Volume 126, Issue 3 e2020JA028217
Research Article
Free Access

Earth's Magnetotail as the Reservoir of Accelerated Single- and Multicharged Oxygen Ions Replenishing Radiation Belts

Mikhail I. Panasyuk

Mikhail I. Panasyuk

Lomonosov Moscow State University, Scobeltsyn Institute of Nuclear Physics, Moscow, Russia

Deceased.

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Elena I. Zhukova

Corresponding Author

Elena I. Zhukova

Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

Correspondence to:

E. I. Zhukova,

[email protected]

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Vladimir V. Kalegaev

Vladimir V. Kalegaev

Lomonosov Moscow State University, Scobeltsyn Institute of Nuclear Physics, Moscow, Russia

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Helmi V. Malova

Helmi V. Malova

Lomonosov Moscow State University, Scobeltsyn Institute of Nuclear Physics, Moscow, Russia

Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

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Victor Y. Popov

Victor Y. Popov

Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

Physics Department, Lomonosov Moscow State University, Moscow, Russia

HSE University, Moscow, Russia

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Natalia A. Vlasova

Natalia A. Vlasova

Lomonosov Moscow State University, Scobeltsyn Institute of Nuclear Physics, Moscow, Russia

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Lev M. Zelenyi

Lev M. Zelenyi

Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

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First published: 17 January 2021
Citations: 1

Abstract

Acceleration of single- and multicharged oxygen ions in the perturbed Earth's magnetotail is investigated as the possible source of energetic heavy ions in the ring current. The numerical model is developed that allows evaluating the acceleration of oxygen ions O+-O+8 in two possible scenarios of characteristic perturbations: (A) passage of multiple dipolarization fronts in the magnetotail; (B) passage of fronts followed by electromagnetic turbulence. It is shown that acceleration processes depend on particle charges as well as characteristic time scales of induced electric field variations. Maximum energies gained by oxygen ions correlate with values of their charges. Our simulations show that all kinds of single- and multiply charged heavy particles can be efficiently accelerated during multiple dipolarizations processes of the type (A) from initial energies 12 keV to maximum energies about several MeV. The gain of energies of heavy ions under the (B) scenario of magnetospheric perturbations is about 10% higher than in (A) scenario. The shapes of obtained in the model energy spectra were shown to be in agreement with experimental spectra in the range of L-shells corresponding to ring/radiation belts. Therefore, we conclude that the Earth's magnetotail can play the role of the depot where oxygen ions of both ionospheric and solar wind origin can be effectively accelerated during magnetic substorms to energies about several MeV and then populate the ring current and radiation belts of the Earth.

Key Points

  • Mechanisms of multicharged oxygen ion acceleration in the Earth's magnetosphere are investigated

  • Simulation results have been compared with experimental energy spectra of oxygen ions in the ring current and proton radiation belt

  • It is shown that substorm dynamics of the magnetotail contributes to the transfer of accelerated ions in the radiation belts

1 Introduction

There is a reliable experimental evidence of two general sources of oxygen ions in the inner magnetosphere: the ionosphere (particle transport and acceleration along high latitude magnetic field lines) and the solar wind (convective transport from the magnetotail, see the review by Kronberg et al., 2014 and references therein). Low charge state oxygen species (i.e., O+1-O+2) are usually originated from ionospheric outflows and further acceleration along magnetic field lines (Balsiger et al., 1983; Johnson et al., 1983; Kistler et al., 20062005; Kremser et al., 1987, 1985; Schulz, 1983; Shelley et al., 1983). On the contrary, high charge states of oxygen ions (i.e., O+3-O+8) are believed to have solar wind origin (e.g., Kremser et al., 1987). Such ions enter Earth's magnetosphere from the magnetosheath and can be additionally accelerated within the magnetosphere (Balsiger et al., 1983; Zelenyi et al., 2011). O+1 is the most abundant charge state of oxygen in the magnetosphere (Allen et al., 2016). Study of the average spatial distributions and charge state spectra of O+1-O+2 ions versus that of O+3-O+8 ions provide an opportunity to investigate the relative contributions of the ionosphere and the solar wind to the energetic ion population in the inner magnetosphere. Such research has become possible due to measurements on the Active Magnetospheric Particle Tracer Explorer (AMPTE; Gloeckler & Hamilton, 1987). This spacecraft carried the charge-energy-mass spectrometer (CHEM) that enabled the separate determination of the charge state, energy and mass of ions (Gloeckler et al., 1985).

