequence of stretching and dipolarization is clearly present in all three models at the appropriate times. However, focusing on field lines tailward of geostationary orbit, they look rather different. As the tail current is modeled differently in each model, the low magnetic flux crossing the magnetotail current sheet leads to large differences in the field line structure in that region. This will result in large differences in mapping from the ionosphere to the magnetotail using the different models, especially at the end of the growth phases when the tail currents are largest. Note, however, that mapping from the magnetotail to the ionosphere leads to much smaller errors, as the magnetic flux closing through the tail is low. In part, the model accuracy in the magnetotail is limited by the amount of input data, which mostly comes from neargeostationary region Current Density and Total Current [32] The current density distribution in the equatorial plane is given in Figure 6 for the time of maximal stretching at 0530 UT (see Figures 4 and 5). All three models show the same order of magnitude of the current density, but the current distribution varies depending on the features of the original model. Most obviously, model 1 does not include an explicit magnetopause, which is clearly seen as a current layer in models 2 and 3. This is an obvious limitation of applicability of model 1 in the dayside magnetosphere. [33] Models 1 and 2 include a possibility to develop an aysmmetric ring current. Indeed, both models show a welldefined dawn-dusk asymmetry with an intense partial ring current widely distributed within the inner magnetosphere. A similar feature was observed during 22 October 2001, sawtooth event in model 1 [Pulkkinen et al., 2006]. Model 3, being based on T96, does not include an asymmetric ring current, which is reflected in a higher intensity of the symmetric ring current and the inner edge of the tail current. Looking at the large-scale features only, even during times when the differences could be assumed to be largest, the three models give a coherent current distribution and roughly similar current density values. [34] The temporal evolution of the total current is shown in Figure 7 (left panel). The J Y component of the total current was computed along the midnight meridian by integrating the current density values first across the current sheet in the Z direction and then along the current sheet in the X direction. All calculations are done in the GSM coordinate system. The color coding gives the total amount of current (in MA) through the Y = 0 plane Earthward of the given X-value as functions of time ( UT) and X ( 2 to 10 R E ). [35] From the contour plots we see again that the total current values are not identical, but show certain similarity. The range of values is similar for all three models. At the time of the dipolarizations, clear and rapid current retreat (current disruption) is visible in each model. Equally, the longer periods of current buildup during the field stretching are included in all three models. All three models demonstrate a gradual current reduction with time in the near-earth region, which may characterize a gradual recovery of the storm. The variations are most smooth in model 2. This probably arises from the constrain that negative B Z values in the magnetotail (formation of a neutral line ) are not allowed in the T01s model, which limits the possibility to strongly increase the tail current. [36] The right panel of Figure 7 shows the current integrated across the current sheet thickness (over Z) as a function of time and X. The color coding gives the current per unit length in X in ma/m. These results show more clearly the strong variability of the tail current in model 2 and the tailward motion of the overall current maximum in model 3 as the storm progresses. Similarly to the integral 8of13

9 Figure 7. Left: The J Y component of total current trough Y = 0 plane earthward of given X-value for model 1 (top), model 2 (middle), and model 3 (bottom). The red line shows a value equal to 2 MA. Right: Current density variations (integrated over the current sheet thickness in Z) with time and radial distance at midnight meridian. White line denotes the location of the geosynchronous orbit distance. values, the peak currents have roughly similar values, and the periodic structure is reproduced in all three models. 5. Interpretation of Model Results [37] In this section, we compare and contrast the results for the three models and for the two events. Using this information, we draw conclusions on the current system characteristics during sawtooth events Magnetic Field and Currents [38] The main conclusion concerning the magnetic field and current structure proposed in earlier studies are as follows. [39] 1. Sawtooth injections are associated with strong stretching of both nightside and dusk sector magnetic field prior to injection and current disruption. This assumption is confirmed by all three models, and all three models give good temporal correlation with the geostationary orbit injections. Models 1 and 2 that do include asymmetric currents produce a very large dusk sector current intensification before the dipolarization (see Figures 5 and 6). [40] 2. The currents are strongest near geosynchronous distance. Especially model 1 produces a current maximum slightly earthward of geostationary orbit (see Figures 6 and 7), but also the other models suggest a strong ring current centering Earthward of the geostationary orbit. The original conclusion may be affected by the usual lack of observations inside geostationary distance. [41] 3. The tail field behavior resembles that of nonstorm substorms. This is true for all three models. Similar sequence of intensification of the tail currents with maximum intensification in the inner magnetosphere and following dipolarization has been reported in a number of empirical model studies concerning nonstorm substorms [see Pulkkinen et al., 1992, Figure 5]. [42] To summarize, the field and current configurations and their variations during sawtooth events closely resemble those found during isolated substorms. The existing differences, such as the wider azimuthal extent and the current 9of13

