Magnetospheric Response to Solar Wind Forcing: ULF Wave – Particle Interaction Perspective

10 Solar wind forcing, e.g. interplanetary shock and/or solar wind dynamic pressure pulses impact on the Earth’s magnetosphere manifests many fundamental important space physics phenomena including producing electromagnetic waves, plasma heating and energetic particle acceleration. This paper summarizes our present understanding of the magnetospheric response to solar wind forcing in the aspects of radiation belt electrons, ring current ions and plasmaspheric plasma physics based on in situ spacecraft measurements, ground-based magnetometer data, MHD and kinetic simulations. 15 Magnetosphere response to solar wind forcing, is not just a “one-kick” scenario. It is found that after the impact of solar wind forcing on the Earth’s magnetosphere, plasma heating and energetic particle acceleration started nearly immediately and could last for a few hours. Even a small dynamic pressure change of interplanetary shock or solar wind pressure pulse can play a non-negligible role in magnetospheric physics. The impact leads to generate series kind of waves including poloidal mode ultra-low frequency (ULF) waves. The fast acceleration of energetic electrons in the radiation belt and 20 energetic ions in the ring current region response to the impact usually contains two contributing steps: (1) the initial adiabatic acceleration due to the magnetospheric compression; (2) followed by the wave-particle resonant acceleration dominated by global or localized poloidal ULF waves excited at various L-shells. Generalized theory of drift and drift-bounce resonance with growth or decay localized ULF waves has been developed to explain in situ spacecraft observations. The wave related observational features like distorted energy spectrum, boomerang 25 and fishbone pitch angle distributions of radiation belt electrons, ring current ions and plasmaspheric plasma can be explained in the frame work of this generalized theory. It is worthy to point out here that poloidal ULF waves are much more efficient to accelerate and modulate electrons (fundamental mode) in the radiation belt and charged ions (second harmonic) https://doi.org/10.5194/angeo-2021-57 Preprint. Discussion started: 23 November 2021 c © Author(s) 2021. CC BY 4.0 License.

in the ring current region. The results presented in this paper can be widely used in solar wind interacting with other planets such as Mercury, Jupiter, Saturn, Uranus and Neptune, and other astrophysical objects with magnetic fields.

Introduction
"We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture." (Evolution of the Solar System by Alfvén and Arrhenius, 1976).

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The European Geosciences Union (EGU) has awarded the Hannes Alfvén Medal to me for the year 2020, I feel deeply honored and very happy to obtain so much recognition for my work, because Hannes Alfvén was one of the giants in space physics and astrophysics, and also one of my heroes.
As we all know, Alfvén received the 1970 Nobel Prize in physics for his work in magnetohydrodynamics (MHD) and plasma physics. While few people know that Hannes Alfvén can speak some Chinese ( Fig. 1) besides Swedish and English 40 as indicated by Wikipedia. In fact, he has visited China twice, his first visit was invited by Prof. Jeoujang Jaw who is the founder of Chinese space program [Zhang &Yin, 2018]. During his in total of 50 days' visiting in China, Hannes Alfvén has given a number of lectures and promoted China's space physics. Also, at the early 1990s, the first text book I took to learn  ULF waves are first observed on the ground and also known as geomagnetic pulsations. The solar storm of 1859 (Carrington, 1860, also known as the Carrington Event) was probably associated with a huge solar coronal mass ejection (CME) hitting the Earth's magnetosphere and induced arguably the largest geomagnetic storm on record on September 1-2, 75 1859 (Stewart 1861). As we can see from Figure 2, the first geomagnetic pulsation has been recorded as quasi-sinusoidal magnetic field variations during the great magnetic storm that occurred in 1859 (Stewart 1861). Geomagnetic pulsations ( Figure 2) are ultra-low frequency (ULF) plasma waves originated in the Earth's magnetosphere.
In fact, the D component of the ground magnetic field on the bottom trace mainly represents the poloidal mode ULF waves . The magnetic field perturbation of the toroidal mode ULF waves is in the azimuth 80 direction, and the electric field is radial perturbation usually associated with a small wave number. Whereas, the poloidal mode ULF waves are often associated with a larger wave number, and the magnetic field of the poloidal mode is radially perturbed.
Oscillations of magnetic field lines can be sustained through the collisionless plasma interaction in the magnetosphere.

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Whereas, the ULF waves can also be diminished when they pass through the Earth's atmosphere and ionosphere due to the ionospheric conductivity [Hughes and Southwood 1983]. In the Earth's ionosphere, due to the presence of collisional plasma and neutral atmospheric population, the oscillated magnetic field in the ULF range would be exponentially decayed via generating an additional Hall current and Pedersen current, and the direction of the magnetic field oscillation will be rotated in 90°. Thus, the decayed ULF waves can eventually propagate to the ground in the form of electromagnetic waves.

