Relativistic electrons dynamics is still challenging to predict during the main phase of a storm. In particular, three dimensions radiation belt models, for which temporal resolution is limited, fail in predicting their behavior, especially when dropouts occur. In this paper we present a new model of magnetopause shadowing losses to be incorporated into the ONERA Salammbô code in order to improve the model accuracy. We show in this paper that above a few hundred keVs, magnetopause shadowing is the first contribution to losses in the outer electron belt during dropout events. Global variations of Earth-magnetopause distance and relativistic electron flux have been analyzed to establish the correlation between the magnetopause shadowing and dropouts on the outer electron radiation belt during geomagnetic storms. To that purpose, a Superposed Epoch Analysis has been done using NOAA Polar-orbiting Operational Environmental Satellite 15 measurements. First, a list of 67 Stream Interfaces has been used to validate the method, and then the Superposed Epoch Analysis has been run over more than one solar cycle. Our results show that the model of magnetopause location we have developed fits well with a Superposed Epoch Analysis performed and that we are able to define a criteria based on it that detect intense dropouts. Finally, we have included this model in the Salammbô code, and we present here the improvements obtained as well as the validation made.
- The prime role of magnetopause shadowing during intense dropouts is highlighted in this work
- A simplistic but functional model of magnetopause shadowing is introduced
- An improved version of Salammbô code is presented, taking into account magnetopause shadowing effect-induced losses
For many years, the strong dynamics of the Earth's radiation belts have been responsible for many hazards both on space and Earth technologies. For example, some geomagnetic storms can be linked to outages or losses on satellites, as Galaxy IV in 1998 or more recently, GOES 15 in 2012. Despite the fact that radiation belt physics has been studied since the beginning of the Space Era, numerous challenges still exist. In particular, trapped particles losses constitute a big challenge in the Earth's radiation belts. Many processes can induce losses, and the net result only consists in a balance between all of them (see Turner et al.  for more details). Among them, typical interactions with the upper atmosphere and electromagnetic waves are a continuous mechanism to loose particles through pitch angle scattering. However, especially in the outer radiation belts, other types of losses are observed. Besides adiabatic losses commonly measured at geostationary orbit (see Onsager et al.  for details), rapid and nonadiabatic losses, commonly named dropouts, can occur during strong geomagnetic disturbances.
First studies about dropouts were done in 1968 by Bailey and 1974 by Larsen and Thomas. They both discussed the intensification of electron precipitation during such events as the prime cause of rapid losses [see also Millan and Thorne, 2007]. Morley et al.  confirmed these studies by performing a Superposed Epoch Analysis using GPS measurements during Stream Interface-induced events. They showed that based on complementary total electron content measurements, the intensification of Chorus waves at high latitudes during these kinds of events can significantly induce rapid and intense scattering of trapped electrons into the atmosphere. At the end of the 90s, Li et al.  discussed another process inducing rapid losses in the outer part of the radiation belts. Due to the combined transport of trapped particles by convection and the dayside compression of the magnetopause when solar wind structures hit the magnetosphere, trapped particles can be lost during their drift around the Earth in crossing the magnetopause. This has been named magnetopause shadowing. Surprisingly, fewer studies focused on this mechanism. Onsager et al.  highlighted such induced losses at geosynchronous orbit using a multimeasurements analysis. More recently, Yu et al.  found that magnetopause shadowing contributes from 93 to 99% for dropouts at geosynchronous orbit, but only 60% at lower orbits, thus implying other mechanisms to become more effective there than direct untrapping. The review from Turner et al.  discusses this complexity of dropouts, as its main cause depends on the considered orbit, the kind of solar wind structure impacting the magnetosphere, and even the energy of particles. They conclude that the global balance between all the processes inducing losses in the radiation belts, which are enhanced during geomagnetic disturbances, shapes the dropouts. Reeves et al.  studied the relative importance of dropouts, no change or increase of relativistic electron flux during geomagnetic storms and showed that effectively, depending on such parameters, the radiation belts can react in different ways.
