© The Authors 2026

1 Introduction

Unlike Earth, Venus does not have a substantial intrinsic magnetic field; however, it is also enveloped by a dense atmosphere (O’Rourke et al. 2019; Phillips & Russell 1987). The ionosphere of Venus, formed through photoionization of its upper atmosphere by solar extreme ultraviolet (EUV) radiation, serves as the primary obstacle to the supermagnetosonic solar wind. The interaction between the solar wind and the highly conductive ionosphere generates electric currents that give rise to an induced magnetosphere. This induced magnetosphere comprises a bow shock (BS), a magnetosheath (MS) filled with shocked solar wind plasma ions, a magnetic barrier resulting from the accumulation and draping of the interplanetary magnetic field (IMF), and an ionosphere that may be magnetized or unmagnetized depending on prevailing solar conditions (Futaana et al. 2017; Luhmann & Cravens 1991). The induced magnetic field provides some magnetic shielding, but it is insufficient to prevent solar wind from having direct access to the Venusian upper ionosphere. As a result, ionospheric ions are scavenged from the dayside, transported across the terminator plane, and carried into the nightside or the induced magnetotail region.

Although Venus induced magnetosphere and ionosphere act as barriers against the solar wind’s momentum and energy, many aspects of its magnetospheric dynamics and planetary ion transport processes remain complex and poorly understood (Xu et al. 2024). Ionospheric ions, as well as neutral atoms ionized by EUV radiation, charge exchange, and electron impact, gain momentum and energy from the solar wind. When the ion generation processes are driven by solar wind, charged particles are primarily accelerated by electric fields, which include the motional electric field, the component associated with the plasma pressure gradient, and the Hall electric field term (Dubinin et al. 2011). In different regions of the Venusian plasma environments, distinct components of the electric field dominate, leading to region-specific characteristics of ion acceleration (Dubinin et al. 2011). The classical pick-up process describes the acceleration of freshly ionized particles under the influence of the motional electric field. However, in regions closer to the planets, where the ion population is denser and more massive, the interaction must be treated self-consistently, thus incorporating the mutual momentum and energy exchange between the solar wind and the planetary plasma (Dubinin & Sauer 1999). As a result of this coupling, the electron fluid decelerates to maintain charge neutrality when dense planetary ions remain nearly stationary. This deceleration leads to a reduction in the motional electric field. Meanwhile, newly ionized particles originating near the source region begin to accelerate. The arising Lorentz force decelerates the streaming protons, enabling momentum transfer to the heavier planetary ions. This momentum exchange is a fundamental aspect of ion dynamics in multi-ion plasmas. For a more spatially extended source region, the heavy ion motion gradually transitions from a modified form of classical pick-up behavior to a comet-like outflow (Dubinin et al. 2011, 1998).

Observations further reveal that the ionospheric plasma at altitudes above approximately 300 km is not stationary, but exhibits a clear tailward motion. This horizontal transport of ionospheric plasma from the dayside toward the terminator and into the nightside tail region is supported by measurements of electron number density altitude profiles (Duru et al. 2008). This motion may result from multiple processes, including (a) polar wind–like escape, (b) trans-terminator ionospheric flow driven by the day-to-night asymmetry in thermal pressure (Knudsen et al. 1980), (c) comet-like tailward expansion under the influence of magnetic tension forces, and (d) wave-driven acceleration mechanisms. All of these mechanisms probably contribute to the bulk ion motion in the top-side ionosphere (Lundin 2011). On the other hand, measurements of the night-side ionosphere revealed unexpectedly high ion densities (Group 1967). Since ionization by solar EUV radiation is not possible on the nightside, and the short ion lifetimes preclude significant accumulation via atmospheric super rotation alone (which occurs on a four-day timescale), this plasma population cannot be explained solely by neutral winds (Group 1967; Persson et al. 2019). Instead, day-to-night transport of ionospheric plasma is likely to play a key role. The Pioneer Venus Orbiter (PVO) provided extensive observations of the Venusian ionosphere. One of its key findings was a substantial horizontal ion flow across the terminator, from the dayside to the nightside, with a mean velocity of 2–3 km s⁻¹. This flow speed was observed to increase with altitude. The ion flux plays a crucial role in sustaining the night-side ionosphere and contributes to its heating (Knudsen et al. 1981).

Orbiter Retarding Potential Analyzer measurements showed that there is an asymmetry between the dawn and dusk region both in the ion density and flow (Knudsen et al. 1980). The observed asymmetry was once interpreted as resulting from a retrograde super rotation (∼400 m s⁻¹) of the upper atmosphere and ionosphere (Miller et al. 1984). Nevertheless, subsequent measurements have demonstrated that the ionospheric flow is in fact prograde at higher altitudes, thereby contradicting the earlier hypothesis (Miller & Knudsen 1987). This inconsistency prompted a shift in focus from atmospheric dynamics to electromagnetic processes as a more plausible driver of ion behavior. In particular, the motion of ions in the Venusian ionosphere is now understood to be strongly influenced by the configuration of magnetic fields. The ionosphere can exist in either a magnetized or unmagnetized state (Angsmann et al. 2011; Russell & Vaisberg 1983). Zhang et al. (2008b) reported that the Venusian ionosphere remains magnetized approximately 95% of the time during solar minimum, but only about 15% during solar maximum. They also found that even during solar minimum, the ionosphere can become unmagnetized when the ionopause altitude is exceptionally high. The magnetization state of the Venusian ionosphere is primarily governed by the pressure balance between the total pressure of the magnetic barrier and the ionospheric plasma pressure. When the magnetic barrier is sufficiently strong, it can depress the ionopause to lower altitudes where collisional processes become significant, thereby magnetizing the ionosphere (Chang et al. 2020).

Since the solar wind interacts directly with the Venusian atmosphere, the entire induced magnetosphere, including the magnetic barrier, is strongly influenced by the IMF. Regarding the large-scale structure of the IMF which extends throughout the solar system, the oldest theoretical work by Parker has been widely accepted (Schatten 1971). Parker derived a model in which the IMF is illustrated as an ideal Archimedes’ spiral in spherical coordinates (Parker 1958). The spiral angle of the IMF is defined as (Chang et al. 2019; Narita et al. 2004; Rubtsov et al. 2023): $$\varphi =\arctan \left(-\frac{B_y}{B_x}\right)$$(1)

in which the X component is sunward and the Y component points to the opposite direction of the planetary motion. The ideal spiral model has been verified and reinforced by analyzing data from Helios, MESSENGER, and Ulysses, for example (Chang et al. 2019). Chang et al. (2019) statistically calculated the distributions of the Parker angle at Venus in Solar Cycle 24. During this time, the IMF angles varied from about –46° to 144°. Chang et al. (2020) discovered that the magnetic barrier becomes weak under a nearly flow-aligned IMF condition. Zhang et al. (2009) indicated that when the IMF is nearly parallel to the Venus–Sun line, the magnetic barrier appears to vanish.

