# A Juno-Era View of Electric Currents in Jupiter's Magnetodisk

Z. -Y. Liu, M. Blanc, Q. -G. Zong

► To cite this version:

Z. -Y. Liu, M. Blanc, Q. -G. Zong. A Juno-Era View of Electric Currents in Jupiter's Magnetodisk. Journal of Geophysical Research Space Physics, 2023, 128, 10.1029/2023JA031436. insu-04473143

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Distributed under a Creative Commons Attribution 4.0 International License
JGR Space Physics

RESEARCH ARTICLE

10.1029/2023JA031436

**Key Points:**

* Four years of Juno magnetic field data are examined to delineate the currents in Jupiter's magnetodisk in the midnight-to-dawn sector

* The radial current and the field-aligned current (FAC) associated with it are consistent with the corotation enforcement model

* The azimuthal current decreases as the local time increases, leading to a FAC emptying the magnetodisk at pre-dawn

**Correspondence to:**

M. Blanc and Q.-G. Zong,
michel.blanc@irap.omp.eu;
qgzong@pku.edu.cn

**Citation:**

Liu, Z.-Y., Blanc, M., & Zong, Q.-G. (2023). A Juno-era view of electric currents in Jupiter's magnetodisk. *Journal of Geophysical Research: Space Physics*, 128, e2023JA031436. https://doi.org/10.1029/2023JA031436

Received 24 FEB 2023

Accepted 17 SEP 2023

© 2023. The Authors.

This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_1.png" /></figure>

A Juno-Era View of Electric Currents in Jupiter's Magnetodisk

Z.-Y. Liu¹ ID, M. Blanc²,³ ID, and Q.-G. Zong¹,⁴,⁵ ID

¹Institute of Space Physics and Applied Technology, Peking University, Beijing, China, ²IRAP, CNRS-Université Toulouse
III Paul Sabatier, Toulouse, France, ³LAM, Pytheas, Aix Marseille Université, CNRS, CNES, Marseille, France, ⁴State
Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, China, ⁵MNR Key
Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China

**Abstract** Recent observations from Juno provided a detailed view of Jupiter's magnetodisk, including its magnetic fields, waves, plasmas, and energetic particles. Here, we contribute to Juno results by determining the electric currents threading the magnetodisk and their coupling to field-aligned currents (FACs) in the midnight-to-dawn local time sector. We first derive from Juno magnetic field data the spatial distributions of the height-integrated radial ($I_r$) and azimuthal ($I_\theta$) currents in the magnetodisk, and then calculate the FACs from the divergence of the two current components. The $I_r$-associated FAC, $J_r$, flows into and out of the magnetodisk at small and large radial distances, respectively, approximately consistent with the axisymmetric corotation enforcement model. On the other hand, $I_\theta$ decreases with increasing local time everywhere in the local time sector covered, indicating an additional FAC ($J_\theta$) flowing out of the magnetodisk. From $I_\theta$ and $J_\theta$, we conclude that the influence of the solar wind, which compresses the dayside magnetosphere and thus breaks the axisymmetry of currents and fields, reaches deep to a radial distance of at least about 25 Jupiter radii. Our results provide observational constraints on Jupiter's magnetosphere-ionosphere-thermosphere coupling current systems, on their relation to the main auroral emission and on the radial mass transport rate in the magnetodisk, which we estimate to be close to ~1,500 kg/s.

# 1. Introduction

Jupiter has the largest magnetosphere among the planets in the solar system. Its magnetosphere is dominated by plasma originating from the moon Io, which orbits Jupiter at about 5.9 $R_J$ (Jupiter radii, about 71,400 km) and supplies about 1-ton plasma per second to the magnetosphere (e.g., Delamere et al., 2005; Thomas et al., 2004). The fresh Iogenic plasma injected into the magnetosphere as a result of ionization of Io torus neutral particles is picked up by the corotating electric field and dragged into corotation with Jupiter. The resulting centrifugal force drives, via interchange of flux tubes (Hill, 1976; Southwood & Kivelson, 1987), a strong outward radial transport of Iogenic plasma to large Jovicentric distances, stretching magnetic field lines near the centrifugal equator and generating an extended magnetodisk at all local times. This magnetic field configuration is supported by an azimuthal current disc (Hill & Michel, 1976) confined near the equator in the middle and outer magnetosphere (e.g., Khurana, 2001; Liu et al., 2021; Smith et al., 1976). Models of the configuration of this magnetodisk, which have clarified the relative contributions of the centrifugal force, plasma pressure gradient force and pressure anisotropy force to its equilibrium, have been developed first by Caudal (1986) and more recently by Nichols et al. (2015) and Millas et al. (2023). The Jovian magnetodisk is rather thin compared to its horizontal extent: in the midnight-to-dawn local time sector, it extends horizontally from ~20 $R_J$ to ~100 $R_J$, whereas in the vertical direction its half-thickness is only ~1–2 $R_J$ in general (e.g., Khurana et al., 2022; Liu et al., 2021).