As a consequence, to fully model and understand dropout dynamics, a reliable radiation belt model is of great interest since it is designed to balance the effects of each process on trapped particles. The Salammbô code has been developed at ONERA to accurately model the dynamics of the electron and proton radiation belts (see Beutier et al.  and Bourdarie and Maget [2012, and reference therein] for more details). However, up to now, magnetopause shadowing effect was not directly modeled inside. Different works have been published to model magnetopause shadowing effect, but quite none validates its prime importance in the dynamics of outer electron and proton radiation belts. Glauert et al.  developed an implementation for their British Antarctic Survey radiation belt model in combining the standoff distance of the magnetopause estimated by Shue et al.  with Matsumura et al.  method. They derived an analytical formula computing the last closed drift shell as a function of pitch angle and the standoff distance of the magnetopause. However, they do not study more in details the impact of this modeling in their global radiation belt model. In particular, dropouts are typical case studies to validate timescales of processes modeled such as radial diffusion and/or wave-particle interactions.
As far as we know, no study has already discussed both the detailed modeling of magnetopause shadowing in a global radiation belt model and its prime role in dropouts induced by any kind of solar wind structures. We consequently propose in this paper a Superposed Epoch Analysis relying on a new model of magnetopause shadowing effect that has also been included in the Salammbô code. Detailed results and comparisons are provided thereafter in order to argue on the prime importance of magnetopause shadowing for both electrons and protons in the radiation belts above a few hundred of keV. In section 2, we present our model of magnetopause shadowing effect added to Salammbô and first validations on typical cases and orbits. Section 3 is dedicated to a Superposed Epoch Analysis based on Polar-orbiting Operational Environmental Satellite (POES) data set which aims at both highlighting the accuracy of the model developed in previous section and highlighting statistically the importance of magnetopause shadowing effect in dropouts, for MeV energy particles in the outer radiation belt, regardless of the structures present in the solar wind. We finally discuss in section 4 the impact that magnetopause shadowing effect may have in the whole radiation belts, independently of the solar wind structure compressing the magnetosphere.
2 A New Model of Magnetopause Shadowing Dedicated to Radiation Belt Models
Estimating the effect of magnetopause shadowing on radiation belt dynamics is not an easy task. The first question rising is how to locate the distortion of the magnetic field properly in the vicinity of the magnetopause that tends to open the drift shells of trapped particles. Current global magnetic field models become more and more accurate, but as consequence, it is also more and more time consuming to compute drift shell with them. For our purpose, we decided to roughly estimate the location of the magnetopause nose (in the magnetic equator) in terms of a “corresponding” Roederer L* parameter (noted in the following). We assume that this approach (described thereafter) is zeroth-order estimation, but one has also to consider all the approximations made in 3-D radiation belt models. In particular, most of them [Glauert et al., 2014; Reeves et al., 2012; Su et al., 2010; Subbotin and Shprits, 2009; Beutier et al., 1995] are considering the dipolar approximation to facilitate computations. We will show in section 4 that even with such a rough modeling, consistent comparisons with observations can be made and conclusions asserted regarding radiation belts simulations results.