Despite increasing attention to the dawn–dusk asymmetry of ion flow in the Venusian ionosphere, the underlying physical mechanisms remain incompletely understood. In particular, the role of the IMF orientation in shaping dayside ion transport has not been fully explored. Given that the IMF governs the configuration of magnetic pileup and electric fields in the induced magnetosphere, we hypothesize that variations in its orientation can lead to differences in the electromagnetic forces acting on planetary ions. For this study, our aim was to investigate how different IMF orientations influence the dayside ion transport, with a particular focus on the dawn–dusk asymmetry acceleration and the resultant planetary ion flux change. Through multi-fluid simulations, we provide new insights into the magnetospheric control of ion dynamics at Venus and offer a potential explanation for the observed asymmetric plasma escape pathways.

2 Model description

The multi-fluid magnetohydrodynamic (MF-MHD) model employed in this study solves the Navier–Stokes (NS) equations for the dominant ion species in the Venusian ionosphere. These equations govern the conservation of mass, momentum, and energy for each ion fluid, and are modified to incorporate electromagnetic forces. The resulting set of equations captures the coupled plasma dynamics under the influence of the solar wind and IMF, and can be expressed as follows (Najib et al. 2011): $$\frac{\partial {\rho }_s}{\partial t}+\nabla \cdot \left({\rho }_s{u}_s\right)=\frac{\partial {\rho }_s}{\partial t},$$(2) $$\begin{array}{l}\frac{\partial ({\rho }_s{u}_s)}{\partial t}+\nabla \cdot ({\rho }_s{u}_s{u}_s+I{p}_s)\hfill \\ =n_s{q}_s(u_s-u_{+})\times B+\frac{n_s{q}_s}{n_{e}e}(J\times B-\nabla p_e)+\frac{\partial M_s}{\partial t},\hfill \end{array}$$(3) $$\begin{array}{l}\frac{\partial e_s}{\partial t}+\nabla \cdot \left[(e_s+p_s)u_s\right]\hfill \\ =u_s\cdot \left[n_s{q}_s(u_s-u_{+})\times B+\frac{n_s{q}_s}{n_{e}e}(J\times B-\nabla p_e)\right]+\frac{\partial E_s}{\partial t}.\hfill \end{array}$$(4)

Here, s denotes the ion species H⁺, ${\text{O}}_2^{+}$, O⁺, and ${\text{CO}}_2^{+}$, which represent the main planetary heavy ions considered in the model. The variables ρ_s, u_s, p_s, m_s, T_s, and q_s correspond to the mass density, velocity, pressure, mass, temperature, and charge of species s, respectively. The total energy density is given by $e_s=\frac{1}{2}{\rho }_s{u}_s^2+\frac{p_s}{\gamma -1}$, where γ = 5/3 is the ratio of specific heats. The charge-averaged ion velocity u₊ is defined as $\frac{1}{e{n}_e}{\displaystyle {\sum }_{s\in \text{ions}}{n}_s{q}_s{u}_s}$. Electromagnetic effects are incorporated into the momentum equation through inclusion of the Hall electric field, ambipolar electric field, and a relative motional electric field. The identity matrix is denoted by I, and all other symbols follow their conventional definitions. The source terms on the right-hand side of Equations (2)–(4), $\frac{\delta {\rho }_s}{\delta t}$, $\frac{\delta M_s}{\delta t}$, and $\frac{\delta E_s}{\delta t}$, represent the changes in mass, momentum, and energy of each ion fluid due to physical collisions and chemical reactions among all species (Chen et al. 2025). By incorporating a prescribed neutral density profile and accounting for the solar EUV flux and optical depth, these terms enable a self-consistent evolution of the Venusian ionosphere within the Hall-MHD framework.

The transport of these produced ions is influenced by the electromagnetic environment of Venus. Within a multi-fluid framework, the electric field: $$E=-u_{+}\times B+\frac{J\times B}{e{n}_e}-\frac{\nabla p_e}{e{n}_e}$$(5)

is derived from the generalized Ohm’s law, which incorporates charge separation effects. In the present multi-fluid MHD model, the electron fluid is not treated with a separate momentum equation. The electron number density (n_e = Σ_i=ions n_i) is determined from the quasi-neutrality condition as the sum of the ion charge densities. To close the system, it is assumed that the electron pressure (p_e = Σ_i=ions p_i) is equal to the total ion thermal pressure, allowing the electron pressure gradient to be consistently included in the generalized Ohm’s law.

When this form of Ohm’s law is substituted into Faraday’s law of induction, the resulting magnetic induction equation includes both the Hall effect and the electron pressure gradient terms, and can be written as follows (Li et al. 2023): $$\frac{\partial B}{\partial t}-\nabla \times \left(u_{+}\times B-\frac{J\times B}{e{n}_e}+\frac{\nabla p_e}{e{n}_e}\right)=0.$$(6)

The simulation was conducted in the Venus Solar Orbital (VSO) coordinate system to facilitate the interpretation of the following results. In this Venus-centered system, the X-axis points toward the Sun, the Y-axis is directed opposite to Venus’ orbital motion, and the Z-axis completes the right-handed orthogonal system, perpendicular to the orbital plane. The computational domain spans from −24 R_V to 8 R_V in the X direction, and from −16 R_V to −16 R_V in both Y and Z directions, where R_V is the radius of Venus (6052 km). A spherical grid structure was employed, comprising 56 blocks and a total of 100 × 120 × 80 = 9 600 000 computational cells. The finest resolution, located at the innermost boundary, reaches 10 km in the radial direction, with the grid size increasing nonlinearly toward the outer boundary. The inner boundary was set at an altitude of 120 km above the Venusian surface, where ion densities were initialized using photochemical equilibrium values.

