Surfing Acceleration of Radiation Belt Relativistic Electrons Induced by the Propagation of Interplanetary Shock

Interplanetary shocks (IPS) can initiate prompt acceleration of relativistic electrons in the Earth's radiation belt, which is related to the generation and propagation of impulsive electric field (IEF). We investigate the effect of IEF on accelerating radiation belt electrons in the 6 September 2017 IPS event. A “surfing” effect of electrons with respect to the electric field, referring to electrons that drift together with the tailward‐propagating IEF in the duskside, is investigated in this study. Our results show that the maximum increase of electron differential flux is at 3.4 MeV by a factor of 2.2, corresponding to a drift velocity of 531 km/s, which is more consistent with the IPS propagating speed of 621 km/s rather than the fast‐mode speed of 1,074 km/s. We suggest that the effect of IPS propagation is important for radiation belt dynamics, and we highlight the potential importance of the parameter of IPS propagation speed.


Introduction
Interplanetary shocks (IPSs) have been reported to be strongly related to eruptive solar activities, such as Coronal Mass Ejections (CMEs) and Corotational Interaction Regions (e.g., Kilpua et al., 2015Kilpua et al., , 2017)).IPSs may further drive intense geomagnetic storms in the Earth's magnetosphere (Borovsky & Denton, 2006;Shen et al., 2017;Turner et al., 2019), which are referred to as Storm Sudden Commencements (SSCs) (Chapman & Bartels, 1940).Many processes in the magnetosphere can be attributed to the arrival of IPSs, such as wave generation at various scales (Fu et al., 2012;W. Liu et al., 2009W. Liu et al., , 2011; Z. Y. Liu et al., 2023;Zhang et al., 2020Zhang et al., , 2023)), enhancements in the rates of energetic particle transport and acceleration (Baker et al., 2016;Li, Baker, Temerin, Cayton, et al., 1998;W. Liu et al., 2009W. Liu et al., , 2016;;Xiang et al., 2017;Zhuang et al., 2023;Zong et al., 2009) and auroral activity caused by particle precipitation (Frey et al., 2019;Zhou & Tsurutani, 1999;Zhou et al., 2017;Zhu et al., 2020).Prompt energetic electron injections during IPSs' initial impact on the Earth's magnetosphere have been previously reported, suggesting that the westward impulsive electric fields (IEFs) induced by the impact of IPSs are the direct driver of such processes (Blake et al., 1992;Blum et al., 2021;Kanekal et al., 2016;Li et al., 1993;Patel et al., 2019;Schiller et al., 2016;Wygant et al., 1994).As the direction of the IEFs is consistent with the drifting path of energetic particles, they may gain energy while crossing the potential drop of IEF.Foster et al. (2015) reported an IPS-induced relativistic electrons' prompt injection based on Van Allen Probes (VAP) measurements and observed an IEF with an amplitude of 12 mV/m.With the assumption that the IEF covers a range of 6 magnetic local times (MLTs) at L ∼ 4, it is estimated that electrons with energy of 3-4 MeV can experience a potential drop of ∼400 kV related to the IEF, thus rapidly gaining energy of ∼400 keV within shock-induced electric field on accelerating radiation belt electrons is investigated • The drift velocity of electron experiencing maximum flux increase is consistent with the interplanetary shock's propagation speed • A new mechanism of how interplanetary shocks' propagation influence the radiation belt dynamics is proposed in this study

