MAVEN Observations of Whistler-mode Waves Within the Magnetic Dips in the Martian Ionopause/Ionosphere

Whistler-mode waves are natural and common electromagnetic emissions observed both surrounding planets and their moons with and without intrinsic magnetic field. Numerous observations have shown that the magnetic dip is a favorable region for the whistler-mode wave generation in the Earth’s magnetosphere. However, up to now, seldom observations of these waves have been reported in such regions at Mars. Based on the measurements from Mars Atmosphere and Volatile EvolutioN mission, quasi-parallel propagating whistler-mode waves are observed within magnetic dip structures in the Martian ionopause and ionosphere. Correspondingly, significant electron beams in the antiparallel direction are observed, and a linear instability analysis shows that f pe/f ce becomes extremely large (∼1500) inside the magnetic dip. Thus, the electron minimum resonant energy of whistler-mode waves decreases to several eV, which increases the number density of resonant beam electrons. Such beam electron distribution results in the necessary free energy for the whistler-mode wave growth. Our study indicates magnetic dips may be favorable regions for the whistler-mode wave excitation even in the Martian ionosphere, which has an extremely high f pe/f ce but does not have a global intrinsic magnetic field.


Introduction
Whistler-mode waves at frequencies below the electron gyrofrequency are natural, intense, and right-handed polarized electromagnetic emissions commonly observed both surrounding planets and their moons with and without a global intrinsic magnetic field (Burtis & Helliwell 1969;Cao et al. 2005Cao et al. , 2007Li et al. 2013;Meredith et al. 2003;Menietti et al. 2012;Yu et al. 2017Yu et al. , 2018Santolik et al. 2011;Halekas et al. 2012;Harada et al. 2014Harada et al. , 2016. They have been extensively investigated due to their crucial role in many important space physical processes, such as the acceleration of radiation belt electrons (Yu et al. 2020), the formation of the pulsating and diffuse aurora (Ni et al. 2008), the variation of electron pitch angle distributions (Cao et al. 2020;Khotyaintsev et al. 2011;Ma et al. 2021), the trigger and modulation of magnetic reconnections (Wei et al. 2007;Cao et al. 2017), and the transfer and cascade of energy (Khotyaintsev et al. 2011).
The generation of whistler-mode waves has received extensive and sustained attention. Temperature anisotropy and electron beams can trigger whistler-mode waves Harada et al. 2016;Kennel & Petschek 1966;Yu et al. 2018;Zhima et al. 2015). At planet bodies without a global intrinsic magnetic field, anisotropic electrons can be formed via significant surface or atmosphere absorption of parallel electrons (Halekas et al. 2012;Harada et al. 2014Harada et al. , 2016Santolik et al. 2011), while electron beams can be caused by significant enhancement of electrons from the solar wind or ionosphere moving upward or downward along the Martian magnetic field lines (Xu et al. 2017;Wang et al. 2021).
Previous studies have theoretically and observationally shown the key role of the background magnetic field in controlling the whistler-mode wave generation. In the Earth's magnetosphere, the "minimum-B-pocket" region, characterized by a smallest magnetic field strength in comparison with that nearby, is a favorable region for the excitation of whistler-mode waves (LeDocq et al. 1998;Santolik 2008;Tenerani et al. 2013;Tsurutani et al. 2009). Thus, whistler-mode waves in the Earth's magnetosphere are usually generated at the magnetic equator in the inner magnetosphere (LeDocq et al. 1998), in the dayside high-latitude regions in the outer magnetosphere (Tsurutani et al. 2009), or at the center of magnetic dips (Tenerani et al. 2013). Although the whistlermode waves at Mars have been reported, they concentrate on the wave generation in the Martian induced magnetosphere and omit the effect of some key factors on this process, such as the magnetic field structures (Harada et al. 2016). How the magnetic field structures control the whistler-mode wave generation has not been reported or investigated at Mars. Compared to Earth, although the interaction of Mars to the solar wind resembles similar space structures (Wang et al. , 2021, Mars lacks a global intrinsic magnetic field leading to a smaller magnetosphere consisting of draped and local magnetic fields (e.g., Nagy et al. 2004). Also, the small background magnetic fields result in large f pe /f ce in the Martian ionosphere. Whether the "minimum-Bpocket" has a similar effect on the whistler-mode wave generation in the Martian space environment remains unknown.
In this letter, we report two events of whistler-mode waves and analyze one of them which are observed at the center of three consecutive magnetic dips by the Mars Atmosphere and Volatile EvolutioN (MAVEN) measurements. This letter is organized as follows. Section 2 shows a brief introduction of MAVEN's instruments. In Section 3, we show observations of whistler-mode waves at magnetic dip centers. Section 4 presents the linear instability analysis on these whistler-mode waves, followed by a discussion in Section 5 and a summary in Section 6.