Regarding the model inputs, we consider two dominant neutral species, CO₂ and O, to represent the Venusian atmosphere. Their density profiles for solar maximum period of Solar Cycle 21 are adopted from Fox & Sung (2001). A uniform neutral atmosphere is assumed regardless of variations in the solar zenith angle (SZA). These neutral density profiles are presented in Chen et al. (2025). The EUV flux variation is incorporated by adjusting the photoionization production rates of neutral species. In our cases, the EUV flux data is based on observations from Viking 1 and 2. The EUV flux at Venus was estimated using the inverse square law, where the ratio of EUV flux between Venus and Earth is given by $(d_1^2/d_2^2)$, with d₁ representing the Sun-Earth distance and d₂ the Sun-Venus distance (Singh et al. 1983; Torr et al. 1979). The Chapman profile can be applied in Venusian ionosphere modeling process due to the photochemical-dominated nature of the dayside ionosphere (Withers 2009). The background neutral atmosphere and ion production rates corresponding to solar maximum conditions were adopted and held constant across simulations with different IMF angles. Based on solar wind parameters upstream of Venus during Solar Cycle 21, the upstream solar wind density and velocity were fixed at 17 cm⁻³ and 400 km s⁻¹, respectively, directed antiparallel to the +X axis (Luhmann et al. 1993). An IMF magnitude of 14.96 nT was chosen to represent average solar maximum conditions, under which the boundaries of the induced magnetosphere and ionosphere tend to be more clearly defined than during solar minimum (Russell et al. 2006).

To investigate the influence of the IMF directions on the asymmetric ion transport in the Venusian dayside induced magnetosphere, we designed a series of simulation cases with IMF angles ranging from 15° to 90° (see Table 1). The IMF is prescribed to lie entirely in the orbital plane, and was rotated within this plane by an angle relative to the +X_VSO direction. The 36° case corresponds to the nominal Parker spiral angle at Venus and represents a typical scenario during Solar Cycle 21. The 90° case was selected to illustrate a configuration in which the IMF is perpendicular to the solar wind flow. Initially, we also considered a nearly parallel IMF orientation (e.g., 5°). However, at such a small angle, the IMF B_Y component becomes too weak, resulting in an unrealistically low magnetic field strength in Venus’ induced magnetosphere and complicating subsequent analysis. After several trials, 15° was chosen instead, providing a more suitable configuration while still capturing the characteristics of a near-parallel IMF. In this study, we define the dawnside and duskside based on the nominal Parker spiral orientation of the IMF at Venus, where the IMF points into the dawnside hemisphere (Y > 0 in the VSO coordinate system). For IMF angles greater than 90°, the configuration would be the mirror -symmetric to those with angles less than 90°, and therefore do not provide independent information. In all simulations, the IMF B_Z component was set to zero. This setup ensures that the solar wind convection electric field points strictly in the Z direction in the VSO coordinate system, so that any variations appearing in the X − Y plane can be attributed solely to the IMF orientation rather than to the direction of the convection electric field.

Fig. 1 (a1–b3) Contours of magnetic field strength (B) and magnetic pressure (PB) for Cases 1–3 in the XY plane. The color scale represents the magnitude of the magnetic field and magnetic pressure. The black dashed lines denote the average position of BS fixed by R = 2/14/[1 + 0/62 × cos(SZA)]. The white dashed lines represent the simulated BS, determined by identifying the peak radial gradient of the upstream solar wind velocity along the X direction. The black arrows show the direction of the magnetic field projected in the XY plane. The complete list of IMF components are given in Table 1.

3 Simulation result

3.1 The magnetic distribution

Figs. 1a1–a3 and b1–b3 separately present the magnetic field strength (B) and magnetic pressure ($P_B=\frac{B^2}{2{\mu }_0}$) for Cases 1– 3 in the equatorial (X–Y) plane. The color scale indicates the magnitude of B and P_B. The black arrows show the direction of the magnetic field projected in the XY plane. The magnetic field distribution in the three cases is consistent with the IMF draping patterns predicted by Masunaga et al. (2011). As the IMF interacts with the ionosphere, the magnetic field is enhanced and accumulated around the planetary obstacle. Xiao & Zhang (2018) reported that the magnetic field strength in the Venusian magnetic barrier detected by VEX can exceed five times the upstream IMF magnitude. And with PVO observation, Luhmann et al. (1987) observed that the field intensities can exceed 100 nT. The black dashed lines indicate the average BS location, given by R = 2/14/[1+0/62×cos(SZA)], taken directly from Zhang et al. (1990). Since the upstream solar wind flows primarily along the −X direction, the BS location in the simulation was determined by calculating the gradient of the H⁺ velocity along multiple lines parallel to the X-axis in the XY plane. For each line, the position corresponding to the maximum velocity gradient was identified, as the BS is characterized by a sharp deceleration of the solar wind. By connecting these peak gradient points across all lines, the simulated BS profile was constructed and depicted in white lines, following the approach of Fang et al. (2015) and Wang et al. (2021). In Fig. 1a2, the simulated BS for the Y > 0 part of the 36° IMF angle case shows good agreement with the observed average BS in the plane. Both Figs. 1a1 and a2 reveal a clear dawn–dusk asymmetry along the BS, which is positioned farther from Venus on the dawnside (+Y) compared to the duskside (−Y). This asymmetrical feature has been reported by simulations and observations (Ma et al. 2013; Zhang et al. 1991; Signoles et al. 2023). And the asymmetries are attributed to the mass loading due to the ion pickup process (Signoles et al. 2023; Xu et al. 2022). Fig. 1a3 exhibits a close agreement with the observed average BS location due to the disappearance of this asymmetry.

As the magnetic field piles up at the dayside ionopause, the resulting P_B reflects the electromagnetic forces that shape the structure and asymmetry of the BS. Across the BS, the solar wind plasma kinetic energy is converted into plasma thermal energy and magnetic energy, resulting in a marked increase in magnetic pressure, which typically peaks near the ionopause (Ma et al. 2013). In Fig. 1b1, corresponding to the IMF angle of 15°, the P_B distribution is highly asymmetric, with significantly higher values on the +Y (dawn) side, indicating strong magnetic field pileup. In contrast, the duskside (−Y direction) exhibits a weaker pressure distribution, reflecting an asymmetric interaction between the IMF and Venus’ induced magnetosphere. In Fig. 1b2, at 36°, the asymmetry remains pronounced. In Fig. 1b3, the P_B distribution becomes nearly symmetric about the X-axis, indicating a highly symmetric magnetic pressure distribution.

