Honeycomb‐Like Magnetosheath Structure Formed by Jets: Three‐Dimensional Global Hybrid Simulations

Magnetosheath jets with enhanced dynamic pressure are common in the Earth's magnetosheath. They can impact the magnetopause, causing deformation of the magnetopause. Here we investigate the 3‐D structure of magnetosheath jets using a realistic‐scale, 3‐D global hybrid simulation. The magnetosheath has an overall honeycomb‐like 3‐D structure, where the magnetosheath jets with increased dynamic pressure surround the regions of decreased dynamic pressure resembling honeycomb cells. The magnetosheath jets downstream of the bow shock region with θBn ≲ 20° (where θBn is the angle between the upstream magnetic field and the shock normal) propagate approximately along the normal direction of the magnetopause, while those downstream of the bow shock region with θBn ≳ 20° propagate almost tangential to the magnetopause. Therefore, some magnetosheath jets formed at the quasi‐parallel shock region can propagate to the magnetosheath downstream of the quasi‐perpendicular shock region.


Introduction
The interaction between the super-magnetosonic solar wind and the Earth's magnetic field forms the magnetosphere whose outer boundary is the magnetopause.The magnetosheath is located between the magnetopause and the bow shock that decelerates the solar wind from super-magnetosonic to sub-magnetosonic (Fairfield, 1971;Peredo et al., 1995).According to the angle (θ Bn ) between the shock normal direction and the interplanetary magnetic field (IMF), the bow shock is categorized into quasi-perpendicular (θ Bn ≳ 45°) and quasi-parallel (θ Bn ≲ 45°).Solar wind particles reflected by the quasi-parallel shock can travel far upstream along the magnetic field lines, generating ion beam instabilities to excite ultra-low-frequency (ULF) waves (Hao et al., 2021;Lembege et al., 2004;Lu et al., 2020;Omidi, 2007;Quest, 1988;Su et al., 2012;Wu et al., 2015).These waves are carried to the magnetosheath by the solar wind and cause turbulence therein.
Magnetosheath jets, also known as high-speed jets, were first reported by Němeček et al. (1998) at Earth and are frequently observed in the magnetosheath downstream of the quasi-parallel shock (Archer et al., 2012;Plaschke et al., 2013).Within the magnetosheath jets, dynamic pressure increases and ion velocity often exceeds the local Alfvén speed, while the plasma temperature is lower and more isotropic than the surroundings (Archer & Horbury, 2013;Plaschke et al., 2013).It is well known that the magnetosheath jets can be formed by the interaction between the upstream waves and the quasi-parallel bow shock (Hietala et al., 2009;Palmroth et al., 2018;Raptis et al., 2022;Ren et al., 2023;Suni et al., 2021).The magnetosheath jets can drive bow waves inside the magnetosheath (Hietala et al., 2009;Liu et al., 2019;Ren et al., 2024), and impact the magnetopause to trigger localized magnetopause indentation (Shue et al., 2009;Yang et al., 2024), reconnection (Hietala et al., 2018), and magnetopause surface waves (Archer et al., 2019).The magnetosheath jets are more likely to reach the magnetopause when the IMF is quasi-radial (LaMoury et al., 2021).Guo et al. (2022) suggested that the alignment between the IMF and the solar wind velocity favors the formation of large magnetosheath jets.Further, Ren et al. (2023) found that the large magnetosheath jets form when upstream compressive structures continuously interact with the bow shock at specific regions.These large magnetosheath jets transport more mass and energy from the solar wind and thus have a more significant influence on the Earth's magnetosphere (Plaschke et al., 2016).
To statistically analyze the scale sizes of magnetosheath jets, Plaschke et al. (2020) assumed the magnetosheath jets to be cylinder-like, whose axial directions are parallel to the propagation directions.They suggested that the magnetosheath jets have median scale sizes of 0.12 R E and 0.15 R E in the parallel and perpendicular directions, respectively.Using multi-spacecraft observations, Karlsson et al. (2012) found that the plasmoids, which are related structures to the magnetosheath jets, have pancake-like structures ("flattened flux tubes") with one dimension shorter than the others.Omelchenko et al. (2021) also demonstrated pancake-like jets using threedimensional (3-D) global hybrid simulations, where the jets have three characteristic sizes: 4 R E in the parallel direction, 6 R E in the dawn-dusk direction, and 0.6 R E in the north-south direction.However, their simulations reduce the scale of the Earth's magnetosphere, which may lead to unrealistic results.
In this study, we conducted a realistic-scale, 3-D global hybrid simulation to demonstrate that the magnetosheath has a honeycomb-like 3-D structure where jets with increased dynamic pressure surround magnetosheath cavities with decreased dynamic pressure (Guo et al., 2022;Katırcıoğlu et al., 2009;Omidi et al., 2016).Our results also indicate that the magnetosheath jets formed downstream of the quasi-parallel shock can propagate to the magnetosheath downstream of the quasi-perpendicular shock, which may be a source of jets downstream of the quasiperpendicular shock.