Data and Instrumentation
MAVEN mission entered a Mars elliptical orbit with a periapsis of 150 km and an apoapsis of 6000 km in 2014 October (Jakosky et al. 2015). The magnetic field vectors with a sampling rate of 32 Hz are detected from the Magnetometer (MAG; Connerney et al. 2015), which are used to calculate the power spectral density of magnetic field in the frequency range of 0-16 Hz by applying short-time fast Fourier transform with a window width of 256 points and a sliding step of 50 points. The power spectral density of the electric field in the frequency range of 1 Hz-2 MHz is from the Langmuir Probe and Waves (LPW; Andersson et al. 2015), and the electron density is estimated from the LPW current-voltage (I/V) characteristic . The ion energy spectra at a cadence of 4 s in the energy range of 25 eV-25 keV are from the Solar Wind Ion Analyzer (Halekas et al. 2015), the mass spectra of ions at a cadence of 4 s are from the SupraThermal and Thermal Ion Composition (McFadden et al. 2015) and the energy spectra and pitch angle distributions of 3-4600 eV electrons are from the Solar Wind Electron Analyzer (Mitchell et al. 2016).  (Trotignon et al. 2006). The following five panels show the magnetic field strength |B|, the electron density N e , the omnidirectional ion energy spectra, the ion mass spectra and the omnidirectional electron energy spectra.

Observations of Whistler-mode Waves at Magnetic Dip Centers
Before ∼02:42 UT, MAVEN traveled in the magnetosheath, where the magnetic field was highly turbulent ( (Figures 1(e)) and suprathermal electrons (Figure 1(g)) are absent. Inside the ionopause, MAVEN detects a large-scale longlived (∼5 minutes) magnetic field dip with strength decreasing from ∼15 to ∼2 nT. Figure 2 shows the zoom-in plot of consecutive small-scale magnetic dips and the whistler-mode waves during the period of 03:11-03:15 UT (between two vertical dashed lines in Figure 1). The panels from top to bottom present the magnetic field strength, the electric power spectral density (E PSD ), the magnetic power spectral density (B PSD ), the degree of polarization, the wave normal angle (θ k ) and ellipticity. The wave propagation and polarization characteristics are determined by analyzing the three components of the magnetic field through the Means method (Means 1972). The narrow lines at a few Hz are probably due to artificial noise from reaction wheels (Connerney et al. 2015). As shown in Figure 2(a), three consecutive small-scale magnetic dips are observed with the magnetic field strength decrease ranging from ∼1 to ∼3 nT and the duration ranging from ∼25 to 45 s. Strong whistler-mode emissions with frequencies between the lower hybrid frequency Figures 2(b)-(f)) and 0.2f ce are clearly identified at the center of three magnetic dips (marked by the vertical dashed lines) with high coherency (degree of polarization >0.8 in Figure 2(d)), right-handed polarization (ellipticity >0.5 in Figure 2(f)), and quasi-parallel propagation (θ k < 30°in Figure 2(e)). Another electromagnetic emission occurs within the magnetic dip near 03:13:47 UT. Such emission has a larger wave normal angle and small ellipticity but with unclear electric signals. Thus, we do not analyze it since we only focus on whistler-mode waves here, which propagate in a quasi-parallel direction.

