Structure and Dynamic of Electron Radiation Belts: Implementation | EE T220, Papers of Microelectronic Circuits

Download Structure and Dynamic of Electron Radiation Belts: Implementation | EE T220 and more Papers Microelectronic Circuits in PDF only on Docsity! Submitted to Proceedings of ESPRIT Workshop Rhodes, Greece, March 25-29, 2003 - 1 - Structure and Dynamics of the Electron Radiation Belts: Implications for Space Weather Modeling and Forecasting D. Vassiliadis1, A.J. Klimas2, S.F. Fung2, D.N. Baker3, R.S. Weigel3, S. Kanekal4 1 USRA at NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA 2 NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA 3 LASP, University of Colorado, Boulder, CO 80309, USA 4 Catholic University of America, Washington, DC 20007 Vassiliadis et al., The Electron Radiation Belts - 2 - Abstract. Since the early 1990s a series of missions have completely transformed our view of electron radiation belts. Here we summarize several key facts on the belt structure and dynamics derived from those missions with emphasis on issues relevant to the development of predictive models. Each section focuses on a specific issue from our group’s research, starting with the radial structure of the outer electron belt in terms of three regions (P0-P2) made distinct by the dynamics of the electron flux. Acceleration and loss processes in these regions produce a rich variety of flux dynamics. These processes are traditionally represented by diffusion-convection models. In addition, a number of new empirical models have emerged in the last two decades. These models are derived from the observed flux datasets and typically account for much of the variance. In each of the Pi regions we derive empirical models for the measured flux and introduce methods of deriving diffusion-convection models from them. Ultimately, of course, the internal processes are driven by the interplanetary activity level and its time variability. In each of the Pi regions we identify a set of solar wind precursors and a corresponding response to these precursors. Input-output empirical models (filters) driven by these interplanetary variables are used to represent the externally driven part of the flux dynamics. The impact of these modeling approaches to radiation belt forecasting is discussed. Keywords: Radiation belts, particle acceleration, solar wind-magnetosphere interaction, space weather forecasting, time series analysis. Vassiliadis et al., The Electron Radiation Belts - 5 - containing by far the largest amount of trapped radiatio and flux amplitudes. Because L=6.6 falls within geosynchronous orbit is qualitatively similar to the vari to L=4. Closer to Earth than L=4, however, is the seco clearly different dynamics. As discussed in Sections 3 a arises because of different internal radiation-belt proce wind. At higher L shells than P1 is a region of low-am (L>7.5). The dynamics of the marginally trapped popul One explanation is that electrons in P2 altitudes pro penetration into the inner magnetosphere. An alternative electrons are accelerated in the cusp [Fritz, 2001]. Finall the observed “leakage”, or outward transport, of electron [Blake et al., 2002]. The classification of outer belt dynamics in three dis with analyses of data from three other missions [Vassi (instrument: RDM), EXOS D, or Ohzora (HEP), and G altitudes. Figure 2. The radial correlation function (1) is calculated from SAMPEX/PET fluxes in the observation interval 1993-2000. Note the division of the outer belt in 3 “blocks,” or structures P0-P2 with different dynamics. The quadrupole-shaped region below P0 is the slot (S); the quadrupole shape means that the flux dynamics at the slot edges are strongly correlated with each other suggesting loss processes that operate coherently over the radial separation of the edges. Figu and Akeb shadi corre same (solid 1996 meas durin regiore 3. Solar cycle variation of the size of regions Pi the slot. Shading indicates the measurements of ono (EXOS-D); the transition of lighter to darker ng in a region indicates the L shell with the widest lation in that region (cf. Fig. 2). Lines indicate the boundaries (dotted) and widest-correlation L shells ) as measured by SAMPEX. The two diamonds in indicate the positions of P1 and boundary P1-P2 as ured by GPS NS-33. Note the strong erosion of P1 g solar maximum in favor of the quasitrapping n P2.n flux than the other two due to its size that range, the flux variation at the ation in other L shells, all the way down nd region P0, at L=3.0±0.1-4.0±0.2 with nd 4 the difference between these zones sses and types of coupling to the solar plitude, transient fluxes designated as P2 ation are significantly different from P1. bably correspond to the plasma sheet view suggests that a percentage of these y the P2 dynamics may also be related to s from the main portion of the outer belt tinct regions is validated by comparisons liadis et al., 2003b]. These are Akebono PS NS-33 (BD II) operating at different Vassiliadis et al., The Electron Radiation Belts - 6 - Solar cycle variations are evident in the radial extent of these regions (Fig. 3). The largest variation is in the P1-P2 boundary: during solar maximum, buffeting of the magnetosphere by shocks and ejecta reduces the long-trapping region P1 in favor of the quasi-trapping region P2. A similar interplay occurs between region P0 (whose greatest radial extent occurs 3 years before solar minimum) and the slot region (3 years before solar maximum). 