To further examine the global structure and asymmetry of the B and P_B on the dayside, we investigated their spatial distribution at an altitude of 350 km for S ZA < 90°. The altitude of 350 km was selected because the maximum P_B, indicative of the strongest magnetic field accumulation region, consistently occurs near this altitude at the dayside hemisphere (S ZA < 90°). The results are shown in a Mollweide projection, which provides an equal-area global view ideal for comparing field structures across dawn and dusk hemispheres and different IMF orientations. Figs. 2a1–a3 and b1–b3 show the spatial distributions of B and P_B respectively, using VSO coordinates. The white dashed lines indicate the 0° meridian and the equator, whose intersection corresponds to the subsolar point in the projection. Gray dashed lines represent meridians spaced at 10° intervals and parallels at 15° intervals. In this projection, longitudes increase from the subsolar point toward the duskside (up to 90°W) and toward the dawnside (up to 90°E). Only the dayside hemisphere of Venus, from 90°E to 90°W longitude, is shown in the maps. The black arrows show the direction of the magnetic field projected in the plane. For the cases with IMF angles of 15° and 36°, both B and P_B exhibit a clear dawn–dusk asymmetry, with significantly stronger values concentrated on the dawnside than on the dusk-side, again reflecting in the spatial distribution of color bands, as areas with comparable magnitudes occupy a larger portion of the dawnside. The asymmetry reflects the uneven pileup of the IMF as it interacts with the Venusian ionosphere. In contrast, for the 90° case, the distributions of both B and P_B become nearly symmetric between the dawn and dusksides, indicating a more uniform interaction of the IMF with the ionosphere under perpendicular IMF conditions.

To better understand the spatial structure and directional characteristics of the magnetic field around Venus, we decomposed the magnetic field into three orthogonal components as shown in Fig. 3: (a1–a3) east–west (longitudinal), (b1– b3) north-south (latitudinal), and (c1–c3) radial directions. The longitudinal component (B_lon) has positive values pointing eastward, toward 90° E longitude, and negative values pointing westward, toward 90° W longitude. The latitudinal component (B_lat) is positive pointing northward, toward the north pole, and negative pointing southward, toward the south pole. The radial component (B_r) is positive when indicating an outward field, away from Venus, and negative indicating an inward field, toward the planet. To highlight the dawn–dusk asymmetry of B_r more clearly, regions where the absolute magnetic field magnitude exceeds 8 nT are outlined with white contours. It should be noted that the colorbars for B_lon, B_lat, and B_r are set to different ranges in order to effectively display the spatial characteristics of each component. The B_lon reaches significantly higher magnitudes than the other two components.

In Figs. 3a1–a3, the B_lon exhibits a pronounced dawn–dusk asymmetry, intensifying and extending over broader regions on the duskside as the IMF angle increases from 15° to 90°. The B_lon exhibits the strongest magnitude among the three components and dominates the total magnetic field structure. Its spatial distribution closely resembles that of the total magnetic field shown in Fig. 2, both in terms of intensity and morphological features. Notably, B_lon consistently maintains the same polarity as the upstream IMF azimuthal component in all three cases, suggesting that the observed east–west magnetic field pattern is largely governed by the IMF draping and pileup on the dayside of Venus, which agrees well with the observation conclusion made by Xu et al. (2023) by that the draped topology is dominant in the near-Venus space environment.

The B_lat displays a clear four-quadrant structure, characterized by negative values in the northeast and southwest regions, and positive values in the northwest and southeast. Specifically, on the dawnside, the magnetic field is directed southward in the northern hemisphere (northeast quadrant) and northward in the southern hemisphere (southeast quadrant), resulting in a contraction of field toward the equator. Conversely, on the dusk-side, the field are directed northward in the northern hemisphere (northwest quadrant) and southward in the southern hemisphere (southwest quadrant), causing an extension toward the polar regions. This meridional asymmetry significantly shapes the overall morphology of the total magnetic field distribution. However, as shown in Figs. 3b1 and b2 for the IMF angles 15° and 36° cases, the poleward extension on the duskside is notably weaker and more confined, indicating a limited latitudinal expansion of the magnetic field in these cases. Compared to the clear equatorward contraction on the dawnside, this reduced duskside expansion contributes to the overall dawn–dusk asymmetry in the magnetic field topology. In contrast, in the 90° case shown in Fig. 3b3, the B_lat displays a more symmetric quadrupolar structure. The equatorward contraction on the dawnside is largely balanced by a more developed poleward extension on the dusk-side, indicating a more symmetric latitudinal reconfiguration of the magnetic field.

The B_r reveals a distinct polarity reversal, characterized by negative values on the dawnside and positive values on the duskside. The negative B_r values on the dawnside indicate that magnetic field lines are directed inward, toward the planetary surface. In contrast, the positive B_r values on the duskside correspond to field lines oriented outward, away from the planet. The polarity reversal is consistent with direct interactions between the Venusian atmosphere/ionosphere and the solar wind, where the penetrating IMF alters local magnetic topology Xu et al. (2021). When the IMF penetrates deep into the ionosphere, the open topology with one end connected to the solar wind and the other end connected to the ionosphere can occur as a result of the draped IMF. Specifically, as shown in Figs. 3c1 and c2, for the 15° and 36° cases, the dawnside negative B_r values cover a relatively broad region compared to the more confined area occupied by the positive B_r values on the duskside. This distribution suggests a pronounced dawn–dusk asymmetry, reflecting stronger inward magnetic flux pileup on the dawnside. However, when the IMF orientation reaches 90° (Fig. 3c3), the negative and positive radial magnetic field regions become nearly symmetric in extent and intensity, indicating that the inward and outward radial magnetic fluxes on the dawn and dusksides, are effectively balanced.

The induced magnetosphere is sustained by a current system generated through the interaction between the solar wind and the conducting ionosphere, which maintains the balance between the induced magnetic field and the IMF (Wang et al. 2024). The corresponding net current system, defined as the quasi-steady large-scale current distribution consistent with the magnetic field topology, can be determined from the spatial gradients of the magnetic field. Using Ampère’s law, the net current density is therefore obtained from J = ∇ × B/µ₀, enabling a quantitative diagnosis of the current structure responsible for maintaining the induced magnetosphere (Parker 2000). To further examine the current structure, we present the latitudinal (J_lat), longitudinal (J_lon), and radial (J_r) components of the net current density in Fig. 4. J_r is defined as positive when directed away from Venus, the J_lat is positive toward the east, and the J_lon is positive toward the north.