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The relationship between ULF waves in the magnetosphere and the magnetic field dissonances on the ground is as follows [Hughes and Southwood 1983]: / ~Σ /Σ (h ) (1) where Σ and Σ are the height-integrated Pedersen and Hall conductivity, respectively, is the magnetic field on the ground and is the ULF field just above the ionosphere, h is the thickness of the ionosphere. As we can see from the formula, the Earth's ionosphere prefers to shield ULF waves with a large wave number k since the thickness of the ionosphere h is insensitive in time. Thus, the poloidal mode ULF waves of large wave numbers will decay significantly when they pass through the Earth's ionosphere, and it is hard to be observed on the ground. However, the toroidal mode ULF waves usually have a small wave number, and it will be easier to pass through the ionosphere and be identified from ground magnetometer records. ULF waves can act as important media of the magnetospheric dynamics for the mass, momentum and energy transport processes. Therefore, it is important to understand the global properties and how the energy is transported from the solar wind to the magnetosphere, ionosphere and finally the ground through the ULF wave -charged particle interactions. Earth's magnetospheric activities are mainly controlled by the solar wind plasma and the accompanying interplanetary magnetic field (IMF) [e.g., Yue et al., 2009;2011a;2011b]. The energy coupling between the solar wind and the 110 Earth's magnetosphere can take various forms, most often would excite different plasma waves inside magnetosphere, one of which is the ULF wave. The energy coupling between the solar wind and the Earth's magnetosphere can take various forms, most often would excite different plasma waves inside magnetosphere, one of which is the ULF wave. In 1940s, the geomagnetic signals related to the interplanetary shock impact have been identified through the ground-based magnetometer observations and named as "Storm Sudden Commencement" (SSC) [Chapman and Bartels, 1940]. Now, it is well known as 115 the impact of dynamic pressure impulses associated with the interplanetary shocks driven by Coronal Mass Ejections (CMEs) or Corotating Interaction Regions (CIRs).
It is now known after extensive studies that the solar wind dynamic pressure pulses (including negative and positive type) as well as the interplanetary shock can have profound effects on the magnetosphere system . The positive or negative pressure pulses correspond to the sudden enhancements or drops of the solar wind dynamic 120 pressures respectively and are often caused by the abrupt changes of solar wind density and/or solar wind speed. One of the typical representatives are the interplanetary shocks.
When solar wind dynamic pressure pulses impinge on the magnetosphere, the sudden raise or drop dynamic pressure will at first compress or inflate the magnetosphere. In the meantime, the fast magnetosonic waves will be launched inside the 125 magnetosphere, and then standing ULF waves usually will be formed subsequently in the magnetosphere, occasionally even inside the plasmasphere [e.g. , Liu et al 2010, thus transporting the energy of solar wind into the magnetosphere. The generation mechanisms of different dayside ULF waves can be distinguished by their preferable occurring region. The K-H instability mechanism needs a shear flow to meet the instability threshold condition, therefore the main occurring region are the dawn and dusk flank side of the magnetopause. The dynamic pressure pulses on the contrary are responsible for the dayside local noon region ( Figure 3).  (Liu et al., 2009). The square root of integrated power spectral density of azimuthal electric field (Ea, poloidal mode) and radial electric field (Er, toroidal mode) in Pc4 and Pc5 frequency ranges are 135 averaged in each bin. Figure 4 shows the responses of both poloidal mode and toroidal model ULF waves to the solar wind forcing at different magnetic local time sectors. It is suggested that Pc4 and Pc5 ULF wave power is mainly supplied from external solar wind sources, i.e. solar wind forcing (Liu et al. 2009(Liu et al. , 2010. As is shown in Figure 4, the distributions of the wave power (square 140 root of integrated power spectral density) of the azimuthal electric field (Ea, poloidal mode) component are averaged from 12 years THEMIS data sets. The wave power is found to be stronger in the dayside magnetosphere compared to that in the nightside. Also, the wave power in the pre-midnight is larger than that in the post-midnight region. The wave power is observed dominantly at higher L shells, which show the consistency with the scenario that the poloidal mode Pc4 and Pc5 ULF wave generally have external sources -solar wind forcing including interplanetary shocks, solar wind positive and 145 negative dynamic pressure pulses (e.g., Zhang et al. 2010;Liu et al. 2010).
The study of magnetospheric response to solar wind forcing related to a sudden change in solar wind dynamic pressure has at least two obvious advantage points: the magnetospheric response to sudden change of the solar wind dynamic pressure will generate significant and easily identified electromagnetic signals; and the energy source for excited ULF waves is rather clear without temporal ambiguity. Thus, in the present paper, based on the ULF wave -charged particle interactions, I will 150 focus on how the magnetosphere response to solar wind forcing --the solar wind dynamic pressure pulses including positive and negative ones. The inner magnetosphere includes radiation belt, ring current and plasmasphere, which are three overlapping regions 160 with energy of their particle population quite different. [Yue et al., 2017a[Yue et al., , 2017b. Van Allan radiation belt is composed of energetic particles with energy greater than 100keV, whereas the ring current contains mainly energetic ion species, (hydrogen, helium, and oxygen) of tens keV to about 400 keV. The ring current and Van Allan radiation belt are overlapped in space with cold plasmaspheric population (typically a few eV).

Charged particles in the inner magnetosphere
The plasma density in the magnetosphere controls the time scale in response to the solar wind forcing. The mass density 165 is one of the key parameters for the Alfvén speed which determines the magnetospheric response to the low-frequency ions variation in the ULF wave range, whereas the background electron density dominates the electrons oscillating in VLF and radio wave range. Thus, the mass density is one of the controlling factors for the radiation belt and ring current dynamic process. Charged particles in the Earth's magnetosphere will experience three kinds of periodical motions corresponding to three different invariants: gyrating around magnetic field lines; bouncing back and forth along the field line between "mirror points" located at lower altitude, and drifting across field lines due to the electric field as well as gradient and curvature of the magnetic field lines, see Figure 5. When the charged particles moving in the inner magnetosphere, the time scales for the three kinds of motion can be estimated with the dipole magnetic field:

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(2) where A is the mass ratio of the particle to the proton, W is the particle's kinetic energy, l 0 is the length along the magnetic field line between two mirror points at the northern and southern hemisphere, r is the distance to the Earth's centre from the equator and B is the magnitude of the magnetic field. The representative values are given in Table 1.

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The dynamics of radiation belt and ring current are strongly governed by the interactions between different charged particle populations that are coupled through the variation of all kinds of electromagnetic waves and wave -particle  [Matsushita et al, 1961, Brown et al, 1961, Ullaland et al, 1970. Enhanced precipitation of~10s keV electrons into the Earth's atmosphere has been observed immediately which last up to~10 minutes when an interplanetary shock impacts on the geospace system [Su et al., 2011;Yue et al., 2013].
The sudden changes of charged particle fluxes in the inner magnetosphere including both relativistic electrons in the 210 radiation belt [Arnoldy 1982, Blake et al, 1992, Li et al, 1993, Hudson et al, 1994, Tan et al, 2004, Hao et al., 2019 and energetic ions [Zong et al, 2012Ren et al. 2016Ren et al. , 2017a in the ring current region are noted to be closely related to SSCs (sudden storm commencement) caused by the interplanetary shock impacting on the Earth's magnetosphere. These results suggest that a significant portion of energetic charged particles in the ring current and radiation belt and region could be produced even before the build-up of the enhanced ring current which produces the 215 magnetic storm.  [Li 220 et al, 1993].
Energetic particles of both electrons and ions up to 15 MeV have been observed in the radiation belt due to the impact of a strong interplanetary shock on the Earth's magnetosphere on 24 March, 1991 [Blake et al, 1992]. It is believed that both relativistic ions and electrons are accelerated quickly by an induced electric field pulse generated by the passage of the 225 interplanetary shock [Li et al, 1993, Hudson et al, 1994. A rapid (a few mins) formation of a new electron radiation belt at L ≃ 2.5 were observed in the slot region besides the inner and outer radiation belts, which lasted for a few years [Blake et al, 1994].
Assumed that a running pulse with a bipolar electric field has been generated inside the magnetosphere by the compression and relaxation of the Earth's magnetosphere caused by the interplanetary shock impinging on the Earth's magnetosphere. As shown in Figure 6, test particles interacting with this assumed asymmetric bipolar electric field pulse ("One Kick") caused by the passage of the interplanetary shock has been proposed to explain the newly formed electron radiation belt at L ≃ 2.5 [Li et al, 1993, Hudson et al, 1994. This simulation has shown that a few MeV energetic electrons at L > 6 could be energized up to 40 MeV and be radially transported to L ≃ 2.5 during a fraction of their azimuthal drift period. The simulation results can reproduce the observed very energetic electron injection and their drift echoes. The acceleration 235 process can be understood as that the first adiabatic invariant is conserved (adiabatic acceleration) and the electrons are accelerated by the assumed single bipolar electric field pulse. The time scale of acceleration processes is about1 min since the electromagnetic pulse would be running away in that time period. This is so called "One Kick" scenario of an interplanetary shock interacting with the Earth's magnetosphere.
Since then, extensive test particle and MHD simulations have been carried on to study the particle acceleration related to 240 the interplanetary shock impact [e.g. Hudson et al, 1995, Kress et al, 2007. It has been pointed out [Friedel et al., 2005]