Simulation Model
This study utilizes a three-dimensional global hybrid simulation model (Lin & Wang, 2005).In hybrid simulations, ions are treated as particles while electrons are treated as a massless, charge-neutralizing fluid.The displacement current is neglected, the electric field is solved through Ohm's law, and the magnetic field is advanced by Faraday's law.The simulation is performed in a spherical coordinate system (r, θ, φ), encompassing a simulation domain of the geocentric distance 3 R E ≤ r ≤ 30 R E , polar angle 10°≤ θ ≤ 190°, and azimuth angle 20°≤ φ ≤ 160°.The simulation grid consists of N r × N θ × N φ = 720 × 420 × 540 cells.Within the inner magnetosphere (r ≤ 6.5 R E ), a cold, incompressible ion fluid is filled to represent the plasmasphere.
Grid spacing in the r direction is nonuniform, with Δr ≃ 0.02R E within 8 R E ≤ r ≤ 14 R E and being larger elsewhere.This setup keeps high resolution in the magnetosheath region while reducing the computational costs.Outflow (open) boundary conditions are applied to all boundaries for particles (fields), except for a conductive field boundary at the inner boundary (r = 3 R E ) and the injection of solar wind particles at the outer boundary (r = 30 R E ).The simulation results are presented in geocentric solar-magnetospheric (GSM) coordinates, with the x-axis points from the Earth's center to the Sun, the z-axis aligned with the Earth's dipole axis, and the y-axis completing the right-handed coordinates system.The simulation time step is Δt = 0.02 Ω 1 i , where the ion gyrofrequency Ω 1 i is determined by the solar wind magnetic field.The initial state involves about 8 × 10 9 macroparticles, and a small, current-dependent collision frequency is used to simulate anomalous resistivity and trigger magnetic reconnection.In the solar wind, the plasma number density is N i = 3.2 cm 3 , and the magnetic field is B = (3.72,0.13, 0.21) nT.The plasma beta values for ions and electrons are β i = β e = 0.22, and the solar wind velocity is V SW = ( 466.48, 12.86, 14.31) km/s.The Alfvén Mach number is therefore M A = 12.27.In our simulation, for the first time, a realistic magnetosphere scale is used, where 1 R E = 50 d i0 , with d i0 representing the ion inertial length in the solar wind.Additionally, to study the effect of reducing magnetosphere scale on the 3-D structure of magnetosheath jets, another simulation is also performed with a reduced scale where 1 R E = 10 d i0 (5 times smaller than reality), while other parameters are kept identical to those of the realistic-scale case described above.Because the Alfvén speed, which measures the evolution speed of kinetic effects, is larger relative to the magnetosphere scale size in the reduced-scale case, the magnetosphere evolves faster than in the realistic-scale case.For a direct comparison of the two cases, the simulation time in the reduced-scale case is presented 5 times larger.