When flowing outward, the plasma angular velocity decreases as a result of the Coriolis force, which works to conserve angular momentum in the flow and drives an outward radial current in the disk. The net divergence of this radial current in turn generates, in a steady state case, a third component of electric currents associated to the disk: a system of magnetic-field-aligned currents which flow into or out of the two conjugate ionospheres and close horizontally inside their conducting layers. Overall, the global current system generated by the outflow of Iogenic plasma transfers angular momentum between the magnetodisk and the upper atmosphere of the planet, thus fully or partly maintaining corotation of the magnetodisk with the planet. Finally, magnetic field lines threading the magnetodisk are drawn out of the meridian plane into a sweep-back configuration under the effect
JGR Space Physics

RESEARCH ARTICLE

10.1029/2023JA031436

**Key Points:**

* Four years of Juno magnetic field data are examined to delineate the currents in Jupiter's magnetodisk in the midnight-to-dawn sector

* The radial current and the field-aligned current (FAC) associated with it are consistent with the corotation enforcement model

* The azimuthal current decreases as the local time increases, leading to a FAC emptying the magnetodisk at pre-dawn

**Correspondence to:**

M. Blanc and Q.-G. Zong,
michel.blanc@irap.omp.eu;
qgzong@pku.edu.cn

**Citation:**

Liu, Z.-Y., Blanc, M., & Zong, Q.-G. (2023). A Juno-era view of electric currents in Jupiter's magnetodisk. *Journal of Geophysical Research: Space Physics*, 128, e2023JA031436. https://doi.org/10.1029/2023JA031436

Received 24 FEB 2023

Accepted 17 SEP 2023

© 2023. The Authors.

This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_2.png" /></figure>

A Juno-Era View of Electric Currents in Jupiter's Magnetodisk

Z.-Y. Liu¹ ID, M. Blanc²,³ ID, and Q.-G. Zong¹,⁴,⁵ ID

¹Institute of Space Physics and Applied Technology, Peking University, Beijing, China, ²IRAP, CNRS-Université Toulouse
III Paul Sabatier, Toulouse, France, ³LAM, Pytheas, Aix Marseille Université, CNRS, CNES, Marseille, France, ⁴State
Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, China, ⁵MNR Key
Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China

**Abstract** Recent observations from Juno provided a detailed view of Jupiter's magnetodisk, including its magnetic fields, waves, plasmas, and energetic particles. Here, we contribute to Juno results by determining the electric currents threading the magnetodisk and their coupling to field-aligned currents (FACs) in the midnight-to-dawn local time sector. We first derive from Juno magnetic field data the spatial distributions of the height-integrated radial ($I_r$) and azimuthal ($I_\theta$) currents in the magnetodisk, and then calculate the FACs from the divergence of the two current components. The $I_r$-associated FAC, $J_r$, flows into and out of the magnetodisk at small and large radial distances, respectively, approximately consistent with the axisymmetric corotation enforcement model. On the other hand, $I_\theta$ decreases with increasing local time everywhere in the local time sector covered, indicating an additional FAC ($J_\theta$) flowing out of the magnetodisk. From $I_\theta$ and $J_\theta$, we conclude that the influence of the solar wind, which compresses the dayside magnetosphere and thus breaks the axisymmetry of currents and fields, reaches deep to a radial distance of at least about 25 Jupiter radii. Our results provide observational constraints on Jupiter's magnetosphere-ionosphere-thermosphere coupling current systems, on their relation to the main auroral emission and on the radial mass transport rate in the magnetodisk, which we estimate to be close to ~1,500 kg/s.

# 1. Introduction

Jupiter has the largest magnetosphere among the planets in the solar system. Its magnetosphere is dominated by plasma originating from the moon Io, which orbits Jupiter at about 5.9 $R_J$ (Jupiter radii, about 71,400 km) and supplies about 1-ton plasma per second to the magnetosphere (e.g., Delamere et al., 2005; Thomas et al., 2004). The fresh Iogenic plasma injected into the magnetosphere as a result of ionization of Io torus neutral particles is picked up by the corotating electric field and dragged into corotation with Jupiter. The resulting centrifugal force drives, via interchange of flux tubes (Hill, 1976; Southwood & Kivelson, 1987), a strong outward radial transport of Iogenic plasma to large Jovicentric distances, stretching magnetic field lines near the centrifugal equator and generating an extended magnetodisk at all local times. This magnetic field configuration is supported by an azimuthal current disc (Hill & Michel, 1976) confined near the equator in the middle and outer magnetosphere (e.g., Khurana, 2001; Liu et al., 2021; Smith et al., 1976). Models of the configuration of this magnetodisk, which have clarified the relative contributions of the centrifugal force, plasma pressure gradient force and pressure anisotropy force to its equilibrium, have been developed first by Caudal (1986) and more recently by Nichols et al. (2015) and Millas et al. (2023). The Jovian magnetodisk is rather thin compared to its horizontal extent: in the midnight-to-dawn local time sector, it extends horizontally from ~20 $R_J$ to ~100 $R_J$, whereas in the vertical direction its half-thickness is only ~1-2 $R_J$ in general (e.g., Khurana et al., 2022; Liu et al., 2021).

When flowing outward, the plasma angular velocity decreases as a result of the Coriolis force, which works to conserve angular momentum in the flow and drives an outward radial current in the disk. The net divergence of this radial current in turn generates, in a steady state case, a third component of electric currents associated to the disk: a system of magnetic-field-aligned currents which flow into or out of the two conjugate ionospheres and close horizontally inside their conducting layers. Overall, the global current system generated by the outflow of Iogenic plasma transfers angular momentum between the magnetodisk and the upper atmosphere of the planet, thus fully or partly maintaining corotation of the magnetodisk with the planet. Finally, magnetic field lines threading the magnetodisk are drawn out of the meridian plane into a sweep-back configuration under the effect
of the radial current, as described by Khurana and Kivelson (1993). This current produces a J × B force toward the east that tends to accelerate the plasma back toward corotation.