Generally, investigations showed that the relative contributions of single- and multicharged oxygen ions are variable and depend on a number of factors. While in the solar wind heavy ions usually constitute <0.1% of the total density (Gloeckler & Geiss, 1989) the contribution of ionospheric ions in the magnetotail correlate with Kp index and can reach the maximum density during magnetospheric substorms. Estimates using Cluster measurements in the magnetotail (Kistler et al., 2005) demonstrated the relative density of oxygen ions in comparison with protons can be of the order of 15% in perturbed periods; the estimate of their contribution in the cross-tail current is about 10% from the total current. During substorm onset the ratio of oxygen ions to protons urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0001can reach the order of 10 (Kistler et al., 2006). Measurements made in the ring current by (Gloekler et al., 1985) for the time preceding and during the geomagnetic storm (September 4–7, 1984) showed that quiet-time ring current consists primarily of ions of solar wind origin with O+ contributing only 2.7% to the total energy density at L shells from 3 to 8. In contrast, O+ constituted a substantial fraction about 29% of the total storm-time ring current energy density, with O+2 contributing 2.4%.

Generally, the ring current consists of ions (mostly protons) with energies about one to few hundreds keV (Daglis et al., 1994). Actually this is the low-energy part of the Earth's radiation belts. Radiation belts are populated by energetic electrons and ions trapped on closed drift trajectories around Earth at L-shells approximately lower than 7 (L-shell is the distance in RE units from the center of Earth to the intersection point of a magnetic field line with the magnetic equatorial plane; e.g., Ukhorskiy et al., 2015). Particle fluxes and ion composition of the ring current and the outer region of the radiation belts can experience significant changes during geomagnetic disturbances (Daglis et al., 1994). Although the details of formation of these areas are still far from clear, increasingly sophisticated satellite borne particle detectors are helping to answer some of the remaining open questions.

Due the researches of ring current dynamics (Daglis et al., 1994; Fritz et al., 2003; Grande et al., 1996; Kistler et al., 1989; Nosé, et al., 2011; Ukhorskiy, et al., 20172015; Turner et al., 2017) it was found that during magnetospheric disturbances particle concentrations and fluxes in the ring current and in the radiation belts can vary by orders of magnitude at different spatial and temporal scale. The main source of these particles is the magnetotail plasma sheet, where electrons and ions originated from the solar wind and ionosphere can be accumulated, then accelerated and moved with convection flow toward the Earth's inner magnetosphere. It is found in experiments on board of AMPTE/IRM satellite (e.g., Gloeckler et al., 1985; Möbius et al., 1985) that during substorms the efficiency of the acceleration of oxygen ions coming into magnetotail from both ionosphere and solar wind is comparable.

During magnetic storms, O+ ions with energies about tens of keV have been detected by S3-3 satellite at low altitudes in the auroral region. These observations gave evidence that the source of heavy ions is the ionosphere that can play a significant role in the dynamics of the ion fluxes in the Earth's magnetosphere. Subsequently, studies of the energy and charge spectra of ions with energies from tens to hundreds of keV in the inner magnetosphere were carried out on satellite AMPTE/CCE (e.g., Möbius et al., 1985). Populations of heavy ions with energies of about 10 MeV were detected in the radiation belts (e.g., Gkioulidou et al., 2016; Kremser et al., 1987; Ukhorskiy et al., 2017). Model calculations by Spjeldvik and Fritz (1978) showed that the charge state distribution should be independent of the ion source at L < 5. Analysis of data obtained on-board spacecraft Molniya-2, Explorer 45, ATS-6, and ISEE-1 shown that energy spectra of the radiation belt ions are approximately similar in E/Q representation (e.g., Panasyuk, 1982). This may indicate the existence of a single mechanism of particle acceleration forming spectrum of the ion population at the Earth's radiation belts.