Simulation Results
An overview of the realistic-scale case under a radial IMF is shown in Figure 1.The bow shock results from the interaction between the solar wind and the geomagnetic field, with the magnetosheath situated downstream of the bow shock.The bow shock is quasi-parallel and rippled around the subsolar region while being quasi-perpendicular around the flank region.Downstream of both quasi-parallel and quasi-perpendicular bow shock, many magnetosheath jets with high dynamic pressure are observed, and some of them impact and dent the magnetopause.In Figure 1b, elliptical magnetosheath cavities with low dynamic pressure are surrounded by magnetosheath jets, illustrating an overall honeycomb-like 3-D structure in the magnetosheath, where the cavities and jets resemble honeycomb cells and their edges.Once the jets form downstream of the quasi-parallel shock, they propagate toward the flank region along the magnetosheath plasma flow.
The magnetosheath jets downstream of the bow shock with θ Bn < 20°are shown in Figure 2. Figures 2b-2e plot the dynamic pressure and ion temperature of one magnetosheath jet ("J1") at t = 671.5 s in two perpendicular slices (pink and cyan slices in Figure 2a).Inside "J1," the ion temperature is decreased and is more isotropic than the surroundings, because the plasma from the solar wind is less heated by the bow shock in the magnetosheath jets.The parallel scale size of "J1" is about 3 R E , and its perpendicular scale sizes are about 3 R E and 0.4 R E in the pink and cyan slices, respectively.This indicates a pancake-like localized structure for "J1," formed by being the edge of two magnetosheath cavities (Figure 1b).Additionally, some magnetosheath jets are located at the vertices of multiple magnetosheath cavities, whose localized 3-D structures are approximately cylinder-like (Figure 1b)."J1" impacts the magnetopause along the normal direction of the magnetopause, causing a localized magnetopause indentation.The magnetopause is dented more severely as "J1" continuously compresses the magnetopause in later times and expands back beyond its original location (not shown), as suggested by Němeček et al. (2023).Moreover, "J1" is meandering in the cyan slice (Figures 2c and 2e), which may be caused by Kelvin-Helmholtz instability (Guo et al., 2022).
Figure 3 shows magnetosheath jets downstream of the bow shock with 20°< θ Bn < 45°.The magnetosheath jet "J2" forms at the bow shock where θ Bn is about 20°, and propagates toward the flank region along the background plasma flow.Similar to "J1," the ion temperature inside "J2" also decreases (Figures 3d and 3e).The parallel scale size of "J2" is about 9 R E and its perpendicular scale sizes are about 2.8 R E and 1 R E , indicating a ribbon-like localized 3-D structure.Within the honeycomb-like magnetosheath structure, the jets in the realistic-scale simulation can have different localized structures than just a cylinder or pancake shape suggested by previous studies (Omelchenko et al., 2021;Plaschke et al., 2016Plaschke et al., , 2018))."J2" propagates almost tangential to the magnetopause, and there is almost no inward pressure to the magnetopause in "J2" (Figure 3f).Therefore, no obvious magnetopause indentation is caused.Magnetosheath jets like "J2" that form downstream of the bow shock with larger θ Bn (>20°in our simulation) may have minor effects on the magnetopause.Some magnetosheath jets can propagate long distances, even enter the magnetosheath downstream of the quasiperpendicular bow shock.Figure 4 shows some magnetosheath jets downstream of the bow shock with θ Bn > 45°.Magnetosheath jets "J3"-"J5" are identified by dynamic pressure exceeding 1.5 times the magnetosheath background value."J3"-"J5" also have ribbon-like localized structures and decreased temperature (Figures 4f-4i), but are weaker than those downstream of the quasi-parallel bow shock.At t = 559.6 s (Figures 4b and 4f), "J3" is located in the magnetosheath downstream of the quasi-parallel bow shock."J3" then propagates along the magnetosheath plasma flow (Figures 4c and 4d) and enters the downstream magnetosheath of the quasiperpendicular bow shock.At t = 559.6 s (Figure 4b), magnetosheath jets "J4" and "J5" are formed at the bow shock where θ Bn is about 45°."J4" and "J5" also propagate long distances (about 10 R E and 5 R E , respectively) in the magnetosheath and have entered the magnetosheath downstream of quasi-perpendicular bow shock at t = 671.5 s.

Discussion
Although magnetosheath jets have been studied for over a decade, their 3-D structure has always been under debate (Karlsson et al., 2012;Omelchenko et al., 2021;Plaschke et al., 2016).By performing a 3-D global hybrid simulation with realistic scale, we find that magnetosheath jets and cavities form an overall honeycomb-like 3-D magnetosheath structure, while the localized 3-D structure of the jets can be pancake-like, cylinder-like, ribbonlike, etc.To demonstrate the significance of the realistic scaling, a reduced-scale simulation with 1 R E = 10 d i0 is also performed for comparison.Figure 5 shows the magnetosheath jets in the reduced-scale case at t = 840.2s.There are only 3 jets-surrounded magnetosheath cavities in this case (Figure 5a), while there are about 16 in the realistic-scale case (Figure 1b).The maximum diameters of the magnetosheath cavities are about 8 R E and 3 R E in this reduced-scale case and the realistic-scale one, respectively.Moreover, in Figures 5b-5e, the parallel size of "J1′" is about 4 R E , with perpendicular sizes of about 5.2 R E and 0.8 R E .Therefore, in the reduced-scale case, like   the ones performed by Omelchenko et al. (2021), the numbers of magnetosheath jets and cavities are underestimated, while their scale sizes are overestimated.
The small and numerous jets in the realistic-scale case can increase turbulence in the magnetosheath and lead to more magnetopause indentations.Moreover, jets with ribbon-like localized structures downstream of the bow shock with θ Bn ≳ 20°are difficult to identify in the reduced-scale case.Only in the realistic-scale case do we find jets formed downstream of the quasi-parallel shock propagate downstream of the quasi-perpendicular shock.Therefore, global simulations with a reduced-scale magnetosphere may not effectively capture physical processes related to the bow shock.The scale sizes of many foreshock structures, such as spontaneous hot flow anomalies (Omidi et al., 2013;Zhang et al., 2013), magnetosheath cavities (Guo et al., 2022;Katırcıoğlu et al., 2009;Omidi et al., 2016), and foreshock bubbles (C.Wang et al., 2021;B. Wang et al., 2020), may be related to the scale size of the magnetosphere.Using a 3-D global hybrid simulation with a reduced-scale magnetosphere (1 R E = 12 d i0 ), Ng et al. (2023) showed that kinetic structures like foreshock cavitons can be seen through soft X-ray imaging.However, it is possible that the scale size of the foreshock cavitons was overestimated in their simulation results.