This description, commonly referred to as the corotation enforcement model, focuses solely on the concurrent roles of internal sources of plasma (Io) and momentum (planetary rotation) in shaping the magnetodisk configuration and its three associated current systems. It was initially formulated by Hill (1979) and later developed in detail and used for predictions at Jupiter (Cowley & Bunce, 2001; Hill, 2001; Ray et al., 2014). One of its main merits has been to provide a successful explanation of the Jovian main aurora, as departures of magnetospheric plasma flows from rigid corotation are observed at radial distances mapping along field lines to the location of the main auroral emission. However, this interpretation of the main aurora has been recently challenged on the basis of Juno and other observations by Bonfond et al. (2020), who showed that it displays significant azimuthal, inter-hemispheric and temporal variations and has been proven to be influenced by solar wind conditions (e.g., Gurnett et al., 2002; Yao et al., 2019, 2022; Xu et al., 2023).

Thus there is no doubt that the effects of solar wind interactions with the Jovian magnetosphere should be added to this picture. Southwood and Kivelson (2001) analyzed the consequences of the time-dependent contractions and expansions of the dayside magnetosphere by the solar wind pressure, which are expected to produce strong local-time asymmetries (particularly dayside-nightside) in plasma flows, current systems and auroral features: see the review of these local time asymmetries by Arridge et al. (2016). Khurana (2001) showed from the analysis of night-side Galileo magnetic field data that magnetodisk radial and azimuthal currents both display strong local time asymmetries and both contribute to the generation of FACs. In their view, the divergence of azimuthal currents at dawn and dusk they deduced from Galileo observations feeds an additional FAC system, superposed to the corotation enforcement one, that results from solar wind control effects deep into the magnetosphere. Khurana et al. (2022) later determined quantitatively the magnetodisk thickness, confirming that it is significantly larger on the dusk-side than on the night-side. They interpreted this feature as the effect of a single Dungey-type circulation cell generating a region of open magnetic flux confined to the dawn-side magnetosphere.

There is currently no consensus on how the solar wind interaction influences internal magnetospheric dynamics: see again Arridge et al. (2016). One view is that it results from merely internal processes modulated by the confinement of plasma flows inside a strongly asymmetric magnetospheric cavity (Delamere & Bagenal, 2010). The other one is that Jovian and interplanetary magnetic fields reconnect over a limited area of the magnetopause on the dawnside, producing there a domain of open flux that distorts the configuration and flows of the magnetodisk and the corresponding auroral features. Both scenarios predict dawn-dusk and noon-midnight asymmetries in magnetodisk and FACs that need to be informed by direct observations. In this context, determination of the actual current systems linked to the magnetodisk is of the utmost interest. In his pioneering work, Khurana (2001) determined the basic morphology of these current systems on the nightside from Galileo data and revealed their dawn-dusk asymmetry. More recently, Lorch et al. (2020) extended this work to all local times. Using all magnetic field data available from space missions until July 2018, including a first set of Juno orbits, they calculated magnetodisk and FAC systems at all local times, mainly confirming the existence of a significant divergence of azimuthal currents and the importance of their determination for future studies of magnetosphere-ionosphere-thermosphere (MIT) coupling at Jupiter.

Magnetospheric science with Juno (Bagenal et al., 2017) has revolutionized our understanding of many open questions. Thanks to its unique eccentric polar orbit, it has provided new insight into the ionospheric component of MIT coupling current systems. Juno observations of the auroral and polar ionosphere not only confirmed the persisting existence of FACs, but also provided for the first time direct measurements of their magnitude and spatial distributions (Kotsiaros et al., 2019). They revealed a large north-south asymmetry in the magnitude of FACs, with northern FAC amplitudes being about half of southern FAC ones.

Furthermore, development for Juno of a multi-instrument method linking UV and IR spectro-imaging observations of the main auroral emission to in situ magnetic field and electron precipitation observations made it possible to retrieve simultaneously the ionospheric components of field-aligned and horizontal currents that close the giant current loop connecting the magnetodisk to the ionosphere-thermosphere (e.g., Al Saati et al., 2022; Wang et al., 2021). It revealed that, although in the southern hemisphere the upward FACs are always located equatorward of the downward FACs, the pattern for the northern hemisphere is more complex. In about 70% of the northern flybys studied by Al Saati et al. (2022), upward FACs are located on the equatorward side as well, while in the other northern flybys the opposite trend was observed. The latter trend indicates that the northern
of the radial current, as described by Khurana and Kivelson (1993). This current produces a J × B force toward the east that tends to accelerate the plasma back toward corotation.

This description, commonly referred to as the corotation enforcement model, focuses solely on the concurrent roles of internal sources of plasma (Io) and momentum (planetary rotation) in shaping the magnetodisk configuration and its three associated current systems. It was initially formulated by Hill (1979) and later developed in detail and used for predictions at Jupiter (Cowley & Bunce, 2001; Hill, 2001; Ray et al., 2014). One of its main merits has been to provide a successful explanation of the Jovian main aurora, as departures of magnetospheric plasma flows from rigid corotation are observed at radial distances mapping along field lines to the location of the main auroral emission. However, this interpretation of the main aurora has been recently challenged on the basis of Juno and other observations by Bonfond et al. (2020), who showed that it displays significant azimuthal, inter-hemispheric and temporal variations and has been proven to be influenced by solar wind conditions (e.g., Gurnett et al., 2002; Yao et al., 2019, 2022; Xu et al., 2023).

