Betatron cooling of electrons in the Martian ionosphere

Betatron cooling of electrons in the Martian ionosphere

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Xu Bai¹^,², ZuZheng Chen¹^,²^,^*, HuiShan Fu¹^,²^,^*, ZhiZhong Guo³, WenDing Fu¹^,², TianYu Zhou¹^,², Zhe Wang¹^,², Jing Wang⁴

Earth and Planetary Physics | 2026, 10(3) : 410 - 416

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Earth and Planetary Physics | 2026, 10(3): 410-416

• RESEARCH ARTICLE •

Betatron cooling of electrons in the Martian ionosphere

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Xu Bai¹^,², ZuZheng Chen¹^,²^,^*, HuiShan Fu¹^,²^,^*, ZhiZhong Guo³, WenDing Fu¹^,², TianYu Zhou¹^,², Zhe Wang¹^,², Jing Wang⁴

Affiliations

¹School of Space and Earth Sciences, Beihang University, Beijing 102206, China

²Key Laboratory of Space Environment Monitoring and Information Processing, Ministry of Industry and Information Technology, Beijing 100191, China

³Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650504, China

⁴Planetary Environmental and Astrobiological Research Laboratory (PEARL), School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai 519082, China

xubai@buaa.edu.cn

Published: 2026-05-01 doi: 10.26464/epp2026043

Outline

Abstract

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Electron dynamics plays a crucial role in the evolution of the Martian ionosphere. However, the adiabatic process, a classical mechanism for modulating electron energy and pitch-angle distributions, has not been reported in this environment. Utilizing data from the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, we present evidence of a decrease in electron perpendicular energy predominantly driven by betatron cooling in the Martian ionosphere. The phenomenon was identified within closed magnetic field lines at the edge of the crustal magnetic fields, a region characterized by a convoluted magnetic field topology comprising both closed and open lines. The observed cooling of 10–150 eV electrons with a power-law distribution, enhancing the cigar distribution, was quantitatively reproduced by an adiabatic model. Our study may promote the understanding of electron dynamics in the Martian ionosphere.

Key words

Mars / Betatron cooling / space plasmas / Martian ionosphere / magnetic fields

Cite this Article

Xu Bai, ZuZheng Chen, HuiShan Fu, ZhiZhong Guo, WenDing Fu, TianYu Zhou, Zhe Wang, Jing Wang. Betatron cooling of electrons in the Martian ionosphere[J]. Earth and Planetary Physics, 2026 , 10 (3) : 410 -416 . DOI: 10.26464/epp2026043

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1　Introduction

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The evolution of the Martian ionosphere is influenced by external environments (Withers et al., 2008; González-Galindo et al., 2021; Peter et al., 2024) and magnetic field topologies and associated internal local plasma processes (Nielsen et al., 2007; Andrews et al., 2018; Guo ZZ et al., 2021; Wang J et al., 2023), with the dominant factors differing significantly between the dayside and nightside regions. The dayside ionosphere, containing a well-defined primary layer and a low-altitude secondary layer (Rishbeth and Garriott, 1969; Gurnett et al., 2008; Haider et al., 2011), results primarily from photoionization of atmospheric neutrals owing to solar extreme ultraviolet (EUV) and X-ray radiation (Gurnett et al., 2008; Morgan et al., 2008; Peter et al., 2024), making it subject to variations driven by solar activity (Mendillo et al., 2006; Bougher et al., 2015; Sánchez-Cano et al., 2016). In contrast, the nightside ionosphere is characterized by a more patchy and sporadic structure (Duru et al., 2006; Nielsen et al., 2007), which is predominantly governed by day-to-night plasma transport (Cui J et al., 2015; Girazian et al., 2017) and the impact ionization by precipitating electrons (Brain et al., 2006; Fillingim et al., 2007).

A convoluted magnetic field topology in the Martian ionosphere (DiBraccio et al., 2018), arising from a combination of crustal magnetic fields and draped interplanetary magnetic fields (IMF), governs particle energy and pitch-angle distributions (Cao YT et al., 2024). The closed crustal magnetic fields serve to shield the ionosphere from the solar wind particles (Brain et al., 2006; Lillis et al., 2009; Dong CF et al., 2015), whereas the open ones facilitate particle precipitation into the ionosphere (Zou H et al., 2010; Hara et al., 2018). Concurrently, the draped IMF may channel solar wind particles for interaction with the ionosphere (Fowler et al., 2021; Azari et al., 2023; Wang J et al., 2023). The magnetic fields also mediate a variety of plasma processes in the ionosphere; for instance, magnetic reconnection driven by interactions between magnetic field lines in opposite directions can energize particles and facilitate their escape from the ionosphere (Drake et al., 2005; Imada et al., 2015; Jiang K et al., 2024; Lin RT et al., 2024a, b, 2025; Fu WD et al., 2025; Huang SY et al., 2025), and field-controlled particle distributions can excite plasma waves that subsequently contribute to particle heating (Ergun et al., 2006; Wang J et al., 2023).