3. Flux dynamics due to acceleration and loss processes Electron acceleration occurs due to a variety of processes [Friedel et al., 2001]. Important among those are the interaction with low-frequency waves which scatter the electrons in energy and/or pitch angle. Other major processes are direct injection and nonlinear diffusion. A standard scenario involving ultra-low-frequency (ULF) waves begins with reconnection producing a seed population of electrons (10-100 keV) during storms and substorms. Velocity variations excite ultra-low-frequency (ULF) waves in the dayside magnetopause and the flanks [Engebretson et al., 1998; Vennerstrom, 1999] primarily as shear-flow instabilities [Farrugia et al., 2001] and compression. These are consistent with occurrence distributions of ULF waves as determined from in situ measurements [Anderson et al., 1990] and remote sensing [e.g., Pilipenko and Engebretson, 2002] (there are significant differences between space and ground observations because of ionospheric absorption). At the end of this growth stage the wave power reaches its peak after 1 day [Rostoker et al., 1998; Mathie and Mann, 2000; O’Brien et al., 2003]. In the second stage the waves accelerate the seed electrons to MeV energies possibly through resonant acceleration. This is supported by simulations which use global-MHD fields as input to guiding center test particle code [Hudson et al., 1999; Elkington et al., 2003]. For that to happen the drift-resonance condition ( )1 0dmω ω− ± = (2) where ω is the wave frequency, ωd is the particle drift frequency, and the ± factor is due to the day-night asymmetry. The energy gain is of the scale of half-width around the resonant ω: ( ) ( ) 1 1 ln 2 1 d m rm m E EE e E rE m ω δ δ ± ± = ∂ ∂ ∆ =  ±    Different types of toroidal and poloidal resonances are capable of producing efficient acceleration [Chan et al., 1989; Elkington et al., 1999]. Even though MHD models do not represent the inner magnetosphere structure (they do not represent the ring current) or time dependence (their time resolution is usually limited to 1-min). Fluxes in the few-MeV range reach their peak after 2-3 days at the geosynchronous region [Paulikas and Blake, 1979; Baker et al., 1990] and a wide L range surrounding it (region P1, or L=4-7.5) [Vassiliadis et al., 2002]. Other mechanisms that involve ULF waves include magnetic pumping via pitch-angle scattering and flux tube motion associated with the waves [Liu et al., 1999]; and cyclotron interaction between trapped electrons and a fast-mode ULF wave [Summers and Ma, 2000]. More generally, other mechanisms are large- and small-scale recirculation [Nishida et al., 1976], cusp acceleration [Sheldon et al., 1998; Fritz, 2001]; direct injection during substorms [Ingraham et al., 2001]; and enhanced diffusion [Hilmer et al., 2001]. Probably the fastest acceleration is during storm sudden commencement which produces a compression and an impulsive injection [Li et al., 1993]. Vassiliadis et al., The Electron Radiation Belts - 7 - The above processes violate one or more of the adiabatic invariants to increase the energetic content. Modeling of flux measurements needs to remove any additional adiabatic changes. The most important of those is the displacement of electrons by an increase in the ring current (the stormtime “Dst effect”) or the magnetopause current. If the acceleration is purely adiabatic, the displacement is temporary and phase space density is preserved. Many actual storms produce both adiabatic and nonadiabatic changes, and in most events the Dst variation can account only for a fraction of the stormtime electron flux change [McAdams and Reeves, 2001; O’Brien et al., 2001]. The synoptic measurements of flux over a wide range of L enable us to develop models for the effective coupling between fluxes of different L shells. We disregard any local acceleration due to changes in interplanetary input or magnetospheric-activity parameter (the effect of these inputs will be examined in the next section) and write the flux on day t+1 as a function of fluxes at nearby L shells on the previous day in the following autoregressive (AR) model: ( ) ( )1; ; N e i e i N j t L a j t L i Lδ =− + = +∑ (3) where the log-flux is ( ) ( ); log ;ej t L J t L= , N is a free parameter and δL=0.1 is the minimum spacing between L shells. Negative (positive) values of i indicate transport of flux from lower (upper) L shells in 1 day. The 0-th term indicates acceleration at a fixed L, again in 1 day. The significant ai determine how large N should be, and endows NδL with the meaning of a correlation length scale (compare (3) with (1)). Note that using daily values effectively removes shorter-term effects, including adiabatic variations due to small storms. The radial coupling coefficients ai are shown in Fig. 4a as a function of i and L. In this diagram a coefficient at position (i,L) indicates the amplitude of the coupling between je(t;L) and je(t;L+iδL). Note that in regions S and P0 the