Numerous experimental and theoretical studies (e.g., Allen et al., 20162017; Gkioulidou et al., 20152016; Hamilton et al., 1988; Kremser et al., 1987; McDonald, 1998; Panasyuk, 19821983; Vlasova et al., 1988; Ukhorskiy et al., 2017; Turner et al., 2017) made it possible to understand that the ion acceleration processes in the magnetotail play an important role in the formation of ion “injection spectrum” in the radiation belts. The measurements of the ion charge spectra, given in (e.g., Allen et al., 2017; Kremser et al., 1987; Panasyuk, 19821983; Schulz, 1983; Turner et al., 2017; Ukhorskiy et al., 2017), demonstrated the presence of particles of both ionospheric and solar origin in the ion composition of the magnetosphere. To date, the problem of mechanisms which are responsible for the transport and acceleration of ions from the tail of the Earth's magnetosphere to the ring current and proton radiation belts remains unsolved. The role of acceleration mechanisms in the Earth's magnetosphere becomes more clear due to Geotail, Cluster, THEMIS, and MMS missions, (e.g., Ashour-Abdalla et al., 2015; Birn et al., 20122013; Grigorenko et al., 20092015; Retino et al., 2008; Sharma et al., 2008; Zelenyi et al., 2011).

It is known that ions of solar wind origin as well as ionospheric ions penetrate into the magnetotail current sheet (CS) region and convect earthward under urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0002 drift. During their convection ions can be demagnetized in the neutral plane and accelerated by the large-scale electric field urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0003 (e.g., Lyons & Speiser, 1982). This process delivers ions into the quasitrapping region near the inner edge of the magnetotail plasma sheet. Further inward transport and acceleration occur through the radial diffusion due to fluctuations of the magnetic and electric fields. At the same time the ions are subjected to loss processes, mainly due to charge exchange (e.g., Spjeldvik & Fritz, 1978) but also due to wave particle interaction. Thus a number of concurrent processes contribute to the distribution of different species of ions in the magnetosphere.

In the growth phase of substorm the magnetic flux increases in the magnetotail lobes. As a result CS is thinning from the transverse scale 1–2RE (RE ≈ 6,400 km is the Earth radius) to several ion gyroradii (e.g., Baker et al., 1985; Sergeev et al., 1992; Zelenyi et al., 2011). Simultaneously, the velocity of earthward plasma convection increases and enhanced plasma fluxes are injected from the magnetotail into the inner magnetosphere (Daglis, 2006, and references therein). Such thin configuration is metastable and can be spontaneously destroyed followed by magnetic reconnection and explosive release of an excess of a free magnetic energy in the form of a wave activity and particle acceleration (Artemyev et al., 2012; Sergeev et al., 20091999; Sharma et al., 2008; Ukhorskiy et al., 2015; Zelenyi et al., 19902011). Large-scale variations of both magnetic and electric fields during the explosive phase of substorm contribute to plasma transport into the inner magnetospheric regions, particle acceleration and the dynamics of radiation belts.

Investigations revealed important details of the actual nature of injection mechanism. The magnetic perturbations in the explosive phase of substorm in the Earth's magnetotail sometimes represent multiple dipolarization fronts propagating toward the Earth (e.g., Fu et al., 2020; Runov et al., 2009). The temporal behavior of a magnetic field is characterized by rapid temporal and spatial jumps of the normal component of the magnetic field urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0004 (Nakamura et al., 2002; Sergeev et al., 2009). Dipolarization fronts during substorms usually appear in the region of magnetotail approximately at −16RE < X < −11RE (Baumjohann et al., 1999) and then propagate in Earthward direction (Hamrin et al., 2013). The statistical analyses (Liu et al., 2016) showed that about 30% of dipolarization fronts can penetrate inside geosynchronous orbit. Sometimes the passage of dipolarization fronts is accompanied by electromagnetic fluctuations (Lui, 2014; Nosé et al., 2000). Data analyses and modeling showed that in the near-Earth magnetotail region protons p+ and O+ ions can be accelerated, correspondingly, to energies about several tens and hundreds of keV during magnetic dipolarizations. At the same time magnetic and electric field fluctuations whose frequencies are close to the gyrofrequency of ions can nonadiabatically accelerate them and make the energy spectrum harder (Ono et al., 2009). Plasma acceleration on dipolarization fronts were studied in many works (e.g., Greco et al., 2009; Longcope & Priest, 2007; Parkhomenko et al., 2019; Ukhorskiy et al., 2017; Zhou et al., 2012; see also review Fu et al., 2020 and references therein). Plasma acceleration due to particle trapping and reflection near dipolarization fronts was studied in (Artemyev et al., 2012; Ashour-Abdalla et al., 2015; Perri et al., 2009; Zhou et al., 2012).