The first step to derive value consists in estimating the spatial location of the magnetopause. Again, following our idea to use this modeling in the Salammbô code, we decided to use an empirical and analytical model of the magnetopause to avoid heavy computations. As a consequence, we implemented the well-used Shue et al.  model. This model uses a functional form based on the interplanetary magnetic field (IMF) Bz and solar wind dynamic pressure Dp to estimate the magnetopause-Earth distance. This version of the model has been upgraded from the 1997 version [Shue et al., 1997] in order to be valid also under extreme solar wind conditions, e.g., for Dp up to 60 nPa and |Bz| up to 20 nT [Shue et al., 1998]. It appeared to us to be the best compromise between an accurate model and a simple one to implement. Shue's models (1997 and 1998) have been used numerous times in different contexts. The Shue et al.  model is used in the OMNI solar wind database to estimate the time shifting of the data through the computation of the nose location of the bow shock along with the Farris and Russell  model. The Shue et al.  one has been used in different Tsyganenko magnetic field models [Tsyganenko, 2002a, 2002b; Tsyganenko and Sitnov, 2005] as the magnetospheric boundary. It is important to note that using models of magnetopause as well as sophisticated magnetic field model has both the advantage and the disadvantage of relying on solar wind parameters. The advantage is that it obviously improves the modeling, but the disadvantage is that solar wind parameters are not always available on the contrary of ground-based indices such as Kp index. From the radiation belt modeling point of view, this is an important point to keep in mind. The Shue et al.  model has already been used in different studies to model magnetopause shadowing effect on radiation belts dynamics. In particular, Matsumura et al.  highlighted the good correlation between the earthward movement of the standoff distance of the magnetopause (in Earth radii) and the outer edge of the outer belt. Following this idea, we made the step to define an equivalent using Tsyganenko 89c magnetic field model [Tsyganenko, 1989]. To estimate this value, we used the IRBEM-lib [see Boscher et al., 2010] and performed the computation in the magnetic equator plane from 12 h magnetic local time (MLT). As mentioned above this is a rough shortcut to the complex and not fully known physical processes acting in this unstable region. However, from a pure computational point of view, this method stays often consistent with the use of the Tsyganenko 89c model. Indeed, it is most of the time possible to compute a corresponding value to the standoff distance of the magnetopause as there is not a magnetospheric boundary implemented in Tsyganenko . When open field lines occur during the computation of , we switch to a simple computation of the last closed drift shell using only the Tsyganenko magnetic field model. In order to avoid discrepancies related to dual magnetic equators as often present in the noon sector, we perform our estimation of the magnetic flux (and related L* value) from 0 h MLT using the IRBEM-LIB. In both cases, we only compute in the magnetic equatorial plane, which corresponds to 90° equatorial pitch angle particles case. We effectively assume that as detailed by Selesnick and Blake , due to shell splitting, particles bouncing outside the magnetic equator along a field line at noon drift along higher L shells. As a consequence, they are even more inclined to be untrapped than equatorial mirroring particles. Besides, we need to mention that some particles bouncing outside the equator along smaller field lines in the noon sector may also be considered as untrapped by our model as they may belong to L shells greater than . Furthermore, Case and Wild  compared the standoff distance of the magnetopause estimated by different models (including the Shue et al.  one) to Cluster magnetopause crossing observations and showed that Shue et al.  overestimates the standoff distance in average by about 1 RE (~9%). Thus, although we are using a rough modeling of the magnetopause location in terms of last closed drift shell, we are confident not to introduce insidious bias in our modeling. We also believe that processes acting inside the radiation belts will tend to react by themselves very rapidly to such disorders, as discussed in section 4.
As we have just explained, our model, which relies on Tsyganenko 89c model, produces a rough estimate of the real location of the magnetopause as seen from the point of view of trapped particles. It is obvious that depending on the magnetic field model we would use in our computation, different estimates would be obtained. As a comparison, we also made the estimation of the L* value of the magnetopause using Tsyganenko 2001 Storm model (see Tsyganenko [2002a, 2002b] for more details) for year 2003 during which intense events occurred. Figure 1 presents results from this comparison. The four bottom panels of the figure highlight the characteristics of year 2003. In particular, two extreme dropout events are clearly observable on NOAA-POES 15 measurements: on 30 May and 20 November. Of course, the Halloween storm also produced an intense dropout, but plotted measurements are “contaminated” by protons during that period. Nonetheless, if we zoom into the data and suppose the dropouts are produced only by magnetopause shadowing, one can roughly estimate the location of the magnetopause at about L* equal 3.5 on 30 May and 3 on 20 November. During these two events, Kp reached high levels and whether the flow pressure of IMF Bz peaked. The comparison between both computations is shown on the upper panel as a correlation plot. First, we can note the large variability in the estimation of the location of the magnetopause between these two models. When the solar wind perturbations are small, computed with Tsyganenko 89c tends to be smaller, thus enhancing the impact of the magnetopause shadowing in the radiation belts. In the contrary, for intense events, we see that Tsyganenko 2001 Storm model provides smaller L* values. In particular, while using Tsyganenko 89c model (only relying on Kp index), we cannot obtain values below 3.8, values of 3 (for 20 November) and 3.35 are obtained with Tsyganenko 2001 Storm model, values which are comparable to observations made by NOAA-POES 15. As a conclusion, using Tsyganenko 2001 Storm could even improve our modeling during intense events. This comparison shows the general trend and variability of the estimation of as a function of the magnetic field model used. Furthermore, it is important to note that due to inconstancies between the spatial location of the nose of the magnetopause and closed drift shells in the magnetic field models used, the value could have been computed only 45% of the time for Tsyganenko 89c model and 5% of the time for Tsyganenko 2001 Storm model. In such case, our logic has been described before, and we compute the last closed drift shell of the model. This can be made easily for Tsyganenko 89c model since it only relies on Kp index, but for Tsyganenko 2001 Storm model, it becomes too massive CPU time consuming since it relies on the combination of many input parameters. This is why we prefer having a first-order guess of using the “simple” Tsyganenko 89c model.