Poloidal ULF wave -charged particle interaction scenario
In the magnetosphere, the energetic charged particles are mainly drifting in the azimuthal direction, with electron drifting eastward and ion drifting toward west. The electric field of poloidal mode ULF waves is also lying in the azimuthal direction.
When both the drift direction of charged particles and the propagating direction of ULF waves are the same, the electric field carried by poloidal ULF waves would accelerate/decelerate the drifting charged particles. However, it should be noted that 250 only those resonant electrons with a drift speed of approximately the wave propagation speed of the poloidal mode ULF wave, could gain energy constantly. Charged particles, bearing both the acceleration and the deceleration processes would cancel out with a relatively small energy gain during one wave period.
As we have already shown in the introduction, ULF waves in the Earth's magnetosphere could be excited by the impinge of positive or negative solar wind dynamic pressure pulses. Energetic charged particle fluxes modulated by ULF waves in 255 the Pc 5 band were found by Brown et al. [1961] at first. A close correlation between the charged particle flux variations and the intensity of ULF waves has been found for both case studies (e.g., Tan et al, 2004, Zong et al 2007 and statistic surveys (e.g., Rostoker et al, 1998, Mathie and Mann, 2001, O'Brion et al, 2003.
Due to the comparable periods between the drift and bounce motions of the charged particles and the ULF waves in inner magnetosphere, drift resonance or drift-bounce resonance may be satisfied. One to one correlation between ULF wave cycles and fluctuations of charged particle fluxes have been found which indicates ongoing wave-particle interactions, and the interactions would accelerate the magnetospheric particle significantly ( [Zong et al 2007.
Now, tremendous efforts have been made to understand how the interplanetary shocks affect the charged particles in radiation belt and ring current region. By using observations from the Cluster and Double Star constellation, it has been found that after solar wind dynamic pressure pulses impinging upon the magnetosphere, the acceleration of radiation belt 265 energetic electrons could start immediately and can last for up to a few hours , Zong et al, 2012. The prime acceleration mechanisms are drift-resonance or drift-bounce resonance with ULF waves excited by the interplanetary shock impacting on the magnetosphere.
A direct observation of such a ULF wave -charged particle interaction scenario is shown in Figure 7.   [Zong et al,2009].

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With an amplitude as high as 40 mV/m, the electric field of poloidal ULF waves on the charged particle drift path can double the energy of electrons with a few hundred keV in only several wave periods. This is much faster than other acceleration processes e.g. gyro-resonances via VLF waves, suggesting that the observed ULF waves are sufficient to explain the observed electron acceleration through drift resonance.
The toroidal and poloidal modes have similar wave powers, however, coherences between the electric fields for both   Liu and Zong, 2015].
This scenario has been further examined by systematically statistics study based on geosynchronous energetic particle observations for 215 interplanetary shock events during 1998-2007 [Liu and Zong, 2015]. It is shown that electron fluxes with an energy less than~300 keV increase after the shock impact whereas electron fluxes with an energy higher than~300 keV show smaller increases, become unchanged or even decrease eventually at geosynchronous orbit ( Figure 8). The 305 electron flux oscillations following the shock arrival have also been investigated. Statistical analyses revealed a frequency preference for energetic electron flux oscillations of 2.2 mHz and 3.3 mHz [Liu and Zong, 2015]. The compressional effect of IP shocks can cause acceleration due to both magnetic field magnitude enhancement and related azimuthal electric field. It is also indicated that energetic electrons with low-energy (high-energy) will resonate with high-m (low-m) ULF waves and have different modulation features. The results show the magnetospheric response to ULF waves excited by the interplanetary shock impact from the energetic particle point of view.
In brief, the interplanetary shock related to energetic electron acceleration in radiation belt starts almost immediately 315 following the shock arrival. The acceleration process includes two contributing steps, the first acceleration is related to the initial magnetospheric compression by the interplanetary shock impact and then immediately followed by drift-resonant or drift-bounce-resonant acceleration by poloidal ULF waves excited by the passage of the interplanetary shock , Zong et al, 2012. This is the shock induced ULF waves -particle interaction scenario. Such a scenario on shock induced ULF waves' interaction with charged particles has been further confirmed by many other satellite

Generalized theory on the drift resonance
In this section, the traditional drift resonance theory will be introduced first, then the generalized drift resonance theory on charged particles resonating with growth and damping ULF waves and charged particles resonating with azimuthal localized ULF waves will be described. Finally, I will show how radiation belt relativistic electrons resonating with localized growth 325 and damping ULF waves in detail.
In the magnetosphere, the frequencies of ULF waves are comparable to the frequency of charged particle's drift or bounce motion. Analogous to gyro-resonance, it is suggested in the 1960s that charged particles trapped by the Earth's magnetic field could resonantly interact with ULF waves standing on a field line through the particles' bounce and drift motions 330 (Dungey 1964, Southwood 1969.
The drift-bounce resonance condition is written as: ( 3) https://doi.org/10.5194/angeo-2021-57 Preprint. location, the resonance energy can be determined in theory if the ULF wave's frequency is known.
The charged particles are moving in the electric field carried by the ULF waves during their drift-bounce motions, thus, their energy can be accordingly changed. The energy change rate of a charged particle interacting with poloidal mode ULF waves can be written as Kivelson 1982,1984]: where , E, V d , and µ are the change rate of the particle energy, the wave electric field, the particle drift velocity and the particle magnetic moment, respectively. The subscript p denotes the component parallel to the background magnetic field.
For energetic electrons resonant with ULF waves, the bounce frequency is usually much higher than the wave frequency and the particle's drift frequency . Therefore, charged particles' interaction with ULF waves via the driftbounce resonance can only be excited at N = 0 (Fundamental mode), as shown in Figure 9. In this way, the drift-bounce resonance degenerates to the drift resonance, the bounce motion has no relationship with the ULF -particle interaction.