In a slowly varying magnetic field, adiabatic processes modulate particle energy and pitch-angle distribution through changes in magnetic field strength and bounce path length (Fu HS et al., 2011, 2013, 2019, 2020a; Chen ZZ et al., 2023). Specifically, betatron acceleration (cooling) occurs in response to magnetic field strengthening (weakening), increasing (decreasing) perpendicular energy and flux near the 90° pitch angle (Fu HS et al., 2011, 2012, 2013, 2020a; Guo ZZ et al., 2021). Likewise, Fermi acceleration (cooling) emerges in response to a shortening (lengthening) bounce path, increasing (decreasing) parallel energy and flux near 0° and 180° (Fu HS et al., 2011, 2013, 2019, 2020a, b). However, the roles of adiabatic processes in particle dynamics have not been investigated in the Martian ionosphere.

In this study, utilizing data from the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission (Jakosky et al., 2015), we present direct evidence of a weakening in electron perpendicular energy and the formation of pronounced cigar pitch-angle distributions arising from betatron cooling. This process was quantitatively reproduced using an adiabatic model as well.

2　Observations

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The level-2 calibrated data from MAVEN are used in this study. Specifically, the magnetic fields are measured by MAVEN’s Magnetometer (MAG; Connerney et al., 2015), the electron measurements are from the Solar Wind Electron Analyzer (SWEA) instrument (Mitchell et al., 2016), and the ion (H⁺, O⁺, and O₂⁺) measurements are from the SupraThermal And Thermal Ion Composition (STATIC) instrument (McFadden et al., 2015). The magnetic field map is produced by using magnetic field data from MAG during the 2015–2020 interval (Langlais et al., 2019). All the data are shown in Mars Solar Orbital (MSO) coordinates unless specified, which is defined with the X-axis pointing from Mars to the Sun, the Y-axis pointing opposite the direction of the Martian orbital velocity component perpendicular to the X-axis, and the Z-axis completing the right-handed system (Trotignon et al., 2006).

The event of interest was observed between 09:18:00 universal time (UT) and 09:21:00 UT on June 4, 2022. An overview of the event is shown in Figures 1a–1f. Specifically, the magnetic field map at an altitude from 332 to 432 km (Figure 1a), the strength and three components of the magnetic field (Figure 1b), the ion mass spectra from STATIC (Figure 1c), the differential energy flux of ions with a mass-to-charge ratio of 12–44 (Figure 1d), pitch-angle distributions of electrons with energy of 10–150 eV (Figure 1e), and electron differential energy flux (Figure 1f) are presented from top to bottom. This magnetic field map was constructed using average measurements of the magnetic field recorded between 2015 and 2020 at altitudes ranging from 332 to 432 km. Figure 1a shows the base-10 logarithm of the average measurements. During this period, MAVEN cruised near the edge (longitude of ~33°W and latitude of ~1°S) of the crustal magnetic fields at an orbital altitude of approximately 383 km (marked by the black arrow in Figure 1a). The detection of heavy ions (O⁺ and O₂⁺) with energies of several tens of electron volts at such a low altitude (Figures 1c and 1d), combined with a solar zenith angle of ~170° (not shown), provide clear evidence that MAVEN has encountered the Martian nightside ionosphere (Zhang MHG et al., 1990; Gurnett et al., 2008; Benna et al., 2015; Girazian et al., 2017). This region exhibits a mixed magnetic topology composed of both closed and open field lines, as indicated by the pitch-angle distributions of electrons with energies of 10–150 eV (Figure 1e). The closed field lines are evidenced before 09:19:38 UT (marked by the right dashed line) by the counter-streaming (field-aligned and antifield-aligned) electrons, whereas the subsequent detection of only field-aligned electrons indicates a shift to open ones (09:19:40–09:20:10 UT; Brain et al., 2007). Across both closed and open field line regions, the magnetic field strength is dictated by variations in the magnitude of the dominant B_x component (Figure 1b). A decrease in the magnitude of the B_x component during the interval from 09:18:41 to 09:19:38 UT resulted in a corresponding weakening of the magnetic field strength (Figure 1b). This structure exhibits the characteristics of a magnetic hole, where the weakening of the magnetic field is caused by a reduction in its dominant component (Huang SY et al., 2017, 2021; Chen ZZ et al., 2024). This weakening magnetic field in the closed field line region was accompanied by a reduction of both perpendicular flux and the electron differential energy flux for 10–150 eV electrons (Figures 1e and 1f), which was most evident where the field was weakest. This reduction of perpendicular flux led to a more pronounced cigar distribution (Figure 1e). This phenomenon indicates the occurrence of betatron cooling.