Finally, based on this model of , we have defined a loss term to be added in the Salammbô code for L* values greater or equal to the current and which relies on the drift periods of particles. It is computed using the dipolar approximation of the drift period [Roederer, 1970] and is consequently energy, equatorial pitch angle, and L* dependents. The loss timescale has been tuned so that almost all particles at a given L* value are lost after one drift period (99%). Physically, this aims to model at first order the direct losses due to magnetopause crossing in the daylight sector while still allowing radial diffusion and other processes to play a significant role. Furthermore, we assume conserving the outer boundary at L* equal 8 active at all times even during dropouts periods. We figure out that as losses depends on energy, we are still able to feed radiation belts at low energies (below a few hundred of keV) while losing higher ones.
As an illustration of this modeling, Figure 2 presents a comparison between our model of and Van Allen Probes data during May and June 2013. Figure 2 (top) shows L* versus time bins of flux levels of 0.728 MeV protons observed by the Magnetic Electron Ion Spectrometer (MagEIS) detector on board Probe A [Blake et al., 2013]. Our magnetopause model is plotted as a red curve using 1 h averaged OMNI solar wind database. Figure 2 (middle) shows 0.7158 MeV electrons observed by the same detector with our model plotted in blue. Figure 2 (bottom) corresponds to the evolution of Kp index during these 2 months. We can note a very good agreement between particles dropouts and earthward movements of , especially during 1 and 29 June, and this for both species. Even if this is only a one-event illustration, this constitutes a strong argument to magnetopause shadowing as the prime trigger of dropouts in the outer radiation belt above a few hundred of keV. Nonetheless, our magnetopause model correlates well with the observed radiation belt dynamics, but also (and for the first time), we introduce evidences that the process inducing dropouts has to be effective for both electrons and protons, thanks to Van Allen Probes observations.
To go further, Figure 3 presents simulations results at geostationary orbit for the same interval of time. Two Salammbô simulations have been performed: one including the dropouts modeling (red curves) and the other one not (blue curves). Both simulations are driven by a constant outer boundary at L* equal 8 derived statistically from Time History of Events and Macroscale Interactions during Substorms (THEMIS) measurements, so that no artifact is induced by geomagnetic dependencies. Figure 3 (bottom) shows again the Kp index evolution during this period. In Figure 3 (top) is plotted . During the geomagnetic disturbances observed here, one can note that the model predicts the magnetopause to get closer to the Earth below L* equal to 5. Figure 3 (first and second panels) compare SEM (Space Environment Monitor) greater than 800 keV and 2 MeV electrons measurements observed onboard GOES 13 [Jocelyn and Grubb, 1985] with Salammbô simulations along the same orbits. The results are pretty convincing, especially for electrons greater than 800 keV. Some differences occur above 2 MeV, but they are mainly due to the constant outer boundary that tends to overestimate the flux level at these energies. However, the rapid and nonadiabatic losses observed at GOES 13 orbit are well modeled by Salammbô.