(5)
Once the drift resonance is satisfied, the resonant electrons with fundamental mode ULF waves seem to be stagnant azimuthally in the ULF wave moving frame. Thus, the resonant electrons can be accelerated very quickly since only uniform electric field can be experienced by the resonant electrons. Resonating with the fundamental poloidal ULF waves is a very efficient way to accelerate electron in the radiation belt region since the electric field of poloidal ULF waves is the same as 355 the charged particle drift direction , 2017, Hao et al, 2019.

Generalized drift resonance with growth & damping ULF waves
In the traditional drift resonance theory, the ULF wave growth rate is assumed as time independent, positive, and the amplitude of the ULF wave is extremely small. This is not agreed with satellite observations in the magnetosphere, and the 360 interplanetary shock induced ULF waves usually have huge amplitudes and experience growth (a positive growth rate) and damping (a negative growth rate) stages , Liu et al 2010. Thus, a more generalized theory dealing with the interaction between ULF waves' and charged particles in the magnetosphere for a time dependent ULF wave evolution is required.  Spectrometer (MagEIS)-like particle detector with finite time and energy resolution .
A drift resonance theory with growth and damping ULF waves has been developed .
In there, a time dependent imaginary wave frequency has been adopted to describe the growth and damping of the waves in the generalized drift resonance theory, therefore, the interactions between charged particles and growth and damping ULF 375 waves can be studied .
The generalized drift resonance theory with growth and damping ULF waves, it allows a time-dependent ULF wave growth rate, which is large and positive in the wave leading growth phase and decreases to negative values gradually in the damping phase. This assumption is based on ULF waves excited by the interplanetary shock impact on the magnetosphere The wave-associated electric field can be given by: where is the magnetic longitude (increasing eastward), is the real part of the wave angular frequency, and is the wave azimuthal wavenumber. Equation (6) describes a Gaussian amplitude envelope of the electric field oscillation.

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The change rate of particle's kinetic energy within the waves is given by: (7) where is particle's kinetic energy, is particle's charge, and is the magnetic gradient and curvature drift velocity. In the terrestrial dipole field, it is approximated by 390 (8) where is Earth's radius, is the equatorial magnetic field on Earth's surface, L is the L shell parameter, and is the relativistic Lorentz factor. For a nonrelativistic, equatorially mirroring particle, can be rewritten as (9) 395 Therefore, the change rate of kinetic energy can be rewritten as which indicates the frequency of is rather than .

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As we can see from Figure 10, with the wave amplitude increasing, the electron flux PSD is oscillating with a gradual enhancement, and the phase difference between difference electrons with a lower and a higher energy is changing from a small value to~180°when the amplitude of the ULF wave stops growing. Whereas, In the ULF wave damping stage, both the variations of energetic electron PSD and the phase shift between electron fluxes with different energies continue to increase till the phase mixing effect attenuates the particle PSD oscillations. A distorted energy spectrum can be expected as 405 the results of energetic electrons resonating with a growth and damping ULF wave.
Resonant charged particles signatures can be explained by the generalized theory whereas equations in the traditional drift resonance theory are invalid. It is found that the distorted energy spectrum predicted from the generalized theory for the interactions between charged particles and growth and damping ULF waves are very well in agreement with observations 410 from Van Allen Probes. Thus, the generalized theory for drift resonance with growth and damping ULF waves can provide new insights into the interactions between ULF waves and charged particles in the magnetosphere. magnetosphere [Hao et al, 2017. Therefore, we have introduced a magnetic longitude dependence of the ULF wave amplitude into generalized drift resonance with localized ULF waves.

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As shown in Li et al [2017], the von Mises function is adopted to study the effect of a localized ULF wave (magnetic longitude dependence) in the ULF wave -charged particle interaction. The spatial localized ULF waves described here are transverse, poloidal ULF waves with azimuthal electric field oscillations. Whereas, the temporal evolution of these ULF waves are the same as the traditional one [e.g. Southwood and Kivelson, 1981], i.e., the wave is time independent and very 425 small in terms of the wave magnitude.
The electric field of the localized ULF waves is given by (12) where m is the ULF wave number, ϕ is the magnetic longitude (increasing eastward), and ω is the ULF wave angular frequency.

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Thus, the average rate of the particle energy gain from the transverse ULF waves is [Northrop, 1963] (13) where the subscript A denotes the average over many gyration periods, q is the particle's charge, and Vdϕ is the azimuthal component of the particle's drift speed.

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The azimuthal drift speed Vdϕ of the particle can be obtained from following equation if an equatorially mirroring particle is considered in the dipole field where L is the L shell number, RE is Earth's radius, and BE is the magnitude of the equatorial magnetic field.
Then, the energy gain δWA from the ULF waves can be obtained if we integrate dWA/dt along the particle's unperturbed drift 440 orbit.

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As demonstrated in Figure 11, shock-induced ULF waves are suggested to be confined in a limited azimuthal region (possibly the plasmaspheric plume), which is westward of the Van Allen Probe spacecraft. Then, ULF wave-modulated energetic electrons drift out of the ULF wave -charged particle interaction region before they are observed by the distant spacecraft. The drift speed of the modulated energetic particle is depending on its energy and pitch angle. The difference in energy and pitch angle of the energetic electrons would produce a drift dispersion, i.e. equatorially mirroring 90∘ pitch 470 angle electrons would drift faster and be observed first. This effect will lead to distorted particle pitch angle stripes to form "Boomerang-shaped" evolutions in pitch angle spectra for each electron energy band. The observed boomerang stripes as well asmodulations in the electron energy spectrogram can be reproduced by using by time-of-flight backward tracing method [Hao et al, 2017.
Furthermore, ULF wave -radiation belt electron drift resonance can be depicted by quasi-periodic stripes, either straight or "Boomerang-shaped", in the pitch angle spectrum of electron fluxes as shown in Figure 12 and Figure 13. Boomerangshaped stripes on pitch angle distribution are evolved from straight ones after resonant electrons drift away from the azimuthally localized ULF wave -particle interaction region. Also, it provides a new method based on the time-of-flight tracing technique to identify the region of ULF waves interacting with particles. Thus, , it is crucial to take both the spatial 480 distribution and temporal evolution of ULF waves into consideration for both drift resonance and drift-bounce resonance [Zhao et al, 2020].  [Zhao et al, 2020].
The study of "Boomerang-shaped" evolutions in pitch angle spectra would tell us not only that where the drift resonance is taking place, but also the possible scale size of the ULF wave -particle interaction at a location distant away from the spacecraft. These results add new understanding to the radiation belt dynamics.