Thus there is no doubt that the effects of solar wind interactions with the Jovian magnetosphere should be added to this picture. Southwood and Kivelson (2001) analyzed the consequences of the time-dependent contractions and expansions of the dayside magnetosphere by the solar wind pressure, which are expected to produce strong local-time asymmetries (particularly dayside-nightside) in plasma flows, current systems and auroral features: see the review of these local time asymmetries by Arridge et al. (2016). Khurana (2001) showed from the analysis of night-side Galileo magnetic field data that magnetodisk radial and azimuthal currents both display strong local time asymmetries and both contribute to the generation of FACs. In their view, the divergence of azimuthal currents at dawn and dusk they deduced from Galileo observations feeds an additional FAC system, superposed to the corotation enforcement one, that results from solar wind control effects deep into the magnetosphere. Khurana et al. (2022) later determined quantitatively the magnetodisk thickness, confirming that it is significantly larger on the dusk-side than on the night-side. They interpreted this feature as the effect of a single Dungey-type circulation cell generating a region of open magnetic flux confined to the dawn-side magnetosphere.

There is currently no consensus on how the solar wind interaction influences internal magnetospheric dynamics: see again Arridge et al. (2016). One view is that it results from merely internal processes modulated by the confinement of plasma flows inside a strongly asymmetric magnetospheric cavity (Delamere & Bagenal, 2010). The other one is that Jovian and interplanetary magnetic fields reconnect over a limited area of the magnetopause on the dawnside, producing there a domain of open flux that distorts the configuration and flows of the magnetodisk and the corresponding auroral features. Both scenarios predict dawn-dusk and noon-midnight asymmetries in magnetodisk and FACs that need to be informed by direct observations. In this context, determination of the actual current systems linked to the magnetodisk is of the utmost interest. In his pioneering work, Khurana (2001) determined the basic morphology of these current systems on the nightside from Galileo data and revealed their dawn-dusk asymmetry. More recently, Lorch et al. (2020) extended this work to all local times. Using all magnetic field data available from space missions until July 2018, including a first set of Juno orbits, they calculated magnetodisk and FAC systems at all local times, mainly confirming the existence of a significant divergence of azimuthal currents and the importance of their determination for future studies of magnetosphere-ionosphere-thermosphere (MIT) coupling at Jupiter.

Magnetospheric science with Juno (Bagenal et al., 2017) has revolutionized our understanding of many open questions. Thanks to its unique eccentric polar orbit, it has provided new insight into the ionospheric component of MIT coupling current systems. Juno observations of the auroral and polar ionosphere not only confirmed the persisting existence of FACs, but also provided for the first time direct measurements of their magnitude and spatial distributions (Kotsiaros et al., 2019). They revealed a large north-south asymmetry in the magnitude of FACs, with northern FAC amplitudes being about half of southern FAC ones.

Furthermore, development for Juno of a multi-instrument method linking UV and IR spectro-imaging observations of the main auroral emission to in situ magnetic field and electron precipitation observations made it possible to retrieve simultaneously the ionospheric components of field-aligned and horizontal currents that close the giant current loop connecting the magnetodisk to the ionosphere-thermosphere (e.g., Al Saati et al., 2022; Wang et al., 2021). It revealed that, although in the southern hemisphere the upward FACs are always located equatorward of the downward FACs, the pattern for the northern hemisphere is more complex. In about 70% of the northern flybys studied by Al Saati et al. (2022), upward FACs are located on the equatorward side as well, while in the other northern flybys the opposite trend was observed. The latter trend indicates that the northern
ionospheric plasma might be temporally in super-corotation, a phenomenon noted previously when studying the equatorial magnetic fields measured by Voyager 1 and 2 (Hairston & Hill, 1986).

In this paper, we contribute to the determination by Juno of the different interconnected components of MIT coupling current systems at Jupiter. We determine from Juno magnetic field data along the current system threading the magnetodisk and its coupling to FACs in the midnight-to-dawn local time sector covered by Juno during its prime mission. We first establish a spatial distribution of the height-integrated perpendicular current density $I_{\perp}$ (in kilo-Amperes per Jupiter radii or kA/R$_{J}$) in the magnetodisk, using Juno/MAG (Connerney, 2017; Connerney et al., 2017) observations of the magnetic fields during 404 magnetodisk crossings in the night-to-dawn sector identified by Liu et al. (2021). Then, using current continuity, we determine FACs from the divergence of $I_{\perp}$. The FACs obtained highlight the contribution of azimuthal currents and allow one to divide the magnetodisk into three sub-regions with respect to their signs. In the remainder of the paper, we first describe the materials and methods (Section 2), then present our results (Section 3), and finally discuss them by comparison with previous publications (Section 4).

## 2. Materials and Method

### 2.1. Juno Observations of Magnetodisk Crossings

Because of Jupiter's rotation and dipole tilt, Juno crosses the magnetodisk periodically. Figure 1 shows a representative crossing on 30 August 2017. The top three panels give the three components ($B_x$, $B_y$, and $B_z$) of the magnetic fields in the Jupiter-Sun-Orbit (JSO) coordinate system during the crossing, whereas the fourth panel shows the magnitude ($B_t$). Before the crossing, Juno is located in the southern lobe, as indicated by the positive $B_x$ and $B_y$. Then, Juno approaches the magnetodisk, showing as $B_x$, $B_y$ and $B_t$ gradually decrease to zero. Finally, $B_x$ and $B_y$ continue to decrease before reaching their most negative values, while $B_t$ returns to its pre-crossing value, signaling the entry of Juno into the northern lobe.