correlation length is small, N=3. The function ai(i) is sharply peaked around i=0 and symmetric, indicating a diffusive process as will be discussed below. On the other hand, regions P1 and P2 are characterized by a much larger correlation length (N=20-22). The function ai(i) has a broad peak around i=0. The peak is not symmetric suggesting a diffusion-convection interpretation. Figure 4. a. Radial transport coefficients ai from AR model (3) as a function of i and L. The left-hand (right-hand) part of the figure indicates transport from lower (higher) L shells, or i<0 (i>0). b. Diffusion coefficient DLL for je. Two different ways of calculating it from (5) are shown. Vassiliadis et al., The Electron Radiation Belts - 10 - Thanks to the availability of a continuous L shell coverage by SAMPEX, we synthesize a composite impulse response H(τ;L) from responses calculated at fixed L. The composite function expresses the amplitude and time of the coupling VSW, as well as the radial location where it occurs (Fig. 5b). Peaks P0 and P1 correspond to the blocks in the radial correlation graph of Fig. 2. Thus there is a good correspondence between the dependence of long-term flux dynamics on L shell and the flux response to VSW (and other inputs). The correspondence suggests that the dynamics are determined to a great extent by the external forcing rather than by internal processes. The filters (6) can be interpreted as direct local acceleration due to processes activated by the solar wind speed (such as ULF wave acceleration). Alternatively increases in j(t;L=const.) can be due to transport from higher L shells. Because the modeling is applied on fluxes at a single energy range, there is an ambiguity between the two interpretations. The ambiguity can be resolved by modeling of flux measurements at multiple energies. In addition to solar wind velocity, other interplanetary variables are important in controlling the flux dynamics. In a separate work [Vassiliadis et al., 2003c] we have examined the response of the electron flux in terms of solar or interplanetary variables, or geomagnetic indices which we use as proxies for the regional electrodynamic activity. We find that a total of 17 such parameters fall into three categories which affect each PI region in a different way. Hydrodynamic parameters such as VSW, ρSW, and PSW can predict up to 36% of the variance in P1 and a smaller amount in P1. The IMF Bz component and magnetic indices that depende on it are a second category. The IMF Bz regulates, primarily through the reconnection rate at the magnetopause, the intensity of electric currents in the tail and its current sheet, field-aligned currents, and ionospheric currents. The electrodynamic activity is quantified in terms of regional or planetary measures of geomagnetic activity which are the geomagnetic indices. Both the IMF Bz and the indices predict the variance of fluxes in P0 and P1 in a very similar manner. The indices such as Kp and the polar cap index, PC, are much more accurate, however, predicting the variance of P1 at a 25% level and the variance of P0 at a 50% level. Much higher percentages can be explained by AR models such as (3) as Fig. 6 shows. The combination of models (3) and (6) are expected to further increase the explained variance of j(t;L). Precursors A more direct way than filters for quantifying the dynamic effects of interplanetary or magnetospheric variables on a radiation-belt region is through identifying and measuring the precursor activity. We briefly sketch out below the precursor analysis which is described at length in [Vassiliadis et al., 2003a]. We denote the daily average J(ti;Lj) as an event of that amplitude at shell Lj. The precursor to that event, in terms of the solar wind velocity, is the activity vector ( ) ( ) ( )( ) ( )( ) ( ) ( )1 , , 1 , , ,SWV SW SW SW SW st V t T V t T V t T V t T = − − − − − + I … … (7) Figure 6. Comparison of the data-model correlations for the AR and FIR (denoted as MA) models. The square of the correlation is the percentage of the variance in the flux data explained by the model. Vassiliadis et al., The Electron Radiation Belts - 11 - or a window in the velocity time series with width T+Ts, where generally 0sT T" # . Similar precursors can be formed for other solar wind and IMF variables. Precursors to events of similar activities are averaged together in a superposed-epoch-type analysis. The key is to identify similar activities over a long dataset. We use the SAMPEX/PET daily flux dataset from 1993 to 2000. The measurements are sorted in order of increasing amplitude and divided in quartiles, each comprising ~730 days. The average flux in the q-th quartile is ( ) ( )e qj L . The average precursor, ( ) ( ) ( ) ;SWV q t LI , a vector of length T+Ts, is obtained by averaging over the corresponding individual precursors (7) for each je(t;L) in the q- th quartile. Note that the precursor depends on L because of the sorting of je. The most geoeffective precursor is that with the highest q-value (here: q=4) corresponding to the top quartile. It is by construction the average of the solar wind conditions that result in the highest flux at a given L shell, or range. Fig. 7 shows the velocity, IMF Bz (in the GSM coordinate