10 maximum location closer to the Earth can be explained by the stronger background currents due to storm disturbances and by the larger than typical energy loading rate Proton Drift Paths [43] The main conclusions reached by earlier studies are as follows. [44] 4. The drifting protons are mostly on open drift paths, which leads to less enhancement of symmetrical ring current and larger variations in asymmetrical ring current (meaning small SYM-H and Dst variations and distinct ASY-H index variations). [45] 5. The strong dusk-sector field stretching produces very fast proton drift times, which allows rapid expansion of the injection front. On the other hand, the near-simultaneous field dipolarization suggests a wide injection front. A wide injection front together with rapid drift times then provides the near-simultaneous configuration changes at all local times. [46] To evaluate these conclusions we made estimations of proton drift speeds and drift paths in the three models. The questions were:(1) will the currents intensifications obtained by the model produce the drift times observed? and (2) will the model based on magnetic filed observations only adequately reproduce particle drifts? The results are presented in Figure 8. The five bottom panels show 200 kev proton fluxes measured by five LANL spacecraft at varying local times. Here we analyze two injections around 0800 UT (top left) and around 1130 UT (top right). The position of each spacecraft is given for both times in the upper panels, with crosses of corresponding color. During the 0800 UT injection, the injection is practically simultaneous at three spacecraft in the dusk sector. However, there is a small delay in the injection arrival for the spacecraft located on the dayside. Having a model of magnetic field, we estimated the drift velocity of 200 kev protons (90 pitch angle) in guiding center approximation as: v dr ¼ cm qb 2 ½B rbšþ c B 2 ½ E B Š; ð3þ where c is the speed of light, q is the proton charge, B is the magnetic field intensity, m is the proton magnetic moment (obtained from perpendicular energy divided by B) and E = 0.1 mv/m is a uniform electric field (lacking observations, assumed constant in time and space). [47] Protons were traced in the model 2 developed here from the location of the LANL-01A spacecraft (black cross, upper left panel) back in time. The resulting trace is shown in black with black numbers indicating times in UT. The times when the LANL spacecraft recorded a flux increase are given in colored numbers near the spacecraft locations. Comparing the results shows that the tracing gives results quite similar to the observations. Tracing forward from both (green) and (red) LANL positions shows that protons at those locations were on open drift paths, as illustrated by the green line starting from spacecraft position. [48] Similar analysis was made for the flux increase around 1130 UT. During this time, the dusk sector was particularly well-observed by three spacecraft. Simultaneous flux increases were observed at s/c and LANL-97A. LANL-01A was the next to record a flux increase, and s/c slightly in the postmidnight sector was the last one to observe the injection front arrival. This leads us to conclude that the injection region was in the premidnight-dusk sector, clearly duskward 0100 MLT. Tracing backward from LANL-01A shows quite good agreement with observations at LANL-02A, and tracing forward a good correlation with LANL Figure 8 shows tracing results only for model 2 for simplicity. Estimations with other models show qualitatively similar results with less than 20% differences in drift times Possible Estimation for the Sawtooth Duration [49] Pulkkinen et al. [2006] conclude that [50] 6. Neither analysis of multipoint magnetic field data using the model nor analysis of the solar wind and IMF variations pointed to any explanation of the 2.5-h recurrence time of the the saw-tooth events. Analysis of the 18 April 2002 event leads to a similar conclusion, no solar wind or IMF variations have similar periodic variations. This is in contrast with results from Huang et al. [2003a] and Lee et al. [2004]. [51] Here we start with the assumption (based on the conclusions above) that the sawtooth events are individual stormtime substorms occurring in sequence, and are caused by reconnection (or current disruption) in the magnetotail. In that case, the constant loading (extended period of negative B Z ) continuously feeds energy to the magnetotail and leads to growth phase features such as cross-tail current intensification and current sheet thinning. All these features are seen in the magnetic field model results. After a large injection and current disruption, some time is needed for the current sheet to thin and intensify before a next activation can take place. The time needed for sufficient loading is determined both by inner magnetosphere properties and the intensity of energy loading characterized by the amount of reconnected magnetic flux (F V X,SW B Z,IMF ). Dependence on the loading rate would mean that the increase of F will cause a reduction in the loading time. [52] Figure 9 shows an analysis of the injection period versus loading during the two events shown in this paper (22 October 2001 and 18 April 2002). Additionally, we show two other sawtooth events on 4 October 2000 and 11 August All four events give a very similar (linear) dependence of the period between two sawtooth injections on the driving solar wind electric field. [53] All four events show roughly similar dependence of the period on the driving electric field within a given event, but the 18 April 2002 event has a longer period for a similar level of driving than the other events. This may be related to the lower solar wind pressure that prevailed during that time. However, further analysis is needed before quantitative conclusions can be drawn; here we only point out a possible cause for the period around 2.5 h. This would then be the time it takes the tail to develop a thin and intense current sheet to the limit of internal instability for a given level of solar wind electric field. 6. Conclusions [54] Empirical event-oriented magnetic field models are useful when the events are recorded by a suitable number of 10 of 13