Radiation belt "relativistic electrons" acceleration by drift resonance
What will happen if charged particles are in drift resonance with both growth and damping ULF waves and localized ULF 495 waves? An excellent example is given in the Figure 14, relativistic energetic electrons resonating with localized growth and damping ULF waves can lead to very rapid ultra-relativistic electron acceleration in the radiation belt region.

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As shown in Figure 14, strong intensifications of relativistic and ultra-relativistic electron fluxes have been observed at by Van Allen Probe B following an interplanetary shock impact on the Earth's magnetosphere during the 16 July 2017 SSC.
This is the result of ultra-relativistic electrons in the outer radiation belts interacting with the interplanetary shock excited ULF waves.

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The relativistic and ultra-relativistic electron fluxes are oscillating strongly in the ULF Pc5 frequency range (Figure 14).
For a relativistic electron with an energy above ∼1 MeV, the oscillation periods modulated by the ULF waves are close to its drift period in the magnetosphere. Thus, the evolution of energy spectrogram modulated by ULF waves resembles energetic electron injection with its drift echoes. At lower energy, nevertheless, the electron oscillation period is controlled predominately by ULF waves, which is almost independent on its energy.  Figure 13. The vertical dashed lines N1, N2, and N3 refer to the simulated energy dispersionless modulations in the energy channels far from resonance. MLT = magnetic local time [Hao et al, 2019].

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According to the generalized drift resonance theory on charged particles resonating with growth and damping ULF waves , the frequency of charged particle flux modulations will shift from the wave frequency to m d if the ULF waves have decayed, and tilted stripes would be formed in the energy spectrum. When ULF waves disappeared, the formed acceleration and deceleration of charged particle stripes will keep drifting with their respective speeds. Energy-dependent drift motion along the drift orbit between the interaction region and the spacecraft causes the 530 charged particle flux oscillation ( Figure 15). Figure 15, the spacecraft observations and numerical simulations based on the generalized charged particles drift resonance theory with both growth and damping ULF waves and localized ULF waves agree each other extremely well.   Before the shock arrival, the PSD distribution f(L*)|μ,K remained almost unchanged. After the shock arrival, the electron distribution was significantly modified by the interplanetary shock impact within 2 hours and the PSD enhancement of over an order of magnitude is found at 4< L* <4.5 [Hao et al, 2019].

As indicated in
It has been found that the shock induced ULF waves with azimuthal wave number of 1 was the dominant component.

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Within an hour, the relativistic electron can be accelerated as much as more than 10 times in terms of electron flux ( Figure   16) by observed ULF waves [Hao et al, 2019]. Therefore, ULF waves are very powerful to accelerate ultra-relativistic electrons in the radiation belt. The energy spectrum of relativistic electrons has confirmed that ULF waves triggered by the interplanetary shock impact can accelerate outer radiation belt ultra-relativistic electrons up to 3.4 MeV very efficiently in less than an hour ( Figure 16). Also, when an interplanetary shock impinging on the magnetosphere, besides the initial adiabatic acceleration, the spectrum of magnetospheric electrons will be rotated first [Wilken et al., 1986]. Further, additional acceleration can happen via drift resonance with ULF waves .
In brief, the radiation belt ultra-relativistic electrons can be effectively accelerated by interplanetary shock induced ULF waves within an hour . It has been shown these observed complex and mixed signatures are in consistence with the generalized drift resonance between relativistic electrons and localized ULF waves with both growth and damping features.

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The observed main features of ultra-relativistic electrons can be reproduced well by numerical results based on the generalized ULF wave -particle drift resonance scenario. This suggests that the generalized drift resonance theory with both growth and damping ULF waves and localized ULF waves is valid and needs to be taken into account for the radiation belt dynamics.

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In this section, the classical drift-bounce resonance concept will be introduced first. Then, a more generalized theory will be described on charged particles' drift -bounce resonance with growth and damping ULF waves. Finally, I will show how poloidal ULF waves interacting with cold plasmaspheric population and the ionospheric outflow.
As mentioned in the above section, the classical drift-bounce resonance condition can be expressed as: ， where N is an integer (normally 0, ±1, ±2), m represents the azimuthal wave number, and ɷ, ɷ d and 565 ɷ b are the ULF wave frequency, the drift and bounce frequencies of the charged particles in the magnetosphere, respectively.
In the Earth's magnetosphere, the bounce frequency of an ion (especially heavy ions, e.g. oxygen ions) is close enough to its drift as well as ULF wave frequencies. Thus, the bounce motion must be considered for charged particles-ULF waves interactions. Charged particles' drift and bounce frequencies (ɷ d and ɷ b ) are dependent on their kinetic energy, thus, the energy of resonant particles can be decided if the ULF wave frequency is already known.
Since the gradient and curvature drifts of charged particles are in the azimuthal direction in the Earth's magnetosphere, thus, the energies of charged particles can be affected significantly by azimuthal electric field oscillations of poloidal ULF waves.
This drift-bounce resonance occurs when particles with a certain energy match the local drift-bounce resonance condition. If the ULF waves are the second harmonic, these resonant charged particles could experience a uniform electric field, as shown in Figure 17. This will lead to fast acceleration of charged particles.  It appears that the resonant ions always stay in the westward wave electric field within each bounce period and will gain a 585 net energy continuously. However, if ions that satisfying the drift-bounce resonance condition in the fundamental mode are considered, these charged particles would experience an accelerating phase (westward electric field) and a decelerating phase (eastward electric field) within a single bounce period and therefore its energy gain can be very small. Also, if energetic electrons are considered, their guiding centre motion will appear as a vertical line in the second harmonic ULF waveThe acceleration and deceleration of the electron will cancel out completely over each bounce period. Thus, only Thus, in principal, energetic ions in the second harmonic poloidal standing waves will be accelerated much more efficiently compared to those in the fundamental mode ULF waves. Furthermore, it has been pointed that the charged particles in the ring current energy range, e.g., oxygen ions could satisfy all n= ±1, ±2 drift-bounce resonance condition easily. This implies that the drift-bounce resonance is preferred for oxygen ions and is potentially an important mechanism for the ring current oxygen acceleration [Zong et al., , 2012Ren et al. 2016Ren et al. , 2017a.