Conclusions
In this study, we investigate the 3-D structure of magnetosheath jets using a realistic-scale, 3-D global hybrid simulation.The magnetosheath has an overall honeycomb-like 3-D structure, where the magnetosheath jets surround magnetosheath cavities like honeycomb cells.The magnetosheath jets downstream of the bow shock with θ Bn ≲ 20°propagate approximately along the normal direction of the magnetopause, while those downstream of the bow shock with θ Bn ≳ 20°propagate almost tangential to the magnetopause.Moreover, some magnetosheath jets formed downstream of quasi-parallel shock can propagate to the magnetosheath downstream of the quasi-perpendicular shock and become a source of jets therein, which is shown in the realistic-scale simulation but not in the reduced-scale one.Our results highlight the necessity of realistic-scale simulation models to study the structures related to the bow shock.

Figure 1 .
Figure 1.Overview of the honeycomb-like magnetosheath structure driven by jets at t = 671.5 s.(a) Dynamic pressure P d in the noon-midnight meridian plane.The gray surface is the magnetopause identified by the boundary of open/closed magnetic field lines.The pink contour indicates where the dynamic pressure is two times the background value in the magnetosheath, as defined in Archer and Horbury (2013).(b) Dynamic pressure in the magnetosheath.The white and red curves indicate the bow shock with θ Bn = 20°and 45°, respectively.

Figure 2 .
Figure 2. Magnetosheath jets downstream of the bow shock with θ Bn < 20°at t = 671.5 s (a) 3-D view of the dynamic pressure P d of the jets.The white and red curves indicate the bow shock with θ Bn = 20°and 45°, respectively.The original point of both the pink and cyan slices is (12.8, 0.77, 2.07) R E , while their normal directions are ( 0.07, 0.697, 0.713) and (0.153, 0.715, 0.683), respectively.(b-c) Dynamic pressure P d in the pink slice (b) and cyan slice (c).(d-e) Ion temperature T i in the pink (d) and cyan (e) slices.The solid white curves indicate the magnetopause, and the dashed white curves indicate the bow shock.

Figure 3 .
Figure 3. Magnetosheath jets downstream of the bow shock with 20°< θ Bn < 45°at t = 671.5 s (a) 3-D view of the jets.The original point of both the pink and cyan slices is (10.6, 6.05, 4.56) R E , while their normal directions are (0.050, 0.656, 0.753) and (0.580, 0.594, 0.557), respectively.(b-c) Dynamic pressure P d , (d-e) ion temperature T i , (f-g) r component of the dynamic pressure P d,r .The variables are taken from the pink (b, d, f) and cyan (c, e, g) slices.The solid white curves indicate the magnetopause, and the dashed white curves indicate the bow shock.

Figure 4 .
Figure 4. Magnetosheath jets downstream of the bow shock with θ Bn > 45°.(a) 3-D view of the jets at t = 671.5 s.The original point of the pink slice is (4.85, 6.09, 12.6) R E , and its normal direction is ( 0.143, 0.911, 0.386).(b-e) Dynamic pressure P d in the pink slice t = 559.6 s, 615.5 s, 643.5 s, and 671.5 s (f-i) Ion temperature T i in the pink slice at the same times.The solid white curves indicate the magnetopause, and the dashed white curves indicate the bow shock.

Figure 5 .
Figure 5. Magnetosheath jets at t = 840.2s obtained from the reduced-scale case where 1 R E = 10 d i0 .(a) Dynamic pressure P d in the magnetosheath.The white and red curves indicate the bow shock with θ Bn = 20°and 45°, respectively.(b-c) Dynamic pressure in the equatorial plane (b) and noon-midnight meridian plane (e).The solid white curves indicate the magnetopause, and the dashed white curves indicate the bow