Supporting Information:
Supporting Information may be found in the online version of this article.
1-2 min.This approach is more efficient than the local acceleration through wave-particle interactions by chorus waves, which is found to be 2-7 MeV in 8 hr (Thorne, 2010).
Direct acceleration refers to the mechanism by which drifting electrons simply experience potential drops, as introduced above.This mechanism is highly efficient in accelerating electrons.However, assuming stationarity of the IEF will lead to an underestimation of the interaction time between the electrons and IEF, which results in the underestimation of the acceleration experienced by the electrons.Thus, drift-in-phase acceleration has been proposed to consider the effects of the propagation of the IEF (Elkington et al., 2002;Hudson et al., 2015).During the impingement of an IPS onto the Earth's magnetosphere, an IEF is initiated from the dayside magnetopause and propagates toward the magnetotail.On the duskside, electrons drift in the same direction as the tailwardpropagating IEF.Electrons whose drifting speed matches the IEF propagation speed can interact for most of the time with the IEF and consequently are most efficiently accelerated, which can be metaphorically associated with electrons being accelerated while "surfing" on (or in phase with) the IEF.This type of resonant acceleration was first suggested via test-particle simulation during the extreme IPS event that occurred on 24 March 1991 (Li et al., 1993).It has been further found that electrons at certain energies with corresponding azimuthal drift velocities comparable to the propagation speed of the IEF stay in phase with the tailward-propagating electric field perturbation and consequently are more intensively accelerated.Such energy-dependent characteristics have also been revealed in numerical simulations (Elkington et al., 2002;Hudson et al., 2017;Li, Baker, Temerin, Reeves, & Belian, 1998;Y. Liu et al., 2019;Sarris & Li, 2005;Sarris et al., 2002).For example, Hudson et al. (2017) modeled the IPS-induced prompt injection of relativistic electrons during the 17 March 2015 SSC event via magnetic hydrodynamics (MHD) coupling test-particle simulation.According to their results, electrons with initial energy of 2.0-2.1 MeV can be accelerated to >3 MeV in 90 s.Considering the drift-in-phase effect by the propagating IEF, the energy gain of electrons is much more efficient than that of electrons estimated for direct acceleration, as described in the previous paragraph.Additionally, the wave-particle interaction between energetic electrons and ultralow-frequency (ULF) waves in the magnetosphere, referred to as drift or drift-bounce resonance, is also an effective way for electrons to gain energy (e.g., Hao et al., 2019;Sarris et al., 2017;Zong et al., 2009); please note that such a process involving ULF waves takes several wave periods to become effective, while this study focuses on the acceleration induced by the IEF in the initial period.
Therefore, understanding the propagation characteristics of the IPS-induced IEF in the magnetosphere could be a key to quantifying of the acceleration and injection of MeV electrons.Thus, we recently simulated the 17 March 2015 IPS event to investigate its propagation characteristics via numerical simulations (Zhang et al., 2022), based on the Space Weather Modeling Framework (Tóth et al., 2005).Through these simulations, a new scenario is proposed in which the IPS-induced IEF is a consequence of the superposition of the fast-mode wave generated from the dayside magnetopause and the compression-induced flow related to the passage of the IPS at the magnetopause flank region.The onset and peak of the electric field impulse correspond to the arrival of the fastmode wave and the IPS normal, respectively, which could explain why the rising time of the IEF differs between dayside and nightside (Korotova et al., 2018;Zhang et al., 2018).
Previous studies have shown that (a) the propagation of the IPS normal controls the position of the peak of the IEF (Zhang et al., 2022) and that (b) electrons drifting with the peak of the IEF should gain more energy and be injected deeper (Elkington et al., 2002;Hudson et al., 2017;Y. Liu et al., 2019).Considering the above two clues, a correlation could be expected between the IPS normal propagation speed and the corresponding drift velocity of the most intensely energized electrons, which in the following are termed the resonant electrons.It can be further speculated that the electron fluxes at the energy channels of the resonant electrons should be expected to vary more compared to neighboring energy channels.However, such a correlation has never been reported in previous related observational studies.In this paper, using the Van Allen Probes (VAP) and Geostationary Operational Environmental Satellites (GOES) observations, we report that an IPS-induced prompt injection occurred on 6 September 2017.A connection between the IPS normal propagation and the radiation belt dynamics is constructed in this study.

Data Set and Method
This study is based mainly on the use of multi-spacecraft observations, and the data used in this study are as follows: Dual VAP operate in the inner magnetosphere in an ecliptic orbit with a perigee of ∼1.1 R E and an apogee of ∼5.8 R E and are used to investigate the response of electric fields and relativistic electrons.The electric field was measured by an Electric Field and Waves (EFW) instrument onboard VAP, and Level 3 data were used in this study (Breneman et al., 2022;Wygant et al., 2013).Relativistic electron flux is measured by the Relativistic Electron and Proton Telescope (REPT) onboard VAP (Baker et al., 2021).In this study, we mainly concentrate on the flux at a 90-degree pitch angle.To remove the background trend of the flux of relativistic electrons, the residual flux at a 90-degree pitch angle J J 0 J 0 is used in this study, where J is the differential flux at a 90-degree pitch angle and J 0 is the 600 s-averaged data of J (e.g., Claudepierre et al., 2013;Hao et al., 2019).GOES-13 and 15 spacecraft operate at the Geostationary Earth Orbit (GEO).The GOES spacecraft is selected for estimating the propagation speed of impulses in the dusk sector because the two spacecraft have an angular separation of 60°.Magnetic field measurements by the onboard magnetometer are used.The geomagnetic index, SYM-H (IYEMORI, 1990), is used to determine the arrival of the IPS at the Earth's magnetosphere.