Drift-bounce resonance with growth and damping ULF waves: "Fishbone" pitch angle distribution 600
In the classical drift -bounce resonance theory, the ULF wave growth rate is assumed to be time independent, positive, and the amplitude of the ULF wave is extremely small. This is not agreed with satellite observations in the magnetosphere, and the interplanetary shock induced ULF waves are usually with huge amplitude and experience a growth (a positive growth rate) and a damping (a negative growth rate) stage [Tan et al 2004, Liu et al 2010. Thus, a more generalized theory dealing with time dependent ULF waves' interaction with charged particles is 605 required.
The change rate of the particle's kinetic energy within the growth and damping stage of the waves is given by [Zhu et al, 2020, Ren et al. 2019a For even harmonic waves: The simulation based on the generalized theory of drift -bounce resonance [Zhu et al. 2020] is employed to reproduce the time evolution of the pitch angle distributions of energetic protons observed by Van Allen Probe A on 28 January 2014 ( Figure 18). This event was first reported by Yamamoto et al. (2019), however, the temporal variations of inclination angles of each "fishbone" is not addressed.
As illustrated in Figure 18, the inclination of pitch angle stripes increases, "Fishbone-like" structures appear in the electron pitch angle distribution when the waves are growing [Liu et al., 2020]. According to the generalized drift-bounce resonance theory [Zhu et al., 2020, Liu et al 2020, Ren et al. 2019a, the increasingly inclined stripes are the manifestation of increasing 625 phase shift across resonant pitch angles. These observational features can be well predicted by the generalized drift-bounce resonance theory. The right column of Figure 18 shows the simulation result. A notable feature is the time change of pitch angles at which flux oscillation is strongest. In other words, the resonant pitch angle changes with time. The black dashed lines illustrate this tendency. At the beginning, protons resonate at middle pitch angles, e.g. ∼ 60• and ∼ 120•, whereas at the end, the resonance pitch angle of hydrogen ions is slightly moving away from middle pitch angles.  Drift-bounce resonance with growth and damping ULF waves can result in the increasingly inclined pitch angle stripes.
When the amplitude of the ULF wave is in growing, the stripes of the hydrogen ion pitch angle become more and more inclined. It is shown in Figure 18  At the beginning of the wave growth stage, the wave growth rate is large enough to "hide" the phase shift, causing relatively vertical stripes. Then, as the wave grows and its growth rate decreases to zero, the "hidden" phase shift gradually appears, causing the stripes to become more and more inclined. "Fishbone-like" pitch angle structures, thus, is formed by interaction with growth & damping ULF waves [Liu et al, 2020].  observations and reproducing them via the generalized drift-bounce resonance theory, it is found that time-varying phase shift across resonant pitch angles can indeed occur, and the effect caused by growth or damping of ULF waves is significant.
As a result, the inclination of pitch angle stripes would increase or decrease with time, causing "Fishbone-like" pitch angle structures.

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It is important to note here that "Fishbone-like" structures in ions' pitch angle distribution observed by Van Allan Probes and THEMIS spacecraft can be well reproduced by the generalized drift-bounce resonance theory, therefore provide a more realistic picture of drift-bounce resonance in the Earth's magnetosphere. Therefore, it is important to investigate the influence of the temporal variations of the wave growth rate on the flux oscillations and their phase shift. The generalized 670 drift-bounce resonance theory sheds light on the wave-particle interaction between charged particles and ULF waves.

ULF waves' interaction with cold plasmaspheric charged particles
How does plasmaspheric charged particles of a very low energy (~eV) response to ULF waves? For a plasmaspheric charged particle with energy of a few eV, its drift frequency is much smaller than the bounce frequency: ωd << ωb. Therefore, 675 the drift-bounce resonance between the plasmaspheric charged particles and the ULF waves should be dominated by the bounce resonance: Ω = N ·ωb.   [Zong et al, 2017b] However, Once the drift-bounce resonance condition being satisfied, cold plasmaspheric electrons can still be affected by 685 the poloidal mode ULF waves (e.g., Pc5 band). Cold plasmaspheric electrons experience acceleration by the azimuthal electric field of poloidal mode ULF waves which is similar to drift-bounce resonance of oxygen or hydrogen ions , Ren et al, 2017a.
where P( ) = 0.35+0.15 sin (Hamlin et al., 1961), is the charged particle equatorial pitch angle, W is the particle energy, L is the McIlwain L shell value, B E is the magnitude of Earth's magnetic field at the equator on the Earth's surface, R E is 695 Earth's radius, Ψ 0 is the electric potential causing the plasma convection in the magnetosphere, Φ is the azimuthal angle and Ω E is the angular frequency of Earth's rotation.
For a given plasma electron with energy between 1 eV to 1 keV, the drift-bounce resonant conditions for N = 1 and N = 2 can be satisfied with a ULF wave number |m| <100 [Ren et al, 2017b[Ren et al, , 2018[Ren et al, , 2019b. As we can see from Figure 20, a sharp 700 enhancement at SYM-H index has been observed, indicating the interplanetary shock arrival. ULF waves with a large amplitude oscillation (~15 mV/m) have been observed immediately after the interplanetary shock impinging on the magnetosphere.
Outstanding and surprising features are that both energy and pitch angle dispersion signatures of plasmaspheric electrons 705 with an energy of 6 eV to 19.9 eV have been observed clearly. In the dispersion, the electron with a small pitch angle (almost the field-aligned (0°)) has been observed first, whereas the anti-field-aligned (180°) electrons are observed at last. Different from the lower energy plasmaspheric electrons, one can see the pitch angle of a higher energy (above 19.9 eV) electron oscillates between 0°and 180°, and the pitch angle dispersion signature cannot be seen clearly. The period of these https://doi.org/10.5194/angeo-2021-57 Preprint. Discussion started: 23 November 2021 c Author(s) 2021. CC BY 4.0 License.
successive dispersion signatures is found to be~40 s, the same as the observed ULF wave period (third harmonic). Therefore, 710 these multi-dispersions are the results of electron bounce resonance with the interplanetary shock induced ULF waves.  [Ren et al, 2017b].
It is worth pointing out that the ULF wave -particle interaction or plasmaspheric charged particle acceleration region can be determined by backward tracing dispersion signatures of both the energy and the pitch angle. Then, the region of electron 720 acceleration is found to be inside the plasmasphere, it is located off-equator at around -32°in the southern hemisphere.
These can be explained by plasmaspheric electrons interacting with the third harmonic ULF waves with large amplitude electric field at the off-equatorial plasmasphere. The pitch angle dispersion signatures are due to the flux oscillation of "local" non-resonant and resonant plasmaspheric electrons but not electrons injected from the Earth's ionosphere.
Furthermore, the energy gain of resonant plasmaspheric electrons can be about 20 percent in one wave cycle from the 725 observed interplanetary shock induced large amplitude ULF wave electric field. . In general, these results agree with the frame work predicted by the generalized drift-bounce resonance theory (Figure 18).