The reason of the appearance of single- and multicharged oxygen ions with high energies in the Earth's ring current and radiation belts remains a conjecture until the present time. Numerical simulation of ion energy distributions can be useful in studying the dynamics of the trapped radiation in the Earth's magnetosphere. In our work a numerical model is developed that describes magnetotail CS during the passage of magnetic dipolarization fronts and the electromagnetic turbulence that often appears after they are finishing (Zhukova et al., 20182017). Such consideration allows to study the energy spectra of accelerated particles during magnetospheric substorms and to compare them with the observed spectra of multicharged ions in the radiation belts. According to the assumption that plasma convection can supply magnetotail plasma to radiation belts, we will try to answer the question whether the magnetotail is the source of ions with several MeV energies in the internal magnetosphere. Thus our aim is to investigate the role of the magnetotail as the source of trapped radiation in the inner magnetosphere.

In our work we analyzed the contribution to the acceleration of oxygen ions with charge numbers 1 ≤ Q ≤ 8 in the frame of the numerical model. Two characteristic scenarios of magnetospheric perturbations are considered: (A) the passage of multiple dipolarization fronts with duration up to 1 min; (B) the perturbation (A) accompanied by electromagnetic turbulence. Below it is shown that the agreement between both experimental and calculated energy distributions of O+-O+8 ion fluxes corresponds to L-shell range 4.5 <L < 7.5. The choice of these values of L-shells is based on the large number of experimental data (e.g., Allen et al., 20162017; Fennel et al., 1996; Hamilton et al., 1986; Kremser et al., 1987, 1985; Panasyuk, 19821983; Turner et al., 2017) for ion fluxes in the equatorial region of radiation belts.

2 Numerical Model

We use here the standard Geocentric Solar Magnetospheric (GSM) system, where X-axis is directed from the Earth to the Sun, Z-axis is directed along the Earth's magnetic dipole to the North, the complementary axis Y is directed from the dawn to dusk. The shape of magnetic field configuration for unperturbed CS model in the GSM coordinate system (basic model) can be described in the general form:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0005(1)
The tangential component urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0006 is selected in the form corresponding to Harris-like CS (Harris, 1962):urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0007. Tangential magnetic field value at the edges of CS urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0008 is taken equal to 20 nT, while the values of the shear and the normal magnetic components are, respectively, By0 = 0 and Bz0 = 4 nT. Large-scale electric field of plasma convection was specified as:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0009(2)
where urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0010, urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0011, urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0012.

Two characteristic scenarios of magnetic perturbations were considered: (A) propagation of multiple dipolarization fronts having characteristic duration time td; (B) passage of multiple fronts followed by later development of electromagnetic fluctuations.

Figure 1 shows corresponding temporal variations of the normal magnetic field in the CS, corresponding to both mechanisms (A) and (B). The total magnetic and electric fields in the model are the superposition of the basic model, multiple dipolarizations and magnetic fluctuations:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0013(3)
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0014(4)
Details are in the caption following the image

Temporal changes of the normal magnetic component for two scenarios in the model: (a) magnetic dipolarization with the total duration t=780 s=13 min, which includes the passage of a series of dipolarization fronts with characteristic time length ∼urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0015 s; (b) passage of dipolarization fronts followed by subsequent electromagnetic wavy activity.