To further investigate this betatron cooling process, a comparative analysis of electron phase space density (PSD) at the energy between 10 and 150 eV was conducted across the magnetic field weakening region (09:18:41–09:19:38 UT, marked by the blue bar in Figure 1e) and its adjacent region (09:18:05–09:18:30 UT, marked by the red bar in Figure 1e) within the closed field line region. Figure 2 presents a comparison of the PSD as a function of electron energy between the two regions, including the profiles for the omnidirectional (Figure 2a), perpendicular (Figure 2b), and field-aligned and antifield-aligned (Figure 2c) directions relative to the magnetic field. Here, the perpendicular direction refers to the pitch angles within ±37.5° of 90°, whereas the field-aligned and antifield-aligned directions correspond to the pitch angles of 0°–37.5° and 142.5°–180°, respectively. The unidirectional definition for field-aligned and antifield-aligned directions is necessary because of the boundaries at 0° and 180°, unlike the symmetric perpendicular case. The decrease in the omnidirectional PSD within the magnetic field weakening region arises primarily from a reduction of the perpendicular PSD, with no significant change in the field-aligned or antifield-aligned PSD across the two regions. Both inside and outside the magnetic field weakening region, the perpendicular PSD follows a power-law spectrum with a nearly identical spectral index of γ = –3.21, demonstrating a uniform scaling of electron energy across different channels—as expected for betatron cooling (Fillingim et al., 2007; Lillis et al., 2009; Fu HS et al., 2011). In both regions, a power-law spectrum can also be observed in the omnidirectional and field-aligned and antifield-aligned directions, obeying spectral indices of γ = –3.18 and γ = –3.10, respectively.

3　Modeling of Betatron Cooling

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Adiabatic theory states that the magnetic moment

$ \mu =\dfrac{mv_{\bot }^{2}}{2B} $

and longitudinal invariant

$ J=\oint m{v}_{\parallel }\mathrm{d}s $

are conserved in a slowly varying magnetic field whose change within a particle’s gyro-period is negligible. Here,

$ m $

$ {v}_{\bot } $

$ {v}_{\parallel } $

are the particle’s mass, perpendicular velocity, and parallel velocity. Consequently, the particle’s perpendicular energy scales with the magnetic field strength (

$ {E}_{\bot }\propto B $

), whereas its parallel energy is inversely proportional to the square of the bounce path length (

$ {E}_{\parallel }\propto {L}^{-2} $

). Accordingly, a weakening (strengthening) of the magnetic field strength and a lengthening (shortening) of the bounce path length leads to betatron cooling (acceleration) and Fermi cooling (acceleration), reducing (enhancing) the particle’s perpendicular and parallel energy, respectively.

To determine whether the adiabatic condition is satisfied, we compared the spatial scale of this structure with the electrons’ gyro-radii, as well as the time for MAVEN to traverse the structure with the electrons’ gyro-period. Given that the magnetic structure co-rotates with Mars, and because Mars’ rotational speed is smaller by an order of magnitude than MAVEN’s orbital speed, the speed of the spacecraft relative to the structure is primarily dictated by its orbital speed. Therefore, the spatial scale is estimated as the product of MAVEN’s speed and the traversal time. The spatial scale of this structure (

$ {{L}}_{{B}}={{V}}_{{M}}\times {{T}}_{{B}} $

~ 189.24 km) significantly exceeds the gyro-radius (

$ {\rho}_{\text{e}}=\sqrt{\text{2}{{m}}_{\text{e}}{{E}}_{\text{e}}}/{{q}}_{\text{e}}{B} $

~ 7.147 km) for 150 eV electrons. Likewise, the MAVEN traversal time (

$ {{T}}_{{B}} $

~ 57 s) is much longer than the electrons’ gyro-period (

$ {{T}}_{\text{e}}=2\pi {{m}}_{\text{e}}/{{q}}_{\text{e}}{B} $

$6.182 \times {\text{10}}^{-{3}} $

s). This confirms that the adiabatic condition is satisfied. Here,

$ {{V}}_{{M}} $

~ 3.32 km/s,

$ {B} $

~ 5.779 nT,

$ {{m}}_{\text{e}} $

$ {{q}}_{\text{e}} $

, and

$ {{E}}_{\text{e}} $

are MAVEN’s speed, the weakest magnetic field magnitude in this structure, electron mass, elementary charge, and electron energy, respectively.