Observations
The data obtained from the Wind spacecraft were used to monitor the solar wind conditions and to analyze the IPS normal.At 23:02:51 UT on 6 September 2017, the Wind spacecraft, which is located at the Sun-Earth L1 point, observed an IPS related to a CME, as shown in the left column of Figure 1.The solar wind speed V sw increased from ∼400 to ∼570 km/s.The proton number density increased from 2 to 7 cm 3 .The magnetic field strength |B| increased from 3 to 10 nT.The dynamic pressure P dyn of solar wind increased from 1 to 6 nPa.These variations suggest that the IPS can be identified as a fast forward shock, as N p and |B| downstream are greater than upstream.The propagation speed of an IPS normal V shock is estimated to be 621 km/s based on the MX3 method, which has been widely used in the determination of the shock rate and propagation speed in previous studies on CME-related IPSs (Kilpua et al., 2015(Kilpua et al., , 2017)).
Observations of the geomagnetic field and relativistic electron flux variations from the two VAP spacecraft (VAP-A and VAP-B) in the inner magnetosphere are summarized in Figures 1e-1g.At ∼23:44 UT, the SYM-H index increased from 18 to 46 nT, as shown in Figure 1e, indicating that the IPS arrived and induced global compression of the Earth's magnetosphere.Moreover, both VAPs exhibited signals of electron flux enhancement and oscillation, as shown in Figures 1f and 1g.The information on the spacecraft locations in the magnetosphere is summarized in Figure 1h.At ∼23:44 UT, VAP-A and VAP-B were both located at noon and near their apogees.The GOES-13 and GOES-15 spacecraft were located at the dusk and post noon sectors, respectively.According to the SYM-H index and VAP electron flux observations during the time interval from 12:00 to 23:00 UT on 6 September 2017, there was no obvious geomagnetic disturbance or radiation belt dynamics prior to IPS arrival.
The electric field and MeV electron observations by VAP-A is presented in Figures 2a and 2b. Figure 2a presents the electric field measured by the onboard EFW instrument, and Figure 2b presents the differential flux of 90degree pitch angle relativistic electrons with energies ranging from 1.8 to 5.2 MeV, as measured by the REPT instrument.At 23:44 UT, VAP-A was located at L ∼ 4.2 and MLT ∼ 10.6, and a dawnward IEF with an amplitude of ∼5 mV/m was observed, accompanied by oscillations of electron differential fluxes.Two different periods can be distinguished: During the first period, an enhancement of electron fluxes of all energies is observed.This enhancement occurred simultaneously at all energies, with relatively small amplitudes.During the second period, the peaks for each energy source are not observed simultaneously with the periods of flux oscillations corresponding to the drifting motion of the electrons.This result is consistent with the signature of IPS-induced dispersed drift-echo, as reported in previous studies (Hudson et al., 2015(Hudson et al., , 2017;;Kress et al., 2007;Li et al., 1993).Compared to VAP-A, VAP-B was also located at noon with an MLT of ∼12.8 but at a higher L of ∼5.7.VAP-B also exhibited simultaneous first enhancements of electron flux for all six energy channels, but there was no obvious drift-echo signal, as shown in Figure S1b of the Supporting Information S1.
To compare the amplitude of the electron flux enhancement for different energy bands, the electron flux at a 90degree pitch angle measured by the REPT instrument onboard VAP-A was normalized to the residual flux (J J 0 )/J 0 , which is presented as a spectral plot in Figure 2c.The red oblique stripe of the first drift-echo, as marked by black squares, indicates that the electrons drifted back to the spacecraft location after experiencing the acceleration by the IEF.The time-of-flight method was further applied as a backward tracing method to identify the region of electron acceleration based on the drift-echo signal in the VAP-A electron flux observation (e.g., Hao et al., 2016;Z. Y. Liu et al., 2017;Turner et al., 2015), as shown in Figure 2d.It is suggested that the relativistic electrons were mainly injected and accelerated in the region of the dusk sector (with an MLT of 18-20).In this region, the electron drift direction is consistent with the IEF propagation direction.Among these energy channels, the maximum value of the residual flux corresponding to the drift-echo for the first period was approximately 1.2 (the original differential flux at a 90-degree pitch angle increased from 2.5 × 10 4 to 1.2 × 10 5 cm 2 s 1 sr 1 MeV 1 ) in the 3.4 MeV energy channel (with the measured energy ranging from 3.0 to 3.8 MeV), which is also presented in Figure 2c.The corresponding velocities of relativistic electrons drifting at the location of VAP-A at different energy channels are also presented in Figure 2e.In the following sections, the drifting speed of electrons and the propagation speed of the IEF are discussed in further detail.