Here, urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0016 are, correspondingly, magnetic and electric fields in the basic CS model. Values urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0017 are the perturbed magnetic and electric fields of multiple dipolarization fronts, chosen from Cluster's observations on July 20, 2013 from 01:33:08 to 01:48:11 UT. Last terms urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0018 and urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0019 are the model wavy fields of plasma fluctuations, depending on spatial coordinates urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0020 and time urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0021. The components of the induced electric field urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0022 were calculated from Maxwell equations under the assumption that plasma is electroneutral, and free charges are absent:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0023(5)
The investigations of fluctuating electric and magnetic fields in space plasma was presented in works (Cattell & Mözer, 1982; Lui, 2014; Ipavich et al., 1984; Nosé et al., 2000), in which it was shown that, immediately after the passage of multiple dipolarization fronts across CS plane, electromagnetic oscillations can be developed in the magnetotail. In theoretical works (Greco et al., 2009; Veltri et al., 1998) the components of magnetic and electric fields of a quiet CS were supplemented by fluctuating magnetic urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0024 and electric urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0025 components:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0026(6)
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0027(7)
whereurn:x-wiley:21699402:media:jgra56240:jgra56240-math-0028; urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0029,urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0030. Сomponents (7) of the electric field are the solutions of Maxwell equations. Frequencies urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0031 and amplitudes urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0032 of each harmonic were chosen from Cluster C4 satellite data (obtained on 20. VII. 2013). Initial phasesurn:x-wiley:21699402:media:jgra56240:jgra56240-math-0033 and wave number urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0034 were proposed to be distributed uniformly on intervals [0, 2π] and urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0035, respectively.
Equations of the motion of charged particle with mass m and charge Ze in electric Eand magneticB fields have the form:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0036(8)

Equation 8 were normalized for calculations and presented in the dimensionless form; then they were solved taking into account the shape of electric and magnetic fields ((3) (4). The detailed description of the numerical solutions and corresponding equations is presented in (Zhukova et al., 2017).

The following scheme of particle launch, shown in Figure 2, have been used: oxygen ions O+-O+8 (with charge numbers 1urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0037) having the average thermal energies 12 keV selected in accordance with results by Kremester et al. (1987) and Turner et al. (2017), were launched into the modeling parallelepiped with sides: urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0038 Here, box coordinates are the following: urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0039 urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0040. Particle number was urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0041 particles in the modeling region. Kappa distribution of particle velocities was taken as the initial velocity distribution:
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0042(9)
Details are in the caption following the image

The basic structure of current sheet model. The magnetic field lines are shown by thick solid lines. The initial positions of particles (a set of points on the plane) and the trajectories of test particles-oxygen ions O+-O+3 are shown.

Here urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0043is the plasma density;urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0044 is the normalized thermal velocity;urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0045 is the parameter of kappa-function;urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0046is the particle drift velocity; urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0047 are, respectively, the parallel and perpendicular components of particle velocities.

3 Simulation Results

To estimate quantitatively the contribution of scenarios (A) and (B), the Equation 8 were solved numerically for the ensemble of 5 × 105 particles. Figure 3 shows the characteristic trajectories of oxygen ions with different charges (panel a); the corresponding energy gain (panel b) and energy gains normalized to particle charges (panel c) in scenario of acceleration A and B.

Details are in the caption following the image

Characteristic trajectories of oxygen ions with different charges (a) and corresponding energy gains of these particles during magnetic dipolarizations in scenarios B and A (which as a part of B). Temporal changes of energies of oxygen ions O+-O+8 are presented in dimensional form (b) and in form normalized to charge numbers Q (c). Vertical lines at t = 780 s separate the periods of multiple dipolarizations in the system and the appearance of electromagnetic oscillations.

Figure 3a shows the characteristic trajectories of oxygen ions with charges 1urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0048 for scenarios (A) and (B), which were traced with the identical initial conditions in the model box. Here we selected the most representative trajectories that passed through the entire modeling area, where they were trapped near CS plane, accelerated and then left the system at the end of the modeling time. One can see that all particle trajectories in Figure 3a have strongly fluctuating character. Figure 3b demonstrate the temporal gain of energy of ions. First 13 min (time period of particle interaction with multiple dipolarization fronts in scenario A) oxygen ions O+-O+2 are accelerated to energies less or about 0.7 MeV, while the oxygen ions with large charges O+3-O+8 reach energies 1.5–2.7 MeV that are two to three times greater. The ion interaction with electromagnetic wavefield at t > 800 s showed that heavy ions O+1-O+8 get the additional energy of the order of 100–200 keV, that is about 10%–15% from the gain of energy in the time interval t < 13 min, when their acquired energies were up to 0.75–3.1 MeV. The contribution of large-scale oscillations of induced electric field on dipolarization fronts to particle energization is larger than energy gain on electromagnetic turbulence. The later seems to be a factor of some additional increase of energy by 10%–15%. This result is in agreement with our previous investigations (Parkhomenko et al., 2019). The finiteness of the transverse size of the magnetotail can play a limiting role in the ion acceleration because energized particles quickly leave the system.