11 Figure 8. Top left: A drift path of a 200-keV proton using model 2 and an adiabatic drift approximation starting at the LANL-01A position at 0806 UT and tracing backward in time (black line). The times along the orbit (in decimal hours) are given in black. The colored crosses show the locations of the LANL spacecraft and the times when the injections were observed at the satellite location. The green line shows a forward tracing from s/c Top right: Same as top left, but at 1140 UT. Black thick line shows tracing backward in time, the thin line shows tracing forward in time. Bottom: 200 kev proton fluxes measured by five LANL spacecraft. Selected injection times (shown in the upper Figures) are shown with vertical lines. 11 of 13

12 Figure 9. Time interval between two sawtooth injections as a function of driving solar wind electric field or amount of reconnected magnetic flux F load = V X,SW B Z,IMF. Four sawtooth events are shown with different colors. well-positioned spacecraft. The models provide a simple way to examine and explain many specific features of the magnetospheric configuration and give realistic representations of the field and current configuration. The models can be used for particle tracing and thus provide estimates of the particle drift times and drift paths. On the other hand, mapping especially from the ionosphere to the magnetotail along magnetic field lines still is not very accurate at times of maximal field stretching, because small errors in field values in the magnetotail can cause large errors in mapping in regions where the amount of flux closing through the current sheet is small. It is worth pointing out that mapping from the magnetotail to the ionosphere will not lead to equally large errors, as all points from a region of low flux crossing the current sheet will map relatively close together. [55] The analysis of two sawtooth events using three independent event-oriented models showed that the main features obtained earlier for sawtooth currents signatures are independent of the event and of the chosen magnetic field model. Thus the following features are repeatable signatures of sawtooth events: (1) strong stretching of both nightside and dusk sector magnetic field prior to injection and current disruption, (2) current maximum resides near or inside geostationary orbit, closer to the Earth than during nonstorm substorms, and (3) the tail field behavior resembles that of nonstorm substorms, but activity is concentrated closer to the Earth than during nonstorm substorms. [56] We showed that the models adequately represent the drift trajectories of energetic protons at geosynchronous orbit, and give reasonable drift times, which are consistent with the energetic particle measurements made at geostationary orbit. We confirm the earlier suggestion that the near-simultaneous injection times are caused by the rapid drift times in the strongly stretched field configuration. We conclude that if a set of magnetic field models equally accurately represent the magnetic field components in different positions around the inner magnetosphere, the global mode magnetic field and currents are sufficiently accurate to lead to reasonably accurate drift times and trajectories. [57] Last, we examine the periodicity of the sawtooth injections during four sawtooth events. We conclude that there is a linear relationship between the time between two injections and the driving electric field for each event. The 18 April 2002 event was found to have a longer period between the injections than the other three events. One difference between that and the other events is that the solar wind dynamic pressure was lower in the April event than during the other events. We suggest that the period is determined by the intensity of the solar wind driving, although we could not identify a simple function (other than the electric field) that would account for the observed pressure dependence. [58] While the large-scale conclusions remain similar for all three models, there are also differences: Model 3 does not include an asymmetric ring current, which leads to weaker ring current as the model forces the ring current to maximize in the midnight meridian. Model 1 does not include an explicit magnetopause, which limits the model use in the dayside outer magnetosphere. The intensity of the tail current varies from model to model, which leads to differences in the amount of flux crossing the current sheet and hence changes the magnetic mapping (and field line) properties. All these features are intrinsically dependent on the background magnetic field model and affect the accuracy of the model results. In any event modeled, it is important to assure that the main features that dominate the current systems are present in the mathematical representation of the model. [59] Acknowledgments. M. Kubyshkina thanks the Finnish Cultural Foundation for financial support. We thank WDC-C (Kyoto) for the preliminary AE and SYM index data, Geoff Reeves for providing the LANL energetic particle data. We thank the NSSDC for maintaining the CDAWeb data facility from where the spacecraft magnetic field and position data were obtained. [60] Wolfgang Baumjohann thanks Chao-Song Huang and another reviewer for their assistance in evaluating this paper. 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