Explaining the Evolution of the Flux Variations
As shown in Figure 2b, the electron drift-echo signal is captured by VAP-A, while the drift-echo is much weaker in VAP-B's observation (please see Figure S1 in Supporting Information S1).Notably, VAP-A and VAP-B were located at L ∼ 4.2 and L ∼ 5.7, respectively.According to Figures 1f and 1g, VAP-A was closer to the peak of the radial distribution of the electron flux.VAP-B may be located at the outer radial boundary of the injected radiation belt electron population, while VAP-A may be located at the core of the radiation belt.Under the effect of the propagating IEF, electrons are dominantly transported from higher L shells to lower L shells.Thus, the different signatures of drift-echoes observed by the two probes are due to their relative radial proximity to the radiation belt, as shown in Figures 1f and 1g.
On the other hand, the relatively weak enhancement of electron flux that simultaneously occurred in all 6 energy channels was first observed at 23:45:10 UT by VAP-A prior to the interested drift-echo, as shown in Figure 2b.At this instance, the IEF arrived at the noon sector of the magnetosphere.According to the results shown in Figure 2d, the interaction between the IEF and relativistic electrons generally occurred at an MLT of 19 and at 23:46:20 UT.This can be understood as a partial, or initial, phase of the acceleration by the IEF.The relatively weak flux enhancement in the first period reflects that electrons were accelerated as the IEF first arrived at the noon sector.Until the IEF arrived at the dusk region, the acceleration by the IEF was completed, and subsequently, electrons at different energies successively drifted back to the location of VAP-A, observed as the dispersed drift-echo.

Energy-Dependent Feature in the Electron Flux Variation
According to VAP-A's observation of the electron residual flux variation, as shown in Figures 2c and 2e, an energy-dependent feature can be shown in the electron flux variation.After the IPS's initial impact on the magnetosphere at 23:44 UT, electrons at different energies successively drifted back to the location of VAP-A, which is observed as a dispersed signature of drift-echo, as marked by the black squares in Figure 2c.Among these relativistic energy channels, the electron flux in the 3.4 MeV channel increased the most, by a factor of 2.2.Moreover, Figure 2d shows that electrons with energies ranging from 1.8 to 5.2 MeV were generally injected in the dusk region.This suggests that electrons at an energy of 3.4 MeV are more likely to stay in the frame and gain more energy from the IEF as they propagate tailward in the dusk region.In other words, the corresponding drift velocity of 3.4 MeV electrons V drift matches the propagation speed of the westward IEF V Prop_IEF , which is required to maximize the energy gain.For other energies, the drifting velocity does not match the V Prop_IEF , which results in a relatively shorter interaction time and hence less energization.The relationship between V drift and V Prop_IEF will be examined, and the factors that determine V Prop_IEF will be investigated in the following section.
Here we briefly estimate the energy gain of the 3.4 MeV electrons.First, we only consider a scenario of nonpropagating IEF.Under such assumption, the 3.4 MeV electrons can only gain energy from IEF as it maintains in the dayside magnetosphere.According to the electric field measurement by EFW instrument onboard VAP-B as shown in Figure S1a of the Supporting Information S1, the amplitude of IEF (E) is ∼8 mV/m and its duration (Δt) is ∼80 s.The drift speed of the 3.4 MeV electron in the dipole field at L ∼ 4 V drift is estimated to be 533 km/s based on method by Schulz and Lanzerotti (1974).Thus, the energy gain under the scenario of nonpropagating IEF is estimated as W 1 ∼ eE∆tV drift ∼ 320 keV.Subsequently, we consider the scenario of propagating IEF.Under this assumption, the 3.4 MeV electrons can gain energy from IEF as they azimuthally fly from dayside toward nightside magnetosphere.Assuming the amplitude of IEF is ∼8 and ∼2 mV/m in the dayside and nightside respectively (Zhang et al., 2018(Zhang et al., , 2022) ) and the 3.4 MeV electrons can stay in the IEF from 9 to 24 MLT (Hudson et al., 2015(Hudson et al., , 2017;;Kress et al., 2007).Thus, the energy gain of the 3.4 MeV electrons interacting with the propagating IEF is estimated as W 2 ∼ 2πLR E ∫ 24 9 E(MLT) dMLT/ 24 ∼ 588 keV.Comparing with the non-propagating scenario, there is extra energy of 268 keV, which can be attributed to resonant effect with the propagating IEF.In the simulation on IPS-induced relativistic electrons acceleration occurred on 17 March 2015 by Hudson et al. (2017), the amplitude of IEF in the dayside was ∼15 mV/m and electrons with initial kinetic energy of 2 MeV were accelerated up to 3.5 MeV (i.e., an energy gain of 1.3 MeV).This result is consistent with our estimation of 588 keV with the amplitude of IEF of ∼8 mV/m in dayside.This energy gain is less than the energy width of the 3.4 MeV channel of REPT instrument (3.2-4.0MeV; Baker et al., 2013Baker et al., , 2021)).Further studies with observations with finer energy resolution will enhance the understanding of this acceleration mechanism, such as the REPT integrated little experiment-2 (REPTile-2; Li et al., 2024) instrument onboard the Colorado Inner Radiation Belt Experiment.