Comparing modeling to observations at geostationary orbit is a first proof of the prime contribution of magnetopause shadowing to dropouts. However, this orbit has already been studied regarding such rapid losses [Ohtani et al., 2009; Onsager et al., 2002; Matsumura et al., 2011]. In the next sections, we aim to extend these conclusions at lower L* values, arguing that processes acting below the location of the magnetopause as modeled here tend to propagate even deeper their effects. Section 3 is dedicated to confirm statistically this assessment using a Superposed Epoch Analysis based on NOAA POES 15 measurements.
3 A Statistical Validation Using a Superposed Epoch Analysis Based On NOAA-POES Data Set
3.1 Methodology and Data Used
As detailed in the previous section, we aim at assessing the prime role of magnetopause shadowing during dropout events in a general way. We thus have implemented a Superposed Epoch Analysis method (noted SEA in the following) [Singh and Badruddin, 2006]. This powerful method characterizes statistically the global variations of a parameter with respect to the time. Moreover, it smooths noisy fluctuations to highlight the general trends. However, one has to be careful regarding the interpretation of the corresponding results, because it returns only the global variations and real cases may be far from it. In particular, strong case has to be taken to assure that the statistical spreading is small enough compared to the average trend observed. For our study, we have defined a 6 day window centered on the beginning of dropouts, noted tev in the following, in order to synchronize the SEA performed. The definition of tev is the critical point of the method.
The different SEAs conducted in this study have been performed on the solar wind parameters, Kp, , and electron flux in the radiation belts. We have used the 1 h resolution OMNI2 solar wind database for the solar wind parameters and Kp. Concerning the electron flux, in order to have a wide coverage in L* values and a significant database, we have used NOAA-POES 15/Medium Energy Proton and Electron Detector data [Evans and Greer, 2000]. This polar-orbiting satellite was launched in 1998 and is still in activity. It offers more than a solar cycle of data along all L* values. For our study, we have used data from July 1998 to December 2013, and we have binned them with a 0.1 resolution in L* and made bins for every 30 min intervals (which is a little greater than quarter of orbits, thus assuring the crossing of all L* values for each bin). We have used the 8 s resolution omnidirectional and integrated flux of the P6 channel. Yando et al.  showed that this channel (initially dedicated to proton measurements) was measuring relativistic electrons outside the South Atlantic Anomaly and was sensitive to electrons of energies greater than 1000 keV as it can be seen on Figure 8 of their paper. Furthermore, as POES 15 is a low Earth orbiting satellite and the onboard detectors are quite directional, we have used for our study the 90° detector which observed trapped electrons in the outer belt for latitudes greater than 35° as discussed in Rodger et al.  with reference to Gamble et al. [2008, Figure 5] therein.
For each SEA done, we have focused on the correlation between and the electron flux. Because of the non-Gaussian distribution of the data, the spreading of the SEA is represented using InterQuartile Range (IQR), which shows 50% of spreading around the average, rather than typical standard deviations. They are plotted as red histograms in the relevant figures discussed thereafter.
3.2 Validation of the NOAA-POES SEA
We have first performed an analysis of the 67 Stream Interfaces (SIs) previously studied by Morley et al.  using NOAA POES 15 data. These events occurred between 2005 and 2008, and their dates are available in Morley et al.  (with a 30 min of accuracy). While the previous study used GPS constellation to analyze electron flux, we instead take advantage of NOAA POES15 data set, which offers a wider coverage in L* and consequently fill up the analysis of relativistic electron fluxes below L* equal 4. This study permits to confirm the previous one realized by Morley et al.  and to get a more complete view of dropouts dynamics.