As shown in Fig. 5, the J_r exhibits a relatively simple structure characterized by opposite polarities between the northern and southern hemispheres. Its magnitude remains moderate compared with the other components, with peak values generally within 40–60 nA m⁻², and shows only weak dependence on the IMF direction. In Figs. 4b1–b3, the J_lat displays pronounced dawn–dusk asymmetries with alternating regions of positive and negative currents in both hemispheres. Its magnitude is significantly larger than that of J_r, with local maxima reaching approximately 80–100 nA m⁻². In contrast, the J_lon shows the largest spatial extent and magnitude among the three components and therefore represents the dominant contribution to the global current system. Its peak intensity reaches 120–140 nA m⁻², clearly exceeding those of both J_r and J_lat.

Fig. 2 Magnetic field strength (a1–a3) and magnetic pressure (b1–b3) at an altitude of 350 km above Venus, shown for IMF angles of 15°, 36°, and 90°. The data are mapped in a Mollweide projection using the VSO coordinate system, where 0° longitude corresponds to the subsolar point. Only the dayside hemisphere (from 90°E to 90°W longitude) is shown. The white dashed lines indicate the 0° meridian and equator; the gray dashed lines denote meridians spaced at 10° and parallels at 15°. The black arrows show the direction of the magnetic field projected in the plane.

Fig. 3 Spatial distributions of the magnetic field components at an altitude of 350 km on the dayside hemisphere of Venus (SZA<90°), presented in Mollweide projection. Panels (a1)–(a3) show the longitudinal (east–west) component (Blon), (b1)–(b3) show the latitudinal (north–south) component (Blat), and (c1)–(c3) show the radial component (Br). Positive Blon points eastward (toward 90°E), positive Blat points northward, and positive Br points radially outward from the planet. White contours in panels (c1)–(c3) mark areas where the absolute magnetic field magnitude exceeds 8 nT.

Fig. 4 Spatial distributions of the net current J = ∇ × B/µ0 components at an altitude of 350 km on the dayside hemisphere of Venus (S ZA < 90°), presented in Mollweide projection. Panels (a1)–(a3) show the radial component (Jr), (b1)–(b3) show the longitudinal (east–west) component (Jlon), and (c1)–(c3) show the latitudinal (north–south) component (Jlat).

3.2 The horizontal transport of planetary ions

The observed dawn–dusk asymmetry in magnetic field at Venus can significantly influence the horizontal transport of planetary ions, which are key indicators of atmospheric water loss and maintenance of the nightside ionosphere (Knudsen et al. 1980). When the IMF penetrates into the Venus ionosphere, it accesses regions with higher ionospheric plasma densities, thus enabling the efficient energization and acceleration of cold planetary ions with energies typically with energies in the electronvolt range (Collinson et al. 2016, 2019).

Fig. 5 presents the distribution of the average O⁺ density, as well as the upper boundary of ionosphere on the dawn and dusksides under three IMF angles. The distributions of log₁₀(O⁺) density are shown as functions of the SZA and altitude, covering the SZA range from 0° to 150°and altitudes between 150 km and 1400 km. The white dashed and solid lines indicate the locations of the 100 cm⁻³ O⁺ isodensity contour on the dawn and dusksides respectively (Knudsen et al. 1980; Brace et al. 1980). Distributions of O⁺ ion density show that the order of magnitude variation with SZA is consistent with the ionospheric model predictions of Whitten et al. (1984) and McCormick et al. (1987). Panels a3, b3, and c3 show the corresponding ionospheric boundary, which are derived in the same way on the dawn and dusksides. The ionospheric upper boundary defined here is an indication of approximately how far the ionosphere extends. For all three IMF angle cases, the upper boundary of the ionosphere reaches the highest point near the terminator, SZA ranging from 90° to 120°, then decreases sharply with the increasing SZA on the nightside. A comparison between the dawnside (dashed lines) and duskside (solid lines) ionospheric upper boundaries clearly illustrates a noticeable asymmetry. In the 15° and 36° IMF angle cases, Figs. 5a3 and b3, the ionospheric upper boundary on the dawnside, particularly near the terminator region, extends to higher altitudes and larger SZAs. This suggests an enhanced horizontal ionospheric transport toward the nightside in the dawn hemisphere, where ionospheric structure is mainly shaped by horizontal transport rather than local production (Song et al. 2023). And the uplifting of the ionosphere near the dawnside terminator region may be caused by a more intense impact ionization process. Conversely, in the 90° IMF angle case (Fig. 5c3), this dawn–dusk asymmetry becomes notably weaker, and the ionospheric upper boundaries on both sides show nearly identical altitudinal extents. This symmetric configuration suggests that when the IMF aligns perpendicularly to the Venus–Sun line, the horizontal plasma transport and ionospheric outflow become more evenly balanced between the dawn and dusk hemispheres. In all three cases, altitudes of the ionospheric upper boundaries on the dawn and dusksides at SZA < 90° remain nearly identical, which indicates that the ionospheric vertical structure on the dayside is predominantly controlled by solar EUV photoionization process. Consequently, the observed dawn–dusk asymmetry in magnetic fields appears to have limited influence on the vertical structure of the dayside ionosphere.

To investigate the origin of the asymmetry in horizontal ionospheric transport toward the nightside, we examined the number density, azimuthal horizontal velocity, and ion flux of planetary O⁺ ions at an altitude of 350 km under different IMF configurations. As shown in Fig. 6, the global distributions of these parameters are presented using a Mollweide projection. Figs. 6a1–a2 present the distribution of O⁺ number density, presented in log scale, at an altitude of 350 km on the dayside hemisphere. It should be noted that the colorbar does not start from zero but spans the range from log₁₀(O⁺) = 2/0 to 4/0 cm⁻³, due to the highly nonuniform of the number density distribution. In all three cases, the central subsolar region (near 0° longitude and latitude) exhibits significantly lower densities. This is primarily attributed to the strong mass-loading effect near the subsolar point, where solar wind energy deposition and momentum transfer are more intense (Biernat et al. 2001; Wang et al. 2004; Xiao & Zhang 2018). The distribution of O⁺ number density shows no significant dawn–dusk asymmetry. This result is consistent with the conclusions drawn from Fig. 5, where the Venusian dayside ionospheric structure is predominantly governed by solar EUV photoionization. The solar EUV radiation leads to relatively uniform ion production, thus maintaining a horizontally symmetric ionospheric density profile. This result is further supported by the modeling assumption that the neutral atmosphere is prescribed as a static, one-dimensional distribution, which does not vary with local time. Since both the photoionization rate and the neutral background remain constant along each local time circle at a given SZA, no significant dawn–dusk asymmetry in ion production is expected under this configuration.