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Ionospheric outflow is one of the predominant plasma sources of Earth's magnetosphere. It has been shown that the dayside ionospheric outflow ions can interact with ULF waves [Liu et al. 2019, Ren et al. 2015. It is evident that polarization drift caused by large amplitude electric fields associated with ULF waves may play a significant role in the modulation of singly charged oxygen ions, which may lead to an additional acceleration of oxygen ions [Yue et al., 2016]. This process can be non-adiabatic if the ULF wave-borne electric field is large enough. It is revealed that the interaction between ULF waves and 745 ionospheric outflow ions occurs predominantly in the perpendicular direction to ambient magnetic field. The cold ionospheric ions are not only added an energy of by ULF waves to make them "visible" obviously, but also to be separated into ion species according to different mass. The ULF wave modulation on the ionospheric outflow is mass dependent, and this indicates that the ULF wave -charged particle interaction can serve as a mass spectrometer to distinguish ion species.   [Liu et al, 2019].
As shown in Figure 22 clearly, ionospheric outflow ions can be modulated by ULF waves driven E x B drift. As a result, 760 the charged particle's energy rises and falls periodically in coincidence to the ULF oscillation. The energy of H + , He + , and O + ions of ionospheric origin can be added as high as ∼75, 300, and 1,200 eV, respectively.
It is worth pointing out that the effect of polarization drift should be taken into account, due to the large amplitude electric field of the ULF waves. The particle's energy (Wtotal) including both E × B drift and polarization drift can be expressed as (20)

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The last term equation (20) represents the effect of polarization drift which is proportional to the ion mass. Therefore, polarization drift effect is more profound for heavier ions (oxygen ions) than lighter ions (hydrogen ions).  [Liu et al, 2019].

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The observations suggest that the ionospheric heavier ions (oxygen) are modulated significantly by ULF wave-induced E × B drift and polarization drift ( Figure 23). It is shown that the polarization drift is contributed mainly from ULF oscillations whose period is less than 1 minute, whereas only ∼20% contributed from oscillations with a period greater than 1 min. It is suggested that O + can be accelerated significantly by both ULF wave-induced E × B drift and polarization drift. This acceleration process is non-adiabatic which agrees with previous theoretical studies (e.g., Cole, 1976;White et al., 2002; 780 Bellan, 2008

outer magnetosphere
In the inner magnetosphere dominated by the dipole field, the bounce and drift frequencies of charged particles are unimodal functions of pitch angle from 0°to 180° [Hamlin et al., 1961]. However, in the dayside outer magnetosphere, there exists off-equatorial magnetic field minima due to solar wind compression, which can change the trajectories of particles, forcing the orbits of particles with pitch angle near 90°to bifurcate and form the so-called Shabansky orbits [Shabansky, 795 1971]. Figure 24 shows the trajectory of a Shabansky particle and the magnetic field profiles. Running in an image-dipole magnetic field model, the trajectory of the test particle with pitch angle near 90°bifurcates in the dayside magnetosphere, as shown in panels a-b. Since the magnetic field strength along one field line gets its minima off the equator in the dayside (the red line in panel c), particles with pitch angle near 90°will bounce between two mirror points in the high-latitude minima.
Through affecting the bounce and drift motions of particles, off-equatorial minima also modify corresponding frequencypitch angle relations and change the conventional ULF wave-particle interaction pattern in the inner magnetosphere.  resonance, manifests as two~180°phase shifts across resonant pitch angles [Zhu et al., 2020]. However, the spectrogram shows more than two~180°phase shifts, indicating more than two resonant pitch angles for given energy.  Li et al., 2021].  The blue ① and purple ② represent particles trapped into the southern high-latitude minima and particles cross the equator, respectively [adopted from Li et al., 2021].

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Besides, off-equatorial minima can also affect the trajectories of energetic electrons, leading to abnormal electron drift features on pitch angle-time spectrograms in the dayside magnetosphere. Figure  that energetic electrons with 90°pitch angle drift faster at fixed energy, which agrees with the charged particle drift motion pattern in the dipole field [e.g., Hao et al., 2017, Zhao et al., 2020. On the contrary, reverse-boomerang stripes indicate an abnormal drift velocity -pitch angle relation that particles with 90°pitch angle drift slower, which is opposite to the pattern of particle drift motion in the dipole field. Test-particle simulations in an image-dipole magnetic field reproduced the 850 observed reverse-boomerang feature at larger L-shells, suggesting that the reverse-boomerang stripes result from offequatorial minima due to the compression of the magnetopause. In this event, the solar wind dynamic pressure is so large (> 10 nPa) that the off-equatorial minima effects can be observed in the inner magnetosphere (at L-shell~5.9). Meanwhile, normal-boomerang stripes can be observed in the inner region (like L-shell~4.0), where the magnetic field is less affected by the solar wind dynamic pressure (the magnetic field is expected to be more dipole-like). [adopted from .
However, the electron reverse-boomerang stripes are not as common as the normal-boomerang stripes from the observations of Van Allen Probes , since the orbits of Van Allen Probes are mainly located in the inner magnetosphere. Therefore, reverse-boomerang stripes on electron pitch angle distributions can be observed by Van Allen Probes only when large compression on the magnetopause forms off-equatorial minima even in the inner magnetosphere.
Besides, particles with pitch angle near 90°will bounce between high-latitude mirror points if off-equatorial minima exist in the dayside magnetosphere (panel a in Figure 24). Consequently, localized second harmonic ULF waves could interact with these Shabansky electrons by drift resonance, which have not been reported before.

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In conclusion, off-equatorial minima can affect the bounce and drift motions of both ions and electrons, changing the conventional ULF wave-particle interaction pattern. These results reveal new kinds of ULF wave-particle interaction, which potentially affect the efficiency of particle energization for magnetospheric activities relevant to particle energization.