Figure 4 shows the global variations of relativistic electron flux (energy above 1 MeV) for this SEA. Global variation of is also overplotted in order to highlight their correlation. We have added the averaged geosynchronous orbit, represented by the dotted line at . As illustrated in this figure, we can see a decrease of the Earth-magnetopause distance, with a minimum synchronized with tev. Nevertheless, this decrease remains relatively weak. Indeed, the magnetopause only reaches geosynchronous orbit . This is due to the fact that the listed SIs have been chosen to well define structures of the solar wind, but not necessarily big ones which would induce strong disturbances in the radiation belts. We note that there is globally a net decrease of the electron flux during the event, within a factor of about 5 at the geosynchronous orbit. Moreover, we observe a strong correlation between the decrease of the Earth-magnetopause distance and the flux decrease, as already discussed in Morley et al. . However, our model locates the nose of the magnetopause inward from the one determine in that study. Although these decreases remain weak, is obviously directly linked to dropouts dynamics and even during such events, its role is of prime importance, along with intensification of wave-particle scattering. By filling up the previous study performed by Morley et al. , we have validated our method, and we have extended this analysis to a wider range of L* thanks to NOAA POES 15 data.
3.3 Using Our Model as an Automatic Dropout Intensity Index
We have then decided to perform the inverse method. Instead of selecting structures in the solar wind, we have defined a criterion on the location of to drive our SEA. This is also a way to study the relevance of our model of as a prime characteristic of intense dropouts.
We have used the NOAA POES 15 data set, from July 1998 to December 2013, encompassing more than 15 years of data. This time coverage is interesting because we can study the correlation between Earth-magnetopause distance and relativistic electron flux on more than a solar cycle. As mentioned above we do not consider “real events” in terms of direct occurrence of solar wind structures at that times but rather define an event if reaches a value below 5.5 with a 1 day window to avoid redundancy of a same event. We thus obtained 396 events thanks to this criterion, which is statistically significant for the SEA method. It is important to note that this filter, as it will be discussed in the following paragraph, corresponds to rather large geomagnetic disturbances in the radiation belts, i.e., larger dropouts than the ones discussed in previous subsection.
Figure 5 represents global variations of with respect to the time during an event defined by the previous criterion, from 3 days to the date tev of the event to 3 days after, as defined in the previous section. Figure 6 represents also the global variations of the geomagnetic activity index Kp, the solar wind density n, the solar wind dynamic pressure Dp, and IMF Bz component. Finally, Figure 7 shows the global variations of the relativistic electron flux (energy above 1 MeV). The global variation of is also overplotted in order to highlight their correlation. Compared to Figure 4, we highlight here a strong correlation between and the electron flux dropout. We can also observe that predropout level is recovered after about 3 days, which corresponds to real losses, indeed refilled at these energies through injections from the plasma sheet and wave-particle energization. With such a criterion, we can note that the average Kp value at the dropout “peak” reaches a value of 6, and fluxes drop by a factor of about 10 at L* equal 6. Effects of the geomagnetic disturbance to which the dropout is linked are also observable below L* equal 3, i.e., in the slot region. Moreover, the spreading of the data is quite small, as represented by the IQR in Figures 5 and 6 in red. At the difference of the list of SI used in Morley et al. , which consists in isolated events, we here melt all kind of structures impacting the magnetosphere (coronal mass ejections (CMEs) as well as strong corotating interaction regions). Moreover, the events taken into account may be severe ones which in consequence may not be uncorrelated to others ones. This explains the difference in the predropout flux level between Figures 5 and 6 as well as the loss amplitude.