Figs. 6b1–b3 show the east–west velocity distribution for O+ ions, with positive values (red) representing eastward flows toward the dawnside and negative values (blue) indicating westward flows toward the duskside. The arrows denote the direction of the horizontal ion velocities. The simulated horizontal velocity of O⁺ ions is consistent with observations from the PVO, which reported large-scale ion flows with typical speeds of 2– 3 km s⁻¹ (Knudsen et al. 1980). In all three cases, near the subsolar longitude (around 0°), the magnitude of the east–west velocities approach zero, and the ion motion in the subsolar longitude region is primarily oriented in the north–south direction. Because in all three cases, in our initial setup with the solar-wind flow and the IMF, the solar wind electric field is oriented predominantly along north–south direction. As the SZA increases toward the terminator, the horizontal plasma flow gradually transitions to an east–west dominant pattern, with increasing velocity magnitudes toward both the dawn and dusk terminators. This is because the draped IMF geometry modifies the orientation of the electric field. In Figs. 6b1–b2, the east–west velocity distribution exhibits a clear dawn–dusk asymmetry. Specifically, regions representing similar velocity magnitude ranges occupy noticeably larger spatial areas on the dawnside compared to the duskside. In contrast, for the 90° case, the dawn–dusk asymmetry in the velocity distribution largely disappears.

Figs. 6c1–c3 present the distribution of the O⁺ ion flux, presented in logarithmic scale, at 350 km, calculated as the product of number density shown in Figs. 6a1–a3 and the absolute value of the east–west velocity shown in Figs. 6b1–b3. The absolute value is taken to emphasize the magnitude of horizontal plasma transport regardless of flow direction. It should be noted that the colorbar does not start from zero but spans the range from 11.0 to 14.0 cm⁻² s⁻¹. In all three cases, the lowest flux values are concentrated near the subsolar region, corresponding to the region of strongest mass loading which has been discussed in Figs. 6a1–a3. The enhanced fluxes are observed as the plasma moves toward the terminator region, indicating regions of intensified horizontal plasma transport from the dayside to the nightside. The ion flux distribution in Figs. 6c1–c2 show a distinct dawn–dusk asymmetry, with a broader region of high flux on the dawnside compared to the duskside. This pattern suggests that more efficient plasma transport occurs on the dawnside.

The comparison between the distributions of velocity, density, and ion flux indicates that the dawn–dusk asymmetry of O⁺ ion flux is primarily driven by the asymmetry in horizontal velocity rather than number density. The O⁺ number density distribution remains nearly symmetric across the dayside Venusian hemisphere, while the east–west velocity distribution exhibits a pronounced asymmetry, with significantly broader spatial extent of regions with comparable velocity magnitudes. As a result, the ion flux pattern confirms that plasma transport asymmetries are predominantly governed by differences in ion dynamics rather than ion production process.

Fig. 5 Distributions of O+ ion density (logarithmic scale) as a function of altitude (150–1400 km, bin size: 20 km) and solar zenith angle (SZA; 0– 150°, bin size: 5°) on the dawnside and duskside for three IMF angles: (a1–a3) 15°, (b1–b3) 36°, and (c1–c3) 90°. The white dashed and solid lines indicate the positions of the ionospheric upper boundary, defined by the 100 cm−3 O+ isodensity contour, on the dawn and dusk sides, respectively. Panels (a3, b3, c3) present direct comparisons of the dawnside (solid lines) and duskside (dashed lines) ionospheric upper boundaries.

Fig. 6 Distributions of O+ ion number density (a1–a3, in logarithmic scale), east–west velocity (b1–b3), and flux (c1–c3, in logarithmic scale) at an altitude of 350 km on Venus. The black arrows represent the horizontal velocity direction.

3.3 Distributions of the electromagnetic forces

When the magnetic field embedded in the solar wind interacts with an unmagnetized planet, it drapes around the ionosphere and facilitates the removal of planetary particles. Compared with heavy planetary ions, electrons are much lighter and can escape readily. As electrons drift upward and escape into space, they remain electrostatically coupled to the positive ions through a polarization electric field, which prevents further charge separation (Collinson et al. 2016). Under such conditions, the resulting electric fields can accelerate planetary ions, reducing the effective potential barrier and enabling their escape into space. To better understand the origin of the ion velocity asymmetry, it is necessary to examine the electromagnetic forces acting on the ions. The electromagnetic forces play a critical role in shaping ion motion and are expected to vary with the orientation of the IMF, thereby contributing to the observed dawn–dusk asymmetries in plasma transport (Dubinin et al. 2011; Song et al. 2023). Deriving from the momentum equation, the electromagnetic force density acted on each ion species is given by n_sq_s (u_s × B + E). Combined with the generalized Ohm’s law, Eq. (5), the electromagnetic force density acting on the plasma can be written as: $$F_{\text{EM}}=\frac{n_s{q}_s}{n_{e}e}\left(J\times B-\nabla p_e\right)+n_s{q}_s(u_s-u_{+})\times B$$(7)

where the electromagnetic force density can be divided into three different force terms: J × B force, ambipolar electric field force (∇p_e force) and relative motion electric field force ((u_s − u₊) × B force).

The J × B force, resulting from the magnetic tension of draped IMF lines, acts to decelerate and deflect the plasma as it enters the magnetosheath. This mechanism has been pointed out as a driver of planetary ion escape on the dayside (Song et al. 2023). The ∇p_e force, associated with electron precipitation and subsequent heating or ionization along magnetic field lines, works together with the J × B force to decelerate incoming solar wind ions at the BS. However, deeper in the lower magnetosheath, the ∇p_e forces tend to reaccelerate and compress the ion flow toward the planet (Ma et al. 2019). The relative motion electric field force includes u_s × B and u₊ × B forces. The u_s × B primarily acts to deflect newly ionized pickup ions. The u₊ × B force dominates in the inner magnetosheath adjacent to the induced magnetosphere, and acts to accelerate ions along the motional electric field direction. Note that the relative motional electric force on planetary ions depends on its relative velocity (Ma et al. 2019). Additionally, order-of-magnitude estimates indicate that at an altitude of ∼350 km the ion-neutral collision frequency is more than two orders of magnitude smaller than the O⁺ gyrofrequency. This implies that collisional drag plays only a minor role, and therefore the present analysis focuses primarily on electromagnetic forces, which dominate the ion acceleration and transport processes.