A model has been established to quantitatively reproduce these adiabatic processes (Fu HS et al., 2013), expressed as

$ {E}_{1\bot }={F}_{b}\cdot {E}_{0\bot },$

(1)

$ {E}_{1\parallel }={F}_{f}\cdot {E}_{0\parallel }, $

(2)

where

$ {F}_{b}={B}_{1}/{B}_{0} $

and

$ {F}_{f}={({L}_{0}/{L}_{1})}^{2} $

are the betatron and Fermi factors, respectively, and the subscripts 0 and 1 refer to the initial state and final state, respectively. According to this adiabatic model along with Liouville’s theorem (Fu HS et al., 2011; Birn et al., 2013), the particle distribution in the final state can be derived from that in the initial state by adjusting the betatron and Fermi factors.

Figure 3 presents the modeling results by treating the electron distribution in the magnetic field weakening region as the final state (marked by the blue bar in Figure 1e) and the electron distribution in its adjacent region as the initial state (marked by the red bar in Figure 1e). The solid curves in Figures 3a and 3b denote the observed pitch-angle distributions (PSDs), time-averaged over the periods 09:18:05–09:18:30 UT and 09:18:41–09:19:38 UT, corresponding respectively to the initial (red) and final (blue) states indicated in Figure 1e. The dashed curves in Figure 3b represent the modeling PSD. The modeling distributions agree well with the observed distributions, where a betatron factor of

$ {F}_{b}=0.82 $

and a Fermi factor of

$ {F}_{f}=1 $

were utilized, roughly consistent with the betatron cooling arising from the magnetic field strength decreasing by a factor of 0.7. The discrepancy of 0.12 between these two parameters indicates that the electron cooling is influenced by nonadiabatic processes alongside the dominant adiabatic process.

4　Conclusions

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Utilizing data from the MAVEN spacecraft in this study, we have presented observations of an electron perpendicular energy decrease predominantly driven by betatron cooling in the Martian ionosphere. The phenomenon was identified within closed magnetic field lines at the edge of the crustal magnetic fields, a region characterized by a convoluted magnetic field topology comprising both closed and open lines. This cooling process was observed in 10–150 eV electrons that exhibit a power-law spectrum. This process resulted in a more pronounced cigar distribution and was quantitatively reproduced by an adiabatic model. Our study may promote the understanding of electron dynamics in the Martian ionosphere.

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doi: 10.26464/epp2026043

Receive Date：2025-12-18
Online Date：2026-06-05
Published：2026-05-01

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Received：2025-12-18
Accepted：2026-03-02

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¹School of Space and Earth Sciences, Beihang University, Beijing 102206, China

²Key Laboratory of Space Environment Monitoring and Information Processing, Ministry of Industry and Information Technology, Beijing 100191, China

³Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650504, China

⁴Planetary Environmental and Astrobiological Research Laboratory (PEARL), School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai 519082, China

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chenzzh@buaa.edu.cn

huishanf@gmail.com

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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Figure 1 Betatron cooling observed in the Martian ionosphere on June 4, 2022. (a) Magnetic field map at an altitude of 332 to 432 km. The black arrowed line in panel (a) denotes MAVEN’s trajectory. (b) Magnetic field B_x, B_y, B_z components and strength (|B|); mso, Mars Solar Orbital coordinates. (c) Ion mass spectra from STATIC. (d) Differential energy flux of ions with a mass-to-charge ratio of 12–44. (e) Pitch-angle (PA) distributions of 10–150 eV electrons. (f) Differential energy flux of electrons (E_e). The arrow in panel (f) denotes the region with the weakest magnetic field. The vertical dashed lines mark the magnetic field weakening region. The blue bar in panel (e) denotes the final state of the betatron cooling, whereas the red bar represents its initial state.

Figure 2 The electron phase space density (ePSD) as a function of electron energy (E_e). (a) The omnidirectional PSD (Omni-ePSD), (b) the perpendicular PSD (Perp ePSD), and (c) the field-aligned and antifield-aligned PSD (Field-aligned ePSD). The blue lines denote the final PSD of the betatron cooling, whereas the red lines represent its initial PSD. The dashed black lines represent the power-law models for fitting electron distributions.

Figure 3 Quantitative analysis of the observed betatron cooling. (a) Phase space density (PSD) versus pitch angles before betatron cooling. (b) PSD versus pitch angles after betatron cooling. The solid curves in panels (a) and (b) denote the observed distributions, whereas the dashed curves in panel (b) represent the modeling distribution.

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