Another interesting point is that if we focus on Figure 6, the solar wind parameters evolutions appear to be synchronized with the date of the event defined by the criterion on . On Figures 5 and 6, we have also plotted the strongest and weakest events of the list (minimum and maximum values of each parameter at tev). Minimum and maximum values at tev are respectively plotted in blue and purple in these figures. We can see that real events can be far from the average for any considered parameter. Thus, we have to keep in mind that a SEA method only returns a global variation of the studied parameters. Depending on the way events are selected for a SEA, it is never easy to get a reduced dispersion in the results. Indeed, in the considered case, the objective of Morley et al.  was to select an isolated SI in order to be sure that the results were not disturbed by other solar wind disturbances. However, depending on the configuration of the Sun-Earth system, one structure may be more or less geoeffective with regard to the radiation belts, and the time tev of the SEA may be more or less well synchronized. As a consequence, dispersions may be important and have to be considered. In order to check if caught events correspond to real events, we have done a comparison with two lists of events, one of 279 CMEs (from July 1998 to December 2009) [see Mitsakou and Moussas, 2014a, 2014b] and another of 443 Stream Interaction Regions (SIRs) (from July 1998 to December 2009) [see Jian et al., 2006]. 129 CMEs and 151 SIRs were caught by our criteria on . The restrictive and arbitrary condition on this criterion and the geoeffectiveness of CMEs and SIRs could explain events which have not been detected by the filter. Indeed, the definition of the beginning of events can be different from a list to another (see Mitsakou and Moussas [2014a, 2014b] and Jian et al.  for more details). It is finally important to keep in mind that the criterion we have implemented tends to filter only the most geoeffective ones. It is nonetheless a simple and accurate measure of the amplitude of dropouts, both for electrons and protons, as it has been shown in Figure 2.
4 Enhanced Results: Salammbô Accuracy and Extreme DropOuts Effects
To go further, we used the average evolutions of Kp index and solar wind parameters obtained with the SEA of previous section to drive a Salammbô simulation over 6 days and compare simulations results to NOAA POES 15 observations. Figure 8 shows such comparisons for two L* values, one at L* equals 5.6 to highlight direct effects of losses due to inward magnetopause shift and another one at L* equals 4.1 to focus on indirect effects and recovery timescales modeled in Salammbô. These plots present normalized flux values to the values at time tev + 3 days, in order to compare them. Indeed, the SEA represents only an average trend of the relativistic electron flux behavior obtained at low Earth orbiting, while the Salammbô simulation tends to reproduce a real case with a given initial state and omnidirectional flux estimated along the whole field line (from the equator to the loss cone). Thus, we only study their relative variations to compare them together. Some differences exist between the normalized SEA and the Salammbô simulation, but we note a good accuracy for both L* values. Indeed, differences are mainly effective close to tev since while SEA represents a general trend (average of multiple events), the Salammbô simulation provides the estimation of the dynamics of a single event (even if it is an average event), which explains the net drop of the electron flux at that time. However, it is of great interest to note that the timescales (again, on average) for particles drop and especially for recovery after the dropout fit well.
We have then compared our simulations outputs during the Saint Patrick geomagnetic storm to the Van Allen Probes data. Figure 9 presents these results. Figure 9 (third to sixth panels) shows the evolutions of the driving parameters (Kp index, flow pressure, and IMF Bz). Then the Van Allen Probes data are plotted in a special L-bin format for 740 keV electrons. Indeed, data from probes A and B have been combined as a L-bin performed along the orbit in order to avoid orbit averaging which may smooth artificially dropouts. Figure 9 (first and second panels) shows the Salammbô outputs with and without taking into account magnetopause shadowing effect. The boundary condition imposed at L* equal 8 for these Salammbô simulations is a Kappa distribution based on a statistical survey performed on THEMIS data for small Kp values. We have chosen to use a static boundary condition in order to highlight the effect of magnetopause shadowing. We could, for example, have used Kp-dependent distributions, but this would have introduced discrepancies since in such a kind of boundary condition, dropouts are partly taken into account through the statistic used to make them. We can see clearly that the introduction of magnetopause shadowing effect modeling in the Salammbô simulation improve drastically the results. Some differences are still present due to the nonperfect balance between all the processes modeled acting during a storm (for example, the balance between radial diffusion and wave-particle interactions), but the global shape and the order of magnitude reproduced are pretty consistent with the observations.
We can conclude that even if approximations have been made in the development of the magnetopause shadowing model added to the Salammbô code, the global model reproduces accurately the dynamics of the radiation belts (at least in average) during intense dropout at MeV energies. In particular, this implies that all the acting processes in the radiation belts are well modeled and balanced each together in Salammbô. Again, this study shows that the criteria on is very powerful, as it is consistent with both observations and global modeling of the radiation belts.