To investigate the role of electromagnetic forces in the Venusian plasma environment, we performed a force analysis on O⁺ ions in our model, which can be seen as the representation of heavy planetary ions. The total electromagnetic force, FEM, and three components, J × B force, ∇p_e force, and (u_s − u₊) × B force, acting on O⁺ in the east–west direction are plotted in Fig. 7. In Figs. 7a1–a3, the FEM exhibits positive values on the dawnside and negative on the dusk, indicating that the force acts in opposite east–west directions across the dayside hemisphere. This pattern is consistent with the divergent horizontal ion flow observed in Fig. 6 and suggests that the electromagnetic force facilitates cross-terminator plasma transport from the subsolar region toward the nightside. To highlight the dawn–dusk asymmetry more clearly, regions where the absolute force magnitude exceeds 4 × 10⁻¹⁶ N m⁻³ are outlined with white contours. In both the 15° and 36° IMF angle cases, the FEM exhibits clear dawn–dusk asymmetry, where regions with comparable magnitudes of FEM occupy a noticeably larger area on the dawnside compared to the duskside. This asymmetry diminishes in the 90° IMF case, as shown in Fig. 7a3, where both the color shading and vector direction show a more symmetric pattern, and the peak magnitudes become comparable between the two sides. These features collectively suggest that the FEM plays a critical role in modulating the dawn–dusk asymmetry in plasma transport, and that its spatial distribution is highly sensitive to the IMF orientation.

The (u_s − u₊) × B force represents the contribution of the differential motion between the heavy ion species and the bulk plasma to the total electromagnetic force. In Figs. 7b1–b3, while the overall magnitudes are relatively low compared to other force components, there are localized regions where the differential motion of O⁺ ions with respect to the background plasma is enhanced, indicating that this kind of force may locally influence ion transport.

In Figs. 7c1–c3, the vector distribution of the ∇p_e force shows some structured patterns, while no evident dawn–dusk asymmetry is observed in this term. The vectors on the dayside appear to converge toward a specific region near the subsolar point. This convergence region coincides spatially with the location of minimum O⁺ number density, as shown in Figs. 6b1–b3. This correlation suggests that the ambipolar electric field responds directly to the electron pressure gradient shaped by the mass-loading effect at the subsolar region. The lower O⁺ density in this region leads to a steeper electron pressure gradient, which in turn drives inward-directed ambipolar electric fields and maintains local quasi-neutrality. In addition, the direction of the vectors near the terminator region consistently points from the dayside toward the nightside. This suggests that the ambipolar electric field contributes to facilitating plasma transport across the terminator.

Figs. 7d1–d2 exhibit the magnitude and directional distributions of the J × B force. Among all the three electromagnetic force components, J × B force exhibits the largest magnitude across the dayside hemisphere. Its peak values are comparable in magnitude to those of the FEM. Moreover, the directional pattern of J × B force closely resemble those of FEM. In regions of low O⁺ number density, the force vectors are predominantly aligned in the north–south direction, while in regions of higher density, the vectors tend to point east–west. Both the magnitude and the direction of the total force are dominantly determined by the J × B force, indicating that it is the primary contributor to the electromagnetic force acting on ions. In the IMF 15° and 36° cases, the J × B force exhibits a clear dawn–dusk asymmetry in terms of the spatial coverage of regions with comparable magnitude. On the dawnside, areas with similar color shading occupy a noticeably broader region compared to the duskside.

Fig. 7 Distributions of the total electromagnetic force (a1–a3), the relative motional electric field (b1–b3), the ambipolar electric field force (c1– c3), and Hall electromotive force (d1–d3), acting on O+ ions at an altitude of 350 km on the Venusian dayside hemisphere. White contours mark areas where the absolute force magnitude exceeds 4 × 10−16 N m−3.

3.4 IMF control of the ion horizontal transport

Fig. 8 is presented to demonstrate the role of the IMF orientation in controlling dawn–dusk asymmetries of plasma transport. We calculate the product of ion number density and the normal component of velocity at each data point on the terminator plane (X = 0 plane) and then sum these products over all points. The dawnside is defined as the region with Y > 0 and the duskside as Y < 0. The relative contributions of dawnside and duskside O⁺ fluxes across the terminator plane are expressed as fractions of the total flux under IMF angles ranging from 10° to 90°. The results reveal a consistent dawn–dusk asymmetry: at small IMF angles (e.g., 10°), the dawnside accounts for nearly 59% of the total escape, while the duskside contributes about 41%. With increasing IMF angle, the dawnside fraction decreases monotonically, whereas the duskside fraction increases correspondingly.

By 90°, the two fractions converge to nearly equal values (~50% each), indicating a nearly symmetric ion flux pattern. This trend demonstrates that when the IMF is oblique to the solar wind flow, dawnside plasma transport dominate, but the asymmetry diminishes as the IMF approaches perpendicular orientation. These results provide an integrated measure linking the local dawn–dusk differences in magnetic field and plasma transport.

Fig. 8 Relative contributions of dawnside (Y > 0) and duskside (Y < 0) O+ fluxes across the terminator plane (X = 0). The flux is calculated as the product of ion number density and the normal component of velocity at each grid point, summed over all points. Results are shown as fractions of the total flux perpendicular to the plane under IMF angles ranging from 10° to 90°.

4 Discussion and conclusions

This study revealed a pronounced dawn–dusk asymmetry in the dayside magnetic field pileup and plasma horizontal transport at Venus, that varies with the orientation or IMF angles of the IMF. Our analysis demonstrates that while the planetary O⁺ ion density remains relatively symmetric between the dawn and dusk hemispheres on the dayside, the flux distribution exhibits strong asymmetry, primarily driven by differences in horizontal velocity. To investigate the underlying drivers of this velocity asymmetry, we examined three electromagnetic force components derived from the generalized Ohm’s law. The J × B force emerges as the dominant contributor in both magnitude and spatial extent.