To analyze the crossing in a more appropriate reference frame, we transform the magnetic field into an LMN coordinate system, which is a local current sheet coordinate system determined by a minimum variance analysis (Liu et al., 2021; Sonnerup & Scheible, 1998) of the observed field. The L axis of this coordinate system (denoted by $x_p$, increasing outward) corresponds to the component of the magnetic fields changing most during crossings. According to the geometry of the magnetodisk (e.g., Khurana, 1992; Khurana & Kivelson, 1989), it represents the direction of the lobe magnetic field. As shown in Figure 3 of Liu et al. (2021), this direction is roughly radial at small radial distances to Jupiter and gradually rotates toward the azimuthal direction as radial distance increases. The N axis (denoted by $x_n$, increasing upward) corresponds to the direction along which the magnetic field changes most, or in other words, the direction of the gradient. This direction can be regarded as the normal to the magnetodisk. Finally, the M axis (denoted by $x_m$, increasing eastward) completes the right-handed coordinates. As we will show in the following subsection, currents in the magnetodisk approximately flow in this direction. The bottom three panels of Figure 1 present the magnetic field in the LMN coordinate system. Consistent with the definition above, most changes are seen in $B_t$, which is about -20 nT before the crossing, becomes zero near the magnetodisk center, and approaches about +20 nT at the end. On the other hand, $B_n$ and $B_m$ do not vary much during the whole crossing.

### 2.2. Height-Integrated Perpendicular Current Density $I_{\perp}$

Next, we compute $I_{\perp}$ from the observed magnetic field profile. This can be done most easily in the LMN coordinates. To see this, we first write down the three components of the current density ($j_t$, $j_m$, and $j_n$) in terms of the magnetic field by virtue of Ampere's law (neglecting displacement current)

$$ \left\{ \begin{aligned} j_t &= \frac{1}{\mu_0} \left( \frac{\partial B_n}{\partial x_m} - \frac{\partial B_m}{\partial x_n} \right) \\ j_m &= \frac{1}{\mu_0} \left( \frac{\partial B_l}{\partial x_n} - \frac{\partial B_n}{\partial x_l} \right), \\ j_n &= \frac{1}{\mu_0} \left( \frac{\partial B_m}{\partial x_l} - \frac{\partial B_l}{\partial x_m} \right) \end{aligned} \right. \qquad (1) $$

where $\mu_0$ denotes the permeability of vacuum. Recalling the definition of the LMN coordinates, we have the ordering $\frac{\partial B}{\partial x_m} \sim \frac{\partial B}{\partial x_l} \ll \frac{\partial B}{\partial x_n}$. One can see that $j_n$ is much smaller than $j_m$, $j_l$ should be much smaller than $j_m$ as well. On the one hand, the first term of $j_l$ is negligible according to the above ordering. On the other hand, since the
ionospheric plasma might be temporally in super-corotation, a phenomenon noted previously when studying the equatorial magnetic fields measured by Voyager 1 and 2 (Hairston & Hill, 1986).

In this paper, we contribute to the determination by Juno of the different interconnected components of MIT coupling current systems at Jupiter. We determine from Juno magnetic field data along the current system threading the magnetodisk and its coupling to FACs in the midnight-to-dawn local time sector covered by Juno during its prime mission. We first establish a spatial distribution of the height-integrated perpendicular current density $I_{\perp}$ (in kilo-Amperes per Jupiter radii or kA/R$_{J}$) in the magnetodisk, using Juno/MAG (Connerney, 2017; Connerney et al., 2017) observations of the magnetic fields during 404 magnetodisk crossings in the night-to-dawn sector identified by Liu et al. (2021). Then, using current continuity, we determine FACs from the divergence of $I_{\perp}$. The FACs obtained highlight the contribution of azimuthal currents and allow one to divide the magnetodisk into three sub-regions with respect to their signs. In the remainder of the paper, we first describe the materials and methods (Section 2), then present our results (Section 3), and finally discuss them by comparison with previous publications (Section 4).

## 2. Materials and Method

### 2.1. Juno Observations of Magnetodisk Crossings

Because of Jupiter's rotation and dipole tilt, Juno crosses the magnetodisk periodically. Figure 1 shows a representative crossing on 30 August 2017. The top three panels give the three components ($B_x$, $B_y$, and $B_z$) of the magnetic fields in the Jupiter-Sun-Orbit (JSO) coordinate system during the crossing, whereas the fourth panel shows the magnitude ($B_t$). Before the crossing, Juno is located in the southern lobe, as indicated by the positive $B_x$ and $B_y$. Then, Juno approaches the magnetodisk, showing as $B_x$, $B_y$ and $B_t$ gradually decrease to zero. Finally, $B_x$ and $B_y$ continue to decrease before reaching their most negative values, while $B_t$ returns to its pre-crossing value, signaling the entry of Juno into the northern lobe.

To analyze the crossing in a more appropriate reference frame, we transform the magnetic field into an LMN coordinate system, which is a local current sheet coordinate system determined by a minimum variance analysis (Liu et al., 2021; Sonnerup & Scheible, 1998) of the observed field. The L axis of this coordinate system (denoted by $x_p$, increasing outward) corresponds to the component of the magnetic fields changing most during crossings. According to the geometry of the magnetodisk (e.g., Khurana, 1992; Khurana & Kivelson, 1989), it represents the direction of the lobe magnetic field. As shown in Figure 3 of Liu et al. (2021), this direction is roughly radial at small radial distances to Jupiter and gradually rotates toward the azimuthal direction as radial distance increases. The N axis (denoted by $x_n$, increasing upward) corresponds to the direction along which the magnetic field changes most, or in other words, the direction of the gradient. This direction can be regarded as the normal to the magnetodisk. Finally, the M axis (denoted by $x_m$, increasing eastward) completes the right-handed coordinates. As we will show in the following subsection, currents in the magnetodisk approximately flow in this direction. The bottom three panels of Figure 1 present the magnetic field in the LMN coordinate system. Consistent with the definition above, most changes are seen in $B_t$, which is about -20 nT before the crossing, becomes zero near the magnetodisk center, and approaches about +20 nT at the end. On the other hand, $B_n$ and $B_m$ do not vary much during the whole crossing.