Finally, we wanted to discuss here a last interesting point according to us since the Salammbô code appears to be enough accurate to reproduce the dynamics of the radiation belts during intense dropouts about a few hundreds of keV. If considering extreme events, during which the magnetopause is intensively pushed inward, one question of great importance would be down to which L* value can a dropout (primarily induced by magnetopause shadowing effect) be effective? In a tentative to answer to such a question, we have considered the March 1991 storm during which Dp has probably (no solar wind data during the main part of the storm) easily exceeded 25 to 30 nPa and IMF Bz fell down below −15 to −20 nT. Table 1 synthetically highlights the saturation of our magnetopause location model when Dp and Bz are enhanced. For realistic values we tend to saturate at L* equals about 4. This can be explained by the limitation of the Tsyganenko 89c model used here which only has one Kp class greater than 6 and the statistics used by Shue et al.  to develop their model. However, even physically, it is not possible to compress indefinitely the Earth magnetic field. Thus, we decided to perform a Salammbô simulation with a magnetopause positioned at L* close to 4 and look at its influence on the global radiation belt shape. Figure 10 presents these results. The black curve represents the normalized flux distribution as a function of L* for electrons greater than 1 MeV 1 h after the magnetopause was pushed down. The other curves show the evolution of this distribution along the next day. We can note that due to outward radial diffusion, losses propagate down to, at least, L* equals 2, after a few tens of hours. This clearly shows that magnetopause shadowing during extreme events can have great influences in the evolution of the radiation belts, even well below its location. Of course, without radial diffusion nor wave-particle interactions, the conclusions would not be the same, but this process may have drastic effects, not only, as too often considered, in the outer part of the radiation belts.
|Dp (nPa)||IMF Bz (nT)|
To conclude, in this paper, we have presented a method to define the Earth-magnetopause distance in terms of Roederer parameter L*, noted . This model has been used on a data set and incorporated to the Salammbô model. Both provide great results for both electrons modeling, and, for the first time for proton observations thanks to the Van Allen probes investigations.
As dropouts can be observed for both electrons and protons, we have then studied the correlation between the Earth-magnetopause distance, with the Roederer parameter , and the net decrease of relativistic electron flux during geomagnetic storms, in order to demonstrate the main part of magnetopause shadowing on dropouts on the outer electron radiation belts during geomagnetic storms. Our SEA fills up the one from Morley et al. . Based on that, we have been able to define simple criteria to automatically detect intense dropouts events with great success based on our model of .
Finally, we have shown that magnetopause shadowing effect is of prime importance during disturbed time in shaping the dynamics of the radiation belts, again both for electrons and protons, even at lower L* values, for MeV particles. Despite these results, it is important to keep in mind that dropouts remain a difficult issue and might even be caused by a combination of several physical processes acting together. To go further, a refined model, taking into account the magnetic local time, would improve these considerations. In the same way, we have also modeled the response of protons during dropouts using a dedicated Salammbô model, and again, good agreements have been obtained when comparing to Van Allen probes data. Moreover, a calculation of taking into account the pitch angle dependency would improve the modeling of magnetopause shadowing and has to be kept in mind. Even if our model of location of the magnetopause is very simple, its uncertainties can be used in data assimilation framework [see Bourdarie and Maget, 2012] to improve the modeling of the radiation belts during dropouts. First simulations have been performed, and this effectively improves the results.
We are thankful to the Van Allen Probes mission, NASA's OMNI, and NOAA's POES for online data access. RBSP-ECT work was supported under NASA prime contract NAS5-01072 to Johns Hopkins University Applied Physics Laboratory (JHU/APL). Work at LANL was performed under the auspices of the United States Department of Energy. Data are available on the CDAweb at http://cdaweb.gsfc.nasa.gov/. D. Herrera is thankful for funding from CNES and ONERA, under grants agreements 15304 and 8414. V. Maget is thankful for funding from the European Union Seventh Framework Programme under grant agreement 606716 for project SPACESTORM.
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