Generation of Whistler-mode Waves at Magnetic Dip Centers
Whistler-mode waves can be excited by anisotropic hot electrons via cyclotron resonance. To examine the excitation of whistler-mode waves inside the dip region, a linear instability analysis is present here. Following previous studies (Kennel & Petschek 1966;Chen et al. 2012), the convective (K i ) linear growth rate for parallel propagating whistler-mode waves can be calculated by the following: where R M is the Mars radius, and Ω e is the electron gyrofrequency. F e is the normalized electron phase space density. v ∥ and v ⊥ are parallel and perpendicular velocities respect to the background magnetic field, respectively. ( ) A V R and h ( ) V R here can roughly denote the temperature anisotropy of resonant electrons and their composition, respectively. The wave group velocity (V G ) and the resonant velocity (V R ) for wave frequency ω are determined by the cold plasma dispersion relation is the Alfvén velocity of the electrons. Figure 3 shows the linear growth rate results for whistlermode waves based on the measured electron velocity distributions, background magnetic fields and electron densities. The panels from top to bottom show the magnetic field strength (black line) and the electron density (red line), the ratio of electron plasma frequency to electron gyrofrequency ( f pe /f ce ), the electron energy spectra with the minimum cyclotron resonant energy of electrons (E min , black line), the pitch angle distributions for 5-10 eV, 10-20 eV, 20-50 eV and 100-1000 eV electrons, the electric power spectral density and the convective growth rate, respectively. The electron minimum cyclotron resonant energy (E min ) is calculated for the whistler-mode waves at 0.2f ce . Generally, the values of f pe /f ce (Figure 3(b)) are anticorrelated with the magnetic field strengths (Figure 3(a)) and the minimum electron cyclotron resonant energy (Figure 3(c)). Inside the dips, the minimum electron cyclotron resonant energy can reduce to several eV and high energy electrons are absent. Thus, electrons in the energy range of 5-1000 eV are used to calculate the growth rates for parallel whistler-mode waves (k > 0). Unlike the magnetic field and f pe /f ce , the electron energy spectrum varies rather weakly (Figure 3(c)), suggesting that it seems less important in the generation of whistler-mode waves. Moreover, the dominantly cold electrons in Figure 3(c) show a typical signature of Martian ionosphere origin, which is also supported by the MAVEN location in the ionopause during this time interval identified in Figure 1. As shown in Figures 3(d)-(f), the 5-50 eV exhibit two different types of pitch angle   distributions. Before 03:13:50 UT when whistler-mode waves are observed, the 5-50 eV electrons show beam features with enhancement mainly in the antiparallel direction. This type of electron distributions can provide sufficient free energy for the growth of whistler-mode waves. The 100-1000 eV electrons are mainly in the parallel direction (Figure 3(g)). It indicates that the magnetic field lines are "open" with one end connecting to interplanetary magnetic fields (IMFs) and the other end connecting to Mars (Xu et al. 2017). After 03:14:10 UT, the 5-50 eV electrons are absent both in the parallel (α < 45°) and antiparallel direction (α > 135°) while 100-1000 eV electrons are present, indicating that the magnetic fields are "draped" with both ends connecting to IMFs. Overall, the convective growth rates show a similar time-frequency pattern with wave spectra. The growth rates are more than ∼500 dB/R M inside the dips, where the whistler-mode waves are strong, and dramatically become negative (blank region) outside the dips, where whistler-mode waves are absent. The growth rate results indicate that the magnetic dip structures can increase the key parameter f/f ce , and thus, decrease the electron resonant energy and increase the resonant electron population for whistler-mode waves, and then, lead to the whistler-mode wave excitation. Figure 4 shows the velocity-distribution functions (VDFs) of electrons outside (left) and inside (right) the dips at selected times (labeled by blue and red vertical arrows in Figure 3) in the velocity space (v ∥ and v ⊥ represent the velocities parallel and perpendicular to the background magnetic field, respectively). The difference between the electron VDFs outside and inside dips is unobvious and both of them show clear electron beam structures. These suggest that in this event the electron VDFs may play a trivial role in controlling the generation of whistler-mode waves. Besides the electron beams, there is a strong temperature anisotropic in Figure 4(h), which is responsible for the large growth rates occurring inside the fourth dip in Figure 3(i).