Factors That Determine the Propagation Speed of IEF
The propagation speed of the fast-mode wave in the azimuthal direction was estimated based on the onset time of the magnetic field enhancement as observed by GOES 13 and 15 V fast_GOES , as shown in Figure S2 of the Supporting Information S1.The time difference ∆t of the observation of the magnetic field enhancement between the two spacecraft was 41 s.GOES 13 and 15, operating at the GEO with L ∼ 6.6, have an MLT separation (∆MLT) of 4. Thus, the propagation speed in the dusk region is estimated to be 2πLR E ∆MLT 24×∆t ∼ 1,074 km/s.This result is consistent with the fast-mode V fast_plasma speed of ∼1,000 km/s in the inner magnetosphere, as estimated from the Alfvén speed calculated from the magnetic field and plasma density obtained from the EMFISIS instrument.In Figure 2e, the drift speed of the 3.4 MeV electron in the dipole field at L ∼ 4 V drift is estimated to be 533 km/s (Schulz & Lanzerotti, 1974), which is nearly half of the propagation speed V fast_GOES (1,074 km/s) but comparable to the shock propagation speed V shock (621 km/s).
The propagation speeds of IEF V prop_IEF in the azimuthal direction can also be estimated based on the IEF observations obtained via EFW measurements onboard the VAP-B spacecraft, as shown in Figure S1a of the Supporting Information S1, and the results of the time-of-flight method are shown in Figure 2d.The IEF was first observed at 23:44:32 UT at the location of VAP-B (Figure S1a in Supporting Information S1), with an MLT of ∼12.According to the results of time-of-flight backward tracing, the interaction between relativistic electrons and IEFs mainly occurred in the region with an MLT of 19 and an L of 4.2 at 23:46:20 UT.Thus, V prop_IEF in the azimuthal direction can be estimated as 2πLR E ∆MLT 24×∆t ∼ 450 km/s, where the value of L is 4.2, determined as the L of the VAP-A and R E represents the radius of the Earth (∼6,377 km).Based on the results of this calculation, V prop_IEF is more likely to be consistent with V drift (533 km/s) and V shock (620 km/s) rather than V fast_GOES (1,074 km/s).
The five speeds mentioned above are summarized as below.The V drift and V shock velocities are approximately 500-600 km/s.The IPS can initiate inward compressional flow from the magnetopause (Sibeck, 1990), which induces the peak of westward IEF (Vasyliunas, 2001).This may indicate that the peak of the IEF can be considered to be moving tailward along with the IPS normal and further determine the greatest resonance energy of the electron.The MHD numerical simulation of the IPS-induced IEF in the Earth's magnetosphere by Zhang et al. (2022) provides supporting evidence: the peak IEF in the simulation generally points westward, and its propagation is consistent with IPS propagation.In this event, V shock may first determine the propagation speed of the peak westward IEF V Prop_IEF, and then V drift of the 3.4 MeV electron may directly match the propagation speed of the peak IEF V Prop_IEF; therefore, the most intense residual flux variation is observed in this energy channel.
On the other hand, V fast_GOES , calculated by the onset timing of GOES spacecraft and V fast_plasma , estimated by the magnetic field and plasma density, are both approximately 1,000 km/s.Propagation of the magnetic pulse in the inner magnetosphere is consistent with the IPS-induced tailward-propagating fast-mode wave but does not match the V drift .This can also be explained by the results of our previous simulation study by Zhang et al. (2022).It is indicated that the variation in the IEF should be interpreted as a superposing effect of the fast-mode wave initially traveling from the dayside magnetopause and inward convective flow instantly induced by the IPS normal, the latter of which dominates the amplitude of the IEF.The compression-related inward flow can induce westward IEF, and its propagation speed greatly relies on the V shock .It is suggested that neither the propagation speed of the magnetic field pulse V fast_GOES nor the fast-mode wave speed V fast_plasma is a good candidate for evaluating the propagation speed of the westward IEF V Prop_IEF ; rather, V shock could be a more appropriate candidate.