### 2.2. Height-Integrated Perpendicular Current Density $I_{\perp}$

Next, we compute $I_{\perp}$ from the observed magnetic field profile. This can be done most easily in the LMN coordinates. To see this, we first write down the three components of the current density ($j_t$, $j_m$, and $j_n$) in terms of the magnetic field by virtue of Ampere's law (neglecting displacement current)

$$ \left\{ \begin{aligned} j_t &= \frac{1}{\mu_0} \left( \frac{\partial B_n}{\partial x_m} - \frac{\partial B_m}{\partial x_n} \right) \\ j_m &= \frac{1}{\mu_0} \left( \frac{\partial B_l}{\partial x_n} - \frac{\partial B_n}{\partial x_l} \right), \\ j_n &= \frac{1}{\mu_0} \left( \frac{\partial B_m}{\partial x_l} - \frac{\partial B_l}{\partial x_m} \right) \end{aligned} \right. \qquad (1) $$

where $\mu_0$ denotes the permeability of vacuum. Recalling the definition of the LMN coordinates, we have the ordering $\frac{\partial B}{\partial x_m} \sim \frac{\partial B}{\partial x_l} \ll \frac{\partial B}{\partial x_n}$. One can see that $j_n$ is much smaller than $j_m$, $j_l$ should be much smaller than $j_m$ as well. On the one hand, the first term of $j_l$ is negligible according to the above ordering. On the other hand, since the
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Juno observations of a magnetodisk crossing on 30 August 2017. From top to bottom, the panels give the x, y, and z components in the Jupiter-Sun-Orbit coordinates, the magnitude, and the n, m, and l components in the LMN coordinates. The blue and red lines in the bottom panel mark the values of $B_{l,n}$ and $B_{l,s}$, respectively.</figcaption></figure>

variation of $B_m$ between the two lobes is much smaller than that of $B_l$ (which is also a property of the LMN coordinates), the second term of $j_l$ is also small compared to the first term of $j_m$. Thus, the total current density $\vec{j}$ can be reduced to $\vec{j} \approx j_m \hat{x}_m$, where $\hat{x}_m$ represents a unit vector in the M direction.

Further, following from the LMN ordering, the second term of $j_m$ should be much smaller than the first term. This statement can be tested directly by observations. As an estimate, we take $\frac{\partial B_l}{\partial x_n} \sim \frac{B_l}{H}$ and $\frac{\partial B_m}{\partial x_l} \sim \frac{\partial B_m}{\partial r}$, where r represents the radial distance to Jupiter and H the half-thickness of the magnetodisk. Taking these quantities from
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Juno observations of a magnetodisk crossing on 30 August 2017. From top to bottom, the panels give the x, y, and z components in the Jupiter-Sun-Orbit coordinates, the magnitude, and the n, m, and l components in the LMN coordinates. The blue and red lines in the bottom panel mark the values of $B_{l,n}$ and $B_{l,s}$, respectively.</figcaption></figure>

variation of $B_m$ between the two lobes is much smaller than that of $B_l$ (which is also a property of the LMN coordinates), the second term of $j_l$ is also small compared to the first term of $j_m$. Thus, the total current density $\vec{j}$ can be reduced to $\vec{j} \approx j_m \hat{x}_m$, where $\hat{x}_m$ represents a unit vector in the M direction.

Further, following from the LMN ordering, the second term of $j_m$ should be much smaller than the first term. This statement can be tested directly by observations. As an estimate, we take $\frac{\partial B_l}{\partial x_n} \sim \frac{B_l}{H}$ and $\frac{\partial B_m}{\partial x_l} \sim \frac{\partial B_m}{\partial r}$, where r represents the radial distance to Jupiter and H the half-thickness of the magnetodisk. Taking these quantities from
Liu et al. (2021) (their Figure 2 for H and Figure 4 for $B_l$ and $B_t$ as a function of r), we obtain $|\frac{\partial B_l}{\partial x_l}|/|\frac{\partial B_t}{\partial x_n}| < 5\%$, supporting the above assertion of $j_m$. Therefore, we can finally write

$$ \vec{j} \approx j_m \hat{x}_m \approx \frac{1}{\mu_0} \frac{\partial B_l}{\partial x_n} \hat{x}_m. \qquad (2) $$

This equation suggests that currents in the magnetodisk are approximately in the M direction and primarily depend on $B_l$.

On the basis of Equation 2, we define height-integrated perpendicular current density, $I_⊥$, explicitly in this study as

$$ I_{\perp} = \int j_m dx_n = \frac{1}{\mu_0} \int \frac{d B_l}{d x_n} dx_n = \frac{1}{\mu_0} (B_{l,n} - B_{l,s}), \qquad (3) $$

where $B_{l,n}$ and $B_{l,s}$ represent the magnetic fields in the northern and southern lobes, respectively. To extract $B_{l,n}$ from observations, we first identify the zero point of $B_l$ in each crossing. Then, we isolate a 1-hour interval before or after the zero point (depending on the direction of the crossing) when Juno is located in the northern lobe. Finally, we calculate the 95th percentile of $B_l$ in this 1-hour interval, and take it as $B_{l,n}$, $B_{l,s}$ is obtained similarly. For the example shown in Figure 1, $B_{l,n}$ and $B_{l,s}$ obtained in this way are marked by the blue and red dashed lines in the bottom panel, respectively. One can see that they capture well the features of the lobe magnetic fields.