Discussions
Such whistler-mode wave phenomenon is not unique whistlermode at Mars. Several other similar events are found and one of them is shown as a representative in Figure 5, which is detected by MAVEN between 07:50 UT and 07:54 UT on 2015 January 9. Similar to the 2015 March 31 event, whistler-mode waves are also observed at centers of three consecutive magnetic dips (Figures 5(a) and (d)) in the Martian ionosphere with extremely high N e (Figure 5b) and f pe /f ce (Figure 5(c) in this event (marked out by vertical dashed lines). These events suggest that the magnetic dips are favorable regions for the generation of whistlermode waves at Mars. Further statistical survey is needed to be conducted to address the question of the relationship between whistler-mode waves and magnetic dips in more detail in the future, such as whistler-mode wave occurrence rates, whistlermode wave amplitude dependence on dip amplitudes, etc.
Through the resonant interaction with electrons, whistler-mode waves play a controlling role in the dynamics of Earth's magnetospheric electrons, such as radiation belt electrons, plasma sheet electrons, suprathermal electrons and so on. Similar to those at Earth, the pitch angle scattering and energy diffusion induced by whistler-mode waves at Mars also can have a significant impact on the electron distribution and precipitation on both open and closed magnetic field lines (Shane et al. 2019;Shane & Liemohn 2021, 2022. However, the depression of magnetic field strength in the magnetic dip interiors at Mars provides a much weaker magnetic field environment from that at Earth. In such regions, the ratio of electron plasma frequency to electron gyrofrequency ( f pe /f ce ) can be larger than 1000 (Figure 3(b)), which is much larger than that at Earth (commonly below 20), resulting in a much lower electron resonant energy. Moreover, with larger f pe /f ce , whistler-mode waves near Mars will propagate much slower than those near the Earth, indicating local excitation may be much more important than propagation for Mars' whistlers. However, how such high f pe /f ce affects the whistlermode wave properties and electron dynamics remains unclear, which will be left for future study.

Summary
In the present paper, we first report an event of whistler-mode waves observed by Mars Atmosphere and Volatile EvolutioN (MAVEN) at the center of three consecutive magnetic dips. The small-scale consecutive magnetic dips are found embedded in a larger magnetic dip structure located on the open magnetic field line in the Martian ionopause in the northern hemisphere. In the magnetic dip interiors, whistler-mode waves are observed at frequencies between the lower hybrid frequency and one-fifth of the electron cyclotron frequency, and the wave property analysis shows that they propagate nearly parallel to the background magnetic field. In the whistler-mode wave generation region, clear electron beams in the energy range of 5-50 eV are observed due to significant enhancement in the antiparallel direction. Based on the measurements of local electron distributions and magnetic fields, we calculate the linear growth rates, which show a similar time-frequency spectrum to the observations, indicating that the parallel propagating whistler-mode waves can be locally excited by the electron beams at the centers of magnetic dips. The f pe /f ce becomes extremely large (∼1500) inside the magnetic dip, which leads to an extremely small electron minimum resonant energy of whistler-mode waves (several eV), and thus, an enormous increase of the number density of resonant electrons. This event together with other events suggests that it is a common phenomenon that whistler-mode waves can be generated in the magnetic dip interiors at Mars, indicating that the magnetic dip structures are also probably favorable for the excitation of whistler-mode waves at planets without a global intrinsic magnetic field like Mars.