Causal Sequence From IPS to Radiation Belts Electrons
By calculating and comparing the five characteristic speeds, we find that the drift velocity of 3.4 MeV electrons (∼533 km/s) and the propagation speed of the IEF (∼479 km/s) are better compared to the propagation speed of the IPS normal (∼620 km/s) than the fast-mode speed in the magnetosphere (approximately 1,000 km/s).It is suggested that the drift-in-phase mechanism is more likely to be controlled by IPS propagation in solar wind than by fast-mode propagation in the magnetosphere.This is different from previous understandings, according to which electrons with a drifting speed comparable to the fast-mode speed were assumed to gain the most energy.
Inferred from the simulation result by Zhang et al. (2022) and the observational results presented in this study, a causal sequence from the propagation of IPS normal to the energization of radiation belts relativistic electrons is proposed and summarized in the sketch of Figure 3.This connection can be divided into 2 steps: In the 1st step, as IPS impinges on the magnetopause, inward flows induced by the compression are generated at the interaction region between the IPS and the magnetopause.Along with the tailward moving of the compression, the westward IEF induced by the inward flows propagates tailward in the inner magnetosphere.Therefore, the peak of the IEF is mainly controlled by compression at the magnetopause, and the propagation characteristics of the IEF are related to the propagation of the IPS along the magnetosphere.In the 2nd step, such a westward IEF can drive the propagating tailward throughout the inner magnetosphere (green region) at the same speed as IPS.In the outer radiation belt (red region), relativistic electrons (yellow dot) drifts eastward (yellow arrow).Among energies ranged of 1.8-5.2MeV, electrons with an energy of 3.4 MeV at radial distance of L ∼ 4.2 drift at a speed of ∼533 km/s, which more likely enables themselves stay in reference with the propagating westward electric field and hence are most effectively accelerated.On comparison, electrons with much smaller (larger) energy are lagged behind (lead ahead) the propagating westward electric field, resulting in less effective energy gain.acceleration of radiation belt electrons.Those electrons with drifting speeds comparable to the propagation speed of the IEF stay longer in the IEF and thus are most intensely accelerated.
The drift velocity of accelerated electrons in response to IPS has previously been believed to interact with the fastmode speed in the magnetosphere, while in this study it is suggested to be related to the IPS propagation speed.The surfing acceleration of 1-10 MeV by the propagating IEF was actually first revealed by Li et al. (1993) through the simulation on radiation belt in response to the extreme IPS occurred at 24 March 1991.The propagation speed of the IPS in this unique event has been estimated at the order of 1,000 km/s (Elkington et al., 2002;Hudson et al., 1997;Shea & Smart, 1996), which exceeds the characteristic fast-mode wave speed in the inner magnetosphere.This may prevent the rigorous discussion on whether the electrons should interact with an induced IEF from the V fast or V shock in related studies.Such a special IPS event has not occurred for over 30 years since then, even in the recent extreme IPS event that occurred on 17 March 2015 V shock was only ∼500 km/s.Recent VAP measurements make this new interpretation possible and offer an opportunity to enhance our understanding on this topic.