## 2.3. Transformation of $I_⊥$ to Global Reference Frame

Since the total current system has to be divergence-free, the FACs are related to the divergence of the magnetodisk currents. To calculate the latter, we have to transform the current density obtained in the LMN coordinates, which varies from crossing to crossing, to a global reference frame chosen to be the same for all crossings. Strictly speaking, this calculation of magnetodisk current divergence must take into account the non-planar shape of the magnetodisk mean position, as described by (e.g., Khurana, 1992; Kivelson et al., 1978). Fortunately, Juno observations suggest several simplifications. First, all crossings are observed near the JSO x-y plane, since their JSO latitudes, shown in Figure 2a, are very close to zero. Second, the lobe magnetic fields are approximately parallel to the JSO x-y plane. As shown in Figure 2b, in most crossings the angle of the L axis to the JSO x-y plane is close to zero. These two results suggest that magnetodisk crossings are well confined to the JSO x-y plane. Finally, Figure 2c shows that the angle from the M axis to the JSO x-y plane (denoted as $\alpha$ hereinafter) is generally small (see the black curve representing its average level), though some low-amplitude scatter is present. Taken altogether, inspection of the parameters plotted in Figure 2 suggests that magnetodisk currents are approximately aligned with the JSO x-y plane. This allows us to use in the remainder of this study the simplifying assumption that the magnetodisk and its embedded currents are approximately confined to the JSO x-y plane (i.e., $\alpha \approx 0^{\circ}$), and to adopt a cylindrical coordinate system using the JSO z-axis as its polar axis as the global reference frame. Transformation of magnetodisk currents from the LMN coordinates to the global reference frame is straightforward. The magnitude is still $I_⊥$, whereas the direction is given by the projection of $\hat{x}_m$ onto the JSO x-y plane (a direction which is almost entirely determined by the L axis).

To evaluate errors arising from the approximation assuming $\alpha \approx 0^{\circ}$, we first compute the relative error in projection, $\sim \frac{1-\cos \alpha}{\cos \alpha}$, for each crossing. Then, we calculate the median value of this relative error for all events, which amounts to 12%. This value represents the overall level of the relative errors introduced by our coordinate transformation. In the following, we will see that this value is comparable with the statistical uncertainty in $I_⊥$, $\sim 15\%$, which is hard to be reduced given the current data set. Therefore, we suggest the errors introduced by our approximation are acceptable.

We then apply the above definitions and methods to the 404 magnetodisk crossings identified by Liu et al. (2021), which provides a spatial distribution of both the magnitude ($I_⊥$) and direction ($\hat{x}_m$) of the magnetodisk currents. Figure 3a shows how magnetodisk currents are distributed in the global reference frame, with colors giving their magnitude and the short lines giving their direction. With a few exceptions possibly representing dynamical events, three statistical features can be noted from this figure: (a) At any given local time ($\phi$), $I_⊥$ decreases as the radial distance to Jupiter (r) increases. (b) At a fixed r, $I_⊥$ decreases as $\phi$ increases. (c) At small r, magnetodisk currents are primarily in the azimuthal direction, and their radial component tends to increase with increasing r.
Liu et al. (2021) (their Figure 2 for H and Figure 4 for $B_l$ and $B_t$ as a function of r), we obtain $|\frac{\partial B_l}{\partial x_l}|/|\frac{\partial B_t}{\partial x_n}| < 5\%$, supporting the above assertion of $j_m$. Therefore, we can finally write

$$ \vec{j} \approx j_m \hat{x}_m \approx \frac{1}{\mu_0} \frac{\partial B_l}{\partial x_n} \hat{x}_m. \qquad (2) $$

This equation suggests that currents in the magnetodisk are approximately in the M direction and primarily depend on $B_l$.

On the basis of Equation 2, we define height-integrated perpendicular current density, $I_\perp$, explicitly in this study as

$$ I_{\perp} = \int j_m dx_n = \frac{1}{\mu_0} \int \frac{d B_l}{d x_n} dx_n = \frac{1}{\mu_0} (B_{l,n} - B_{l,s}), \qquad (3) $$

where $B_{l,n}$ and $B_{l,s}$ represent the magnetic fields in the northern and southern lobes, respectively. To extract $B_{l,n}$ from observations, we first identify the zero point of $B_l$ in each crossing. Then, we isolate a 1-hour interval before or after the zero point (depending on the direction of the crossing) when Juno is located in the northern lobe. Finally, we calculate the 95th percentile of $B_l$ in this 1-hour interval, and take it as $B_{l,n}$, $B_{l,s}$ is obtained similarly. For the example shown in Figure 1, $B_{l,n}$ and $B_{l,s}$ obtained in this way are marked by the blue and red dashed lines in the bottom panel, respectively. One can see that they capture well the features of the lobe magnetic fields.