system), and solar wind density ρSW for q=4. Precursors are shown for 3 L shell regions: P1, P2, and the entire inner magnetosphere (L=1-10). The precursor for P0 is not different from P1 at the daily resolution so it is not shown. There is strong similarity between the precursors between P1 and the entire inner magnetosphere, as might be expected. However, there is also a strong contrast between those for P1 and P2. The former similarity is understandable because P1 is by far the greatest contributor to the total flux in the radiation belts, and therefore sorting its flux data (which determines the precursor profile) is essentially tantamount to sorting the average fluxes in the entire inner magnetosphere. The differences between P1 and P2 are partly explained by the stable trapping in P1 and marginal long-term trapping in P2. The picture is more complicated than that, however: the precursor for P1 has a Southward IMF Bz (middle panel of Fig. 7), consistent with energization through reconnection; it is less clear why the precursor for P2 has a Northward IMF Bz. That orientation produces reconnection poleward of and close to the cusp. Acceleration in the cusp is well established [Sheldon et al., 1998; Fritz, 2001] and is easily observable under Northward Bz conditions (although it occurs under a variety of conditions). It is also of interest that the most geoeffective precursor for P2 is a low-speed, high-density structure (top and bottom panels of Fig. 7). The contrast between the two regions is discussed in more detail elsewhere [Vassiliadis et al., 2003a]. Figure 7. Precursors for P1, P2, and the entire inner magnetosphere (L=[1-10]). Precursors are shown in terms of VSW, IMF Bz, and ρSW for the last T=20 days before a high- amplitude event (also shown are the Ts=5 days following the event). Vassiliadis et al., The Electron Radiation Belts - 12 - 5. Summary and discussion Synoptic flux measurements over the entire radial extent of the radiation belts allow us to model the temporal dynamics of the flux and determine the corresponding spatial structure in unprecedented ways. Because the new synoptic datasets span significant intervals of time, they are suitable for dynamical modeling in these regions. Correlation analysis has revealed three regions of distinct dynamical behavior, identified in regions P0 (L=3-4), P1 (L=6-7.5), and P2 (L>7.5). Flux dynamics in the slot S (L=2.0-3.0) are different from any of the three regions. The dynamics itself as obtained from AR modeling can be classified as diffusion- or convection-like. The functional form in regions S and P0 is consistent with diffusion while regions P1 and P2 include additional convection terms in their equations. Input-output analysis of the fluxes in terms of the preceding solar wind/IMF variations shows that geoeffective solar wind inputs are different for each region and at varying degrees: the variance in P1 flux is partly explained by changes in the solar wind velocity, VSW. The impulse response H(τ;L=LP1) shows a τ=2-3 day delay relative to the arrival of the solar wind. The response is well-known for j(L=6.6) and occurs for high-speed streams. The impulse response in P0 peaks more rapidly, at τ<1 day, a response which is consistent with recent observations during magnetic cloud and interplanetary coronal-mass-ejection passages. A different set of precursors is found for the third region, P2. Thus the input-output analysis suggests that, as the turbulent interplanetary input varies randomly, it excites the three regions as nonlinear modes of the inner magnetosphere. In practical terms, a first notable point is that the differences between regions Pi should be taken into account in regional modeling. A model which is accurate in reproducing fluxes at L=6.6 will have a different functional form than a model at lower or higher L shells. Second, a combination of the FIR (6) and AR (3) approaches will result in ARMA (autoregressive moving- average) models. These will increase the percentage of explained variance of je(t;L). More generally, dynamic modeling is expected to contribute to our understanding and in improvement in the predictive capabilities of radiation environment models. These models are used in tandem with radiation effects models to quantify the space weather hazards on specific spacecraft components. Current models have evolved from the static NASA AE-8 model [Vette, 1991], but are still limited in spatial and temporal coverage [Heynderickx, 2002]. This is the main reason due to which the traditional models are still the industry standard. Integrated approaches such as the interaction between empirical and physical models promoted by the Center of Integrated Space Weather Modeling (CISM) are expected to further improve the predictability of the radiation belt environment. Acknowledgments. We are thankful to the ESPRIT organizers, and especially Ioannis Daglis, for the invitation to present this work and general review to this Advanced Research Workshop. We thank T. Nagai and R. Friedel for providing additional mission data. Research was supported by the NASA/LWS TR&T program and the NASA/NSSDC research program. We also thank the data providers in NSSDC, and the Kyoto and Copenhagen World Data Centers.