Concerning the charge content of ions the results of simulations indicate a greater acceleration of multicharge ions in comparison with single-charge ones what is consistent with work by Catapano et al. (2017). What are the reasons of such particle behavior in the process of their interaction with dipolarization fronts and electromagnetic turbulence? Previous investigations showed that particle interaction with abrupt changes of the magnetic field during substorms and with chaotic oscillating electric and magnetic fields depend, on the one hand, on the spatial and temporal properties of the system and, on the other hand, on particle mass, charges and initial energies, that is, the size of their gyroradii relatively the characteristic scales of a spatial inhomogeneity of magnetic field (Parkhomenko et al., 2019).

In thin CSs gradients of magnetic field near the neutral plane can be such strong that ion gyroradii become comparable with the scale of a magnetic inhomogeneity; as a result ions are demagnetized near equatorial plane and move along specific serpentine-like trajectories named quasiadiabatic (Büchner & Zelenyi, 1989). During CS crossing such particles can be accelerated by the electric fields in this region (Zelenyi et al., 2011). It was shown in (Parkhomenko et al., 2019) that plasma acceleration in the fast-changing environment has the resonant character: the closer particle gyroperiod to the time scale of dipolarizations the more effective is the transfer of energy from fields to particles. In the turbulent fields which are the set of randomly propagating wave packets the Fourier transform allows to identify the waves of a certain frequency that resonantly accelerate individual types of particles with different masses and charges (Zelenyi et al., 2011 and references therein; Artemyev et al., 20152012; Parkhomenko et al., 2019).

In our simulations the gyrofrequencies of oxygen ions O+-O+2 were the closer to the time scales of dipolarization fronts in comparison with multicharged ions O+3-O+8. As a result, these ions were quickly accelerated and leaved the system. On the contrary, multicharged ions were effectively trapped in CS plane and accelerated better to larger energies.

Figure 3b demonstrates the temporal energy gain by several particles with different charges. It is seen that energy gain has non-monotonous shape; periods of energy increase by two or three orders of magnitude alternate with periods of energy dissipation. If we take into account the chaotic fluctuations appearing after the passage of dipolarization fronts (scenario B) ions experience the additional random drift in the plane of a minimum magnetic field and their energies are monotonously increased by 100–300 keV.

Figure 3c demonstrates the temporal changes of energies of oxygen ions O+-O+8 normalized to charge numbers Q. We see that energy gain normalized to charge states is larger for ions with small charges. For particles with charge state Q urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0049 the value of energy gain per nucleon becomes quite close. We will see below that this last effect should be important in the formation of particle energy spectra representing the E/Q dependences.

Figure 4 demonstrates the comparison of calculated spectra of oxygen ions O+-O+8 and experimental observations obtained by Magnetospheric Ion Composition Sensor on board the CRRES spacecraft (Fennel et al., 1996). Energy values E were digitized and divided by the charge number Q and are presented in dimensional units keV. Calculated spectra are marked by the set of color lines mentioned in figure captions; experimental normalized spectra of ions O+-O+8 are shown by pink dashed lines. Figure 4a is obtained in a frame of scenario A, Figure 4b demonstrates results of scenario B realization. Particles were traced in the same initial conditions; their densities urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0050 corresponded to available observational data from (Kremser et al., 1987; Turner et al., 2017). Figure 2 from the work by (Fennel et al., 1996) was digitized and experimental data were averaged over the range of L-shells in the diapason urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0051.

Details are in the caption following the image

Energy distributions normalized to charge numbers E/Q of accelerated oxygen ions O+-O+8 during (a) interaction with multiple dipolarization fronts (scenario A); (b) interaction with multiple dipolarization fronts and subsequent of electromagnetic fluctuations (scenario B) in comparison with experimental energy spectra in (Fennel et al., 1996).