The distribution of the J × B force shows a clear dawn– dusk asymmetry that is directly responsible for the horizontal plasma transport considered in this study. According to the vector cross product, the east–west component of the J × B force can be expressed as J_lonBr − J_rB_lon. As shown in Figs. 3 and 5, the J_r is characterized by opposite polarities between the northern and southern hemispheres, forming a largely hemispherically symmetric structure. Meanwhile, the Blon maintains a nearly uniform westward direction across the dayside without a clear dawn–dusk reversal. As a result, the term J_rBlon is unlikely to be the primary source of the observed east–west asymmetry in the J × B force. In contrast, the dominant contribution to the east–west J × B force arises from the term J_lonBr. The B_r reverses polarity between the dawn and dusk sectors due to the draping configuration of the IMF, while the J_lon maintains a relatively coherent southward direction. The coupling between these current and magnetic field structures naturally leads to opposite directions of the east–west Lorentz force on the dawn and dusksides. This provides a self-consistent explanation for the observed asymmetry in the Hall-driven horizontal ion transport.

It is further noted that for small Parker spiral angles the IMF contains a strong radial B_X component. In our simulations this effect is particularly evident on the dawnside, where the 15° case exhibits a noticeably larger maximum B_r value than the 36° and 90° cases. In this configuration, the enhanced radial IMF component modifies the magnetic field penetration and pileup pattern on the dayside, thus leading to changes in the spatial distribution of magnetic pressure gradients and current density distribution. These effects strengthen the dawn–dusk contrast in both B_r and J_lon, thereby amplifying the asymmetric J × B force. Additionally, according to Chang et al. (2020) and Zhang et al. (2008a), the ionosphere of Venus is weakly ionized and magnetized for nearly 95% of the time at solar minimum and for nearly 15% at solar maximum. We can assume that under solar minimum conditions, the deeper magnetic field penetration on the dayside may lead to enhanced current density gradients and potentially more pronounced J × B -driven horizontal transport asymmetry compared to solar maximum conditions.

Finally, while MHD models can capture large-scale plasma dynamics and self-consistently resolve magnetic field pileup, they treat ions and electrons as fluid populations and do not fully resolve kinetic effects, which can be better captured by the hybrid model. Hybrid simulations, which treat ions as particles and electrons as a fluid, can better capture kinetic-scale processes in the ionosphere and magnetosheath, probably leading to different estimates of field-line draping, ion acceleration, and cross-terminator ion transport. Another limitation is the availability of in situ observations for validation. Observation data that simultaneously satisfy stable solar wind velocity and density, with only the IMF direction varying, are extremely limited. This scarcity constrains our ability to systematically compare model outputs with observations under controlled upstream conditions. Future potential missions at Venus would provide valuable opportunities for assessing the validity of simulated dawn–dusk asymmetries and for exploring the role of magnetic topology under a broader range of IMF configurations.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 42241114 and 12150008, the Postdoctoral Fellowship Program of CPSF under Grant GZC20233367.

References

All Tables

All Figures

Fig. 1 (a1–b3) Contours of magnetic field strength (B) and magnetic pressure (PB) for Cases 1–3 in the XY plane. The color scale represents the magnitude of the magnetic field and magnetic pressure. The black dashed lines denote the average position of BS fixed by R = 2/14/[1 + 0/62 × cos(SZA)]. The white dashed lines represent the simulated BS, determined by identifying the peak radial gradient of the upstream solar wind velocity along the X direction. The black arrows show the direction of the magnetic field projected in the XY plane. The complete list of IMF components are given in Table 1.

In the text

Fig. 2 Magnetic field strength (a1–a3) and magnetic pressure (b1–b3) at an altitude of 350 km above Venus, shown for IMF angles of 15°, 36°, and 90°. The data are mapped in a Mollweide projection using the VSO coordinate system, where 0° longitude corresponds to the subsolar point. Only the dayside hemisphere (from 90°E to 90°W longitude) is shown. The white dashed lines indicate the 0° meridian and equator; the gray dashed lines denote meridians spaced at 10° and parallels at 15°. The black arrows show the direction of the magnetic field projected in the plane.

In the text

Fig. 3 Spatial distributions of the magnetic field components at an altitude of 350 km on the dayside hemisphere of Venus (SZA<90°), presented in Mollweide projection. Panels (a1)–(a3) show the longitudinal (east–west) component (Blon), (b1)–(b3) show the latitudinal (north–south) component (Blat), and (c1)–(c3) show the radial component (Br). Positive Blon points eastward (toward 90°E), positive Blat points northward, and positive Br points radially outward from the planet. White contours in panels (c1)–(c3) mark areas where the absolute magnetic field magnitude exceeds 8 nT.

In the text

	Fig. 4 Spatial distributions of the net current J = ∇ × B/µ0 components at an altitude of 350 km on the dayside hemisphere of Venus (S ZA < 90°), presented in Mollweide projection. Panels (a1)–(a3) show the radial component (Jr), (b1)–(b3) show the longitudinal (east–west) component (Jlon), and (c1)–(c3) show the latitudinal (north–south) component (Jlat).
In the text

Fig. 5 Distributions of O+ ion density (logarithmic scale) as a function of altitude (150–1400 km, bin size: 20 km) and solar zenith angle (SZA; 0– 150°, bin size: 5°) on the dawnside and duskside for three IMF angles: (a1–a3) 15°, (b1–b3) 36°, and (c1–c3) 90°. The white dashed and solid lines indicate the positions of the ionospheric upper boundary, defined by the 100 cm−3 O+ isodensity contour, on the dawn and dusk sides, respectively. Panels (a3, b3, c3) present direct comparisons of the dawnside (solid lines) and duskside (dashed lines) ionospheric upper boundaries.

In the text

	Fig. 6 Distributions of O+ ion number density (a1–a3, in logarithmic scale), east–west velocity (b1–b3), and flux (c1–c3, in logarithmic scale) at an altitude of 350 km on Venus. The black arrows represent the horizontal velocity direction.
In the text

	Fig. 7 Distributions of the total electromagnetic force (a1–a3), the relative motional electric field (b1–b3), the ambipolar electric field force (c1– c3), and Hall electromotive force (d1–d3), acting on O+ ions at an altitude of 350 km on the Venusian dayside hemisphere. White contours mark areas where the absolute force magnitude exceeds 4 × 10−16 N m−3.
In the text

	Fig. 8 Relative contributions of dawnside (Y > 0) and duskside (Y < 0) O+ fluxes across the terminator plane (X = 0). The flux is calculated as the product of ion number density and the normal component of velocity at each grid point, summed over all points. Results are shown as fractions of the total flux perpendicular to the plane under IMF angles ranging from 10° to 90°.
In the text