Nonlinear and multiple drift/drift -bounce resonances
In the traditional drift or drift-bounce resonance theory, the weak ULF wave-particle interaction is assumed and charged particle trajectories are unperturbed, thus, a linearization theory can be applied. However, the observed ULF waves in the magnetosphere are usually with a larger magnitude, therefore, the traditional theory needs to be extended into a nonlinear 880 regime since charged particle trajectories are strongly disturbed [Li et al, 2018, Degeling et al, 2019. In this section, the concepts on the nonlinear and multiple drift/drift-bounce resonances will be presented.  channels. [Li et al, 2018] A nonlinear theory of drift resonance has been developed to formulate the charged particle motion due to the ULF wave of a large amplitude [Li et al, 2018, Degeling et al, 2019. Observable signatures such as rolled-up structures in the energy spectrum are predicted. As shown in the panel l of Figure 28, the W oscillations are strongest at the resonant energy 895 of 54 keV, and there appears a sharp, 180∘ phase shift across the resonant energy. A rolled-up structure eventually appears at around the resonant energy, this feature could not be predicted by the linear theory. Such a rolled-up structure has been observed in the energy spectrum by the Van Allen Probes [Li et al, 2018]. This provides a solid evidence for the nonlinear drift resonance. The nonlinear drift resonance can be very important in ULF wave -charged particle interactions in the radiation belts [Li et al, 2018, Degeling et al, 2019. Multiple drift and/or drift-bounce resonances can occur with different plasma species or the same species at different energies simultaneously. As shown in Fig. 29, it is probable that ULF waves can interact with the energetic oxygen ions at two different energies via both drift-resonance (N=0) and drift-bounce resonance (N=2) simultaneously [Rankin et al 2020].

5.2Multiple drift and/or drift-bounce resonances
It is found that the oxygen ion differential flux is strongly peaked at the equator. Oxygen flux for drift-bounce resonance 915 peaks at much higher latitudes than those for drift resonance, this can be understood as pitch-angle dependence of the resonance energy.
More observations are needed to verify the features of flux modulations resulting from simultaneous multiple resonances of drift and drift-bounce in more detail, and the resulting ring current dynamics caused by poloidal mode ULF waves in Earth's magnetosphere. Singly charged oxygen ions undergoing drift resonance and drift-bounce resonance can yield new insight 920 into the ring current dynamics of heavy ions that interact with ULF waves.  Another aspect is that multiple ULF waves with different m can interact with single plasma population simultaneously.

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Ultra-high energy resolution data from MagEIS on board Van Allen Probes [Hartinger et al., 2018] in Figure 30 are used to show how magnetospheric charged particles response to a negative solar wind dynamic pressure pulse. As shown in Figure   30, the residual fluxes for electrons with an energy less than 800 keV are decreasing or dropouts, whereas ones with an energy larger than 800 keV are increasing following the negative dynamic pressure pulse arriving. The estimated arrival time of electron drift are over-plotted by the black dashed curves.

935
The electron fluxes oscillations are consistent with the scenario described in the Section 3.3. For the energetic electron with an energy above ∼800 keV, the modulated periods by the ULF waves (low m) are close to its drift periods. However, for energetic electrons with an energy less than ∼800 keV, the oscillation is controlled by ULF waves (high m). These mixture signatures are consistent with that energetic electrons at different energies are resonating with ULF waves of different azimuthal wave numbers.

940
Also, it has been shown that ULF waves can interact with relativistic electrons by drift-resonance and ions by drift-bounce resonance at the same time , Ren et al. 2016]. Thus, multiple drift and/or drift-bounce resonances can occur simultaneously. These provide a basis for further understanding the dynamic coupling between the radiation belt electrons and the ring current populations in the magnetosphere response to solar wind forcing.

Outstanding questions and concluding remarks
Magnetospheric physics is now in an extremely vibrant phase with several ongoing and highly-successful missions, e.g.
Cluster, THEMIS, Van Allen Probes, and MMS spacecraft, providing amazing observations and data sets. Since there are https://doi.org/10.5194/angeo-2021-57 Preprint. Discussion started: 23 November 2021 c Author(s) 2021. CC BY 4.0 License. many unsolved fundamental problems, in this paper I have addressed selected topics of ULF wave -charged particle interactions, which encompass many special fields of radiation belt, ring current and plasmaspheric physics. Although great progress has been made over the recent decades, , clear answers have not been found yet as the following: Do ULF waves mediate coupling between plasmasphere and ring current ion species and radiation belt energetic electrons?
If so, do the ring current ion-excited second-harmonic poloidal ULF waves of moderate m-number cause the energization of 955 radiation belt electrons?
What role do the high-m poloidal mode ULF waves play in the energization of storm-time ring current ions? Is it a prerequisite for a super magnetospheric storm or not?
How common do the high-m poloidal mode waves occur at the plasmapause, and can they be seen as the signature of existence of the plasmapause? What is the role of the plasmaspheric ion constituency in it? Are high-m poloidal mode ULF 960 waves generated mainly by an exterior solar wind driver or excited by the ring current ions?
What is the role of ULF waves in other planets with a magnetosphere, e.g. Saturn, Jupiter, Mercury's magnetosphere? What is the role of ULF waves in other planets or comets without a magnetic field, e.g. Mars, Venus and Comets?
The response of magnetosphere to the impact by interplanetary shock or solar wind dynamic pressure impulse is not just a "one-kick" scenario. Instead, the impact generates a series of waves including poloidal mode ULF waves. A generalized 965 theory of drift-bounce resonance with growth or decay and/or localized ULF waves has been developed to explain observations. Energy and pitch angle dependent behaviours for both resonant and non-resonant populations can be well predicted by the generalized drift resonance theory.
The studies on ULF waves' interaction with charged particles will magnificently enrich our understanding of the interactions of the solar wind and solar wind forcing with the planet's magnetosphere (often cause large geomagnetic 970 disturbances), which is a ubiquitous phenomenon occurring throughout the plasma universe but uniquely accessible within the Earth's magnetosphere. It is realized that the poloidal ULF wave is more effective to accelerate and modulate electrons (fundamental mode) in the radiation belt, as well as charged ions (second harmonic) in the ring current region.
A part of ultra-high energy resolution data already provides us new insight into the drift or drift-bounce resonance, especially for multiple drift and/or drift-bounce resonances. Any future magnetospheric mission plans should take into consideration the allowed charged particle detectors to have high energy resolution, high pitch angle resolution and the capability to separate ion mass and charge compositions.

Data availability.
No data sets were used in this article.