We see that simulated energy spectra in Figure 4a are softer and lie below experimental dependences for oxygen ions with large charges O+3-O+8. On the contrary simulated spectral dependencies for low-charge ions lie above the experimental one. It seems that scenario A should contain some additional mechanism to describe in the better way the spectra of multicharged ions in the Earth's radiation belts. Moreover, the soft decreasing of spectra at large ion charges are not sufficiently agree with results of the earlier works by (Panasyuk, 19821983) where the similar decay of the E/Q spectra for large oxygen charges was predicted. This discrepancy of model results and observed data is substantially less in Figure 4b where the characteristic for substorm turbulent oscillations after dipolarization fronts were taken into account. The corresponding to scenario В spectra of low-charged oxygen ions O+1-O+2 in Figure 4b are descended and became more consistent with observations. As for the E/Q dependence for ions with a large charge, the decay of the spectra for high energies clearly has a similar character and more consistent with the observational data. These changes of calculated spectra for low-charged ions are due to their enhanced escape from the simulated area because of the additional acceleration in the turbulent wavefield. At the same time energy dependences are rising higher and become more hard for multicharged ions, which can be explained by the additional particle energization by electromagnetic chaotic oscillations in the magnetotail.

Table 1 presents the characteristic parameters of accelerated particles as the values of initial energies urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0052maximum energies urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0053 and the ratio Emax/Q for scenarios A and B; the next columns show the relative energy gains for particles interacting with turbulence in scenario B and with dipolarization fronts in scenario A. One can see that maximum energies of multicharged particles with charge value of urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0054 are in the diapason 5–7 MeV, while the maximum energies of lower-charged particles with urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0055 are about 2–5 MeV. Energies of lower-charge particles interacting with dipolarization fronts increases by about two orders of magnitude in comparison with their initial energy 12 keV. Maximum energy of lower-charged oxygen ions after propagated dipolarization fronts is found to be about 1–4 MeV. Energies of higher-charged ions reach 5–7 MeV (about three orders of magnitude). Interaction with chaotic wavefield after the passage of dipolarization fronts give the gain of energy for all particles about 200–400 keV. This is no more than 5%–12% from gain during the dipolarization fronts passage in scenario A. Thus, the obtained results show that the main contribution to heavy ion acceleration is made by magnetic dipolarizations during substorms, but the smaller contribution of electromagnetic turbulence should also be taken into account. One can say that the order of relative gains of energy during magnetic jumps are stronger changed for the lower-charged ions and slowly changed for ions with charges urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0056. This last result confirms the similar character of multicharged ion energy spectra, as modeled as experimental ones, in a wide range of energies. Therefore our model, taking into account large-scale magnetospheric perturbations predicts two to three orders of the gain of energy by multicharged oxygen ions in the magnetotail. This result in order of magnitudes is in agreement with the observed spectra borrowed and then digitized from the work by Fennel et al. (1996); the shape of spectral dependencies are consistent well with the observed spectra if we take into account both magnetospheric dipolarizations and electromagnetic turbulence characteristic for substorms.

Table 1. Parameters of Particle Acceleration in Scenarios A and B: Values of Initial Energies urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0057, Maximum Energies urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0058 and Ratio urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0059 for Scenarios A and B, the Relative Increase of Energies (in Comparison With the Initial One) on Chaotic Waves and the Dipolarization Fronts (DFs)
Q urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0060, keV Scenario A Scenario B Relative gain of ion energies on turbulence (% from energy) The order of urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0061 energy gain at DFs
urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0062 keV urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0063, keV urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0064, keV urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0065, keV Δurn:x-wiley:21699402:media:jgra56240:jgra56240-math-0066,urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0067 urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0068urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0069 / urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0070) urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0071 urn:x-wiley:21699402:media:jgra56240:jgra56240-math-0072
8 12 7,000 875 7,400 920 400 (∼6%) 45 6.0 × 102
7 12 6,600 940 7,000 1,000 400 (6%) 60 5.5 × 102
6 12 5,900 980 6,250 1,040 350 (∼6%) 60 5.0 × 102
5 12 5,100 1,020 5,370 1,070 270 (∼5%) 50 4.3 × 102
4 12 4,400 1,100 4,650 1,162 250 (∼6%) 62 3.6 × 102
3 12 3,800 1,260 4,050 1,350 250 (∼7%) 90 3.0 × 102
2 12 2,900 1,450 3,100 1,550 200 (∼7%) 100 2.4 × 102
1 12 1,700 1,700 1,900 1,900 200 (∼12%) 200 1.4 × 102