Summary
Based on multi-spacecraft observations, we investigate the IPS-induced relativistic electron injection that occurred on 6 September 2017.The VAP-A observed a drift-echo signature of relativistic electrons, and the variation in the electron residual flux at an energy of 3.4 MeV was the most intense.This energy dependence indicates that 3.4 MeV electrons gain more energy; this is attributed to their common drift together with the propagation of the IEF, which herein is referred to as "surfing" acceleration.For other energies, the interaction time is found to be shorter, resulting in a smaller residual flux enhancement.
By comparing five characteristic speeds, it is found that V prop_IEF is better compared to V drift (533 km/s) and V shock (620 km/s) rather than V fast_GOES (1,074 km/s).This leads us to propose a new mechanism to describe the effect of IPS propagation on radiation belt dynamic.Such causal chain from the IPS in the solar wind to the relativistic electrons in the radiation belt is reported in this observational study together with a previous simulation study.Through these investigations, the role of the propagation speed of IPS normal that plays in the radiation belt dynamic is revealed, which determines the energy of "surfing" (drift-in-phase) acceleration of radiation belt electrons.

Figure 1 .
Figure 1.(Left column) overview on the solar wind condition.From top to bottom, the solar wind (a) ion density, (b) speed, (c) dynamic pressure and (d) the interplanetary magnetic field strength observed by Wind spacecraft.The red vertical dashed line marks the onset time of the IPS at L1 point.The blue vertical dashed lines mark the interval for upstream and downstream.(Middle column) overview of observations in the inner magnetosphere.From top to bottom, (e) SYM-H index obtained from OMNI database.Orange vertical dashed line marks the arrival of IPS at the Earth's magnetosphere.(f) Electron differential flux at 90-degree pitch angle measured by Relativistic Electron and Proton Telescope instrument onboard VAP-A.Energy channels are marked by different colors.(g) Same format with (f) but for VAP-B.(Right column; h) Location of spacecraft orbiting in the inner magnetosphere at 23:44 UT 6 September 2017.Colored squares mark the location of spacecraft.

Figure 2 .
Figure 2. The electric field and relativistic electron flux observation by VAP-A.(a) The Y component of the in situ electric field measured by Electric Field and Waves instrument onboard VAP-A spacecraft.(b) The differential flux of relativistic electrons at a pitch angle of 90°measured by ECT-REPT instrument onboard VAP-A spacecraft.Each energy is marked with different color.(c) A spectrum plot of the residual flux (J J 0 )/J 0 of the relativistic electrons obtained from REPT-A observation.Black squares mark the peak value of the residual flux at each energy channel.(d) A plot of estimation on the tracing injection region.Black squares are derived from and consistent with them in the top panel.Slope of lines correspond to the angular drifting velocity of electrons at different energies.(e) The peak values residual flux corresponding to the first-period echo of relativistic electrons at different channels are marked by blue squares.Width of each channel as marked by blue dashed lines represents the upper and lower limit of each energy channel.Calculated results of drifting velocity of relativistic electrons at L = 4.2 in the dipole field of different energies are marked by red dots.Black dashed lines are the drifting velocity at other L shells for reference with red line.The error bars are induced by the upper and lower limit of each energy channel.Cyan shade marks the energy channel of 3.4 MeV with most intense residual flux variation observed.

Figure 3 .
Figure3.A sketch on the interpret of the controlling sequence from the propagation of IPS to the radiation belt relativistic electrons dynamic.As the IPS normal (gray light line) propagates tailward (gray arrow) at a speed of ∼620 km/s, compression-related inward flow is generated, which further drives impulsive westward electric field (white shade) propagating tailward throughout the inner magnetosphere (green region) at the same speed as IPS.In the outer radiation belt (red region), relativistic electrons (yellow dot) drifts eastward (yellow arrow).Among energies ranged of 1.8-5.2MeV, electrons with an energy of 3.4 MeV at radial distance of L ∼ 4.2 drift at a speed of ∼533 km/s, which more likely enables themselves stay in reference with the propagating westward electric field and hence are most effectively accelerated.On comparison, electrons with much smaller (larger) energy are lagged behind (lead ahead) the propagating westward electric field, resulting in less effective energy gain.