4 Conclusions

In this work we present the results of investigation of a fundamental physical question about the presence of accelerated multicharged oxygen ions originated from the solar wind in the Earth's radiation belts and ring current. The comparative analysis of two characteristic acceleration mechanisms in the Earth's magnetotail is proposed in a frame of the numerical model that describes the near-Earth edge CS during large-scale magnetospheric perturbations. The first mechanism is related with the beginning of the explosive phase of substorms when magnetic reconnection in the magnetotail CS begins and fast dipolarization fronts propagate in earthward direction. This development of magnetoplasma processes is named in our model as “scenario A.” Sometimes after the passage of magnetic dipolarization a residual electromagnetic turbulence of the medium is observed that can be the additional source of plasma acceleration and thermalization. This combined development of perturbations is called as “scenario B.” Parameters of magnetic dipolarizations as well as the temporal consequence of dipolarizations, shown in Figure 2, were taken from observational data.

Particle tracing results showed that repeated substorm perturbations in the Earth's magnetosphere can be the sources of the acceleration of magnetotail ionospheric and solar wind ions to MeV energies with the consequent earthward drift, contributing the population of the ring current and radiation belts. Two main acceleration scenario that we have chosen as most effective (Zhukova et al., 2018) were considered: (A) magnetic perturbation in the magnetotail consisting from the set of dipolarization fronts; (B) the set of dipolarization fronts accompanied by large-scale wavefield; their contribution to the energy increase of oxygen ions O+-O+8 was studied. The maximal gain of energies in order of magnitude was estimated in both scenarios of acceleration. Multiple jumps of the magnetic field under the propagating dipolarization fronts and general increase of the normal magnetic field were shown to lead to the generation of induced electric fields interacting with oxygen ions in a resonant way. In a frame of the model the higher the charge number Q the more effective the transfer of energy from fields to particles as it is seen from the Тable 1. The modeling confirms also the results from the work by Panasyuk et al. (19821983) demonstrated the real invariance of the energy gain for O+-O+8 ions in E/Q representation in the low-energy region (<150 keV).

Investigations of the averaged spatial distributions of oxygen ions O+-O+8 in the inner magnetosphere provide a possibility to estimate the relative contributions of the solar wind to the formation of energetic ion population in the inner magnetosphere. Experimental energy spectra of multicharged oxygen ions in radiation bells (Fennel et al., 1996) were compared with simulation results. It was obtained that heavy ions acceleration in the model of a near-edge magnetotail CS can provide the similar spectral dependencies with the observed data, and proposed model is capable to adequately describe the distribution of charged oxygen ions O+-O+8 in the Earth's radiation belts and ring current. The most effective scenario is found to be scenario A, taking into account the passage of dipolarization fronts. The modeling of the B scenario demonstrates that the wave activity near the CS can give the additional gain of energy for oxygen ions about 6%–12%. Finally, we conclude that combination of mechanisms of multiple dipolarizations followed by electromagnetic turbulence that are often observed in the Earth's magnetotail during substorms can substantially accelerate oxygen ions to energies of the order of 2 MeV.

Acknowledgments

The authors acknowledge Cluster Science Archive (http://www.cosmos.esa.int/web/csa) for providing the data. To obtain the data, one should start the CSA GRAPHICAL USER INTERFACE; and then to download the data, just select the particular instrument and time interval. The work by H. V. M., E. I. Z., and V. Y. P. is supported by RFBR (Grant no.19-02-00957).

    Data Availability Statement

    The FGM magnetic field data downloaded at http://www.cosmos.esa.int/web/csa. The data (http://doi.org/10.5281/zenodo.3466072) which are in Zenodo database contains the program code that was done with Geany.