## 2.3. Transformation of $I_\perp$ to Global Reference Frame

Since the total current system has to be divergence-free, the FACs are related to the divergence of the magnetodisk currents. To calculate the latter, we have to transform the current density obtained in the LMN coordinates, which varies from crossing to crossing, to a global reference frame chosen to be the same for all crossings. Strictly speaking, this calculation of magnetodisk current divergence must take into account the non-planar shape of the magnetodisk mean position, as described by (e.g., Khurana, 1992; Kivelson et al., 1978). Fortunately, Juno observations suggest several simplifications. First, all crossings are observed near the JSO x-y plane, since their JSO latitudes, shown in Figure 2a, are very close to zero. Second, the lobe magnetic fields are approximately parallel to the JSO x-y plane. As shown in Figure 2b, in most crossings the angle of the L axis to the JSO x-y plane is close to zero. These two results suggest that magnetodisk crossings are well confined to the JSO x-y plane. Finally, Figure 2c shows that the angle from the M axis to the JSO x-y plane (denoted as $\alpha$ hereinafter) is generally small (see the black curve representing its average level), though some low-amplitude scatter is present. Taken altogether, inspection of the parameters plotted in Figure 2 suggests that magnetodisk currents are approximately aligned with the JSO x-y plane. This allows us to use in the remainder of this study the simplifying assumption that the magnetodisk and its embedded currents are approximately confined to the JSO x-y plane (i.e., $\alpha \approx 0^{\circ}$), and to adopt a cylindrical coordinate system using the JSO z-axis as its polar axis as the global reference frame. Transformation of magnetodisk currents from the LMN coordinates to the global reference frame is straightforward. The magnitude is still $I_\perp$, whereas the direction is given by the projection of $\hat{x}_m$ onto the JSO x-y plane (a direction which is almost entirely determined by the L axis).

To evaluate errors arising from the approximation assuming $\alpha \approx 0^{\circ}$, we first compute the relative error in projection, $\sim \frac{1-\cos \alpha}{\cos \alpha}$, for each crossing. Then, we calculate the median value of this relative error for all events, which amounts to 12%. This value represents the overall level of the relative errors introduced by our coordinate transformation. In the following, we will see that this value is comparable with the statistical uncertainty in $I_\perp$, $\sim 15\%$, which is hard to be reduced given the current data set. Therefore, we suggest the errors introduced by our approximation are acceptable.

We then apply the above definitions and methods to the 404 magnetodisk crossings identified by Liu et al. (2021), which provides a spatial distribution of both the magnitude ($I_\perp$) and direction ($\hat{x}_m$) of the magnetodisk currents. Figure 3a shows how magnetodisk currents are distributed in the global reference frame, with colors giving their magnitude and the short lines giving their direction. With a few exceptions possibly representing dynamical events, three statistical features can be noted from this figure: (a) At any given local time ($\phi$), $I_\perp$ decreases as the radial distance to Jupiter ($r$) increases. (b) At a fixed $r$, $I_\perp$ decreases as $\phi$ increases. (c) At small $r$, magnetodisk currents are primarily in the azimuthal direction, and their radial component tends to increase with increasing $r$.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** The geometry of the LMN coordinates. (a) The Jupiter-Sun-Orbit (JSO) latitude of the magnetodisk crossings (b) The angle from the L axis to the JSO x-y plane. (c) The angle from the M axis to the JSO x-y plane. The gray dots in these panels show individual crossings, whereas the black squares and curves represent the mean value in each bin of radial distance.</figcaption></figure>

## 2.4. Field-Aligned Current Density $J_\parallel$

Using the aforementioned definitions and approximation, we can now compute the divergence of $I_\perp$, which, according to the divergence-free current condition, gives the FACs. Since a cylindrical coordinate system is adopted here, we decompose these currents into their radial ($I_r$) and azimuthal ($I_\phi$) components, as illustrated in Figure 3b. In this way, one can write that the divergence of $I$ vanishes as:

$$J_{\parallel,n} + J_{\parallel,s} = \frac{1}{r} \frac{\partial(rI_r)}{\partial r} + \frac{1}{r} \frac{\partial I_\phi}{\partial \phi}, \quad (4)$$

where $J_{\parallel,n}$ and $J_{\parallel,s}$ denote the FAC density (in $kA/R_\parallel^2$) flowing between the magnetodisk and the northern and southern ionospheres, respectively. As mentioned in the Introduction, Juno observations show that these two quantities are generally unequal (Al Saati et al., 2022; Kotsiaros et al., 2019). In the absence of direct information on their relative amplitudes in the data used for this study, we deal only with their average, $J_\parallel = \frac{1}{2}(J_{\parallel,n} + J_{\parallel,s})$. One can easily obtain $J_{\parallel,n}$ and $J_{\parallel,s}$ from $J_\parallel$ by specifying a ratio of $J_{\parallel,s}$ to $J_{\parallel,n}$.

Furthermore, for the sake of discussion, we introduce two additional variables representing the relative contributions of $I_r$ and $I_\phi$ to $J_\parallel$, $J_r = \frac{1}{2} \frac{\partial(rI_r)}{\partial r}$ and $J_\phi = \frac{1}{2} \frac{\partial I_\phi}{\partial \phi}$. However, it should be noted that $J_r$ alone does not necessarily represent currents in the field-aligned direction, as $I_r$ could divert to either the azimuthal direction or the field-aligned direction, or any arbitrary combination of them. The same applies to $J_\phi$. Nonetheless, both explanations yield the same total FACs, indicating that, from a practical standpoint, $J_r$ and $J_\phi$ can be viewed as indicators of the contributions of $I_r$ and $I_\phi$ to FACs, respectively. Hence, for simplicity, we will refer to $J_r$ and $J_\phi$ directly as FAC densities associated with $I_r$ and $I_\phi$, respectively, in what follows. However, it is important for the reader to bear in mind the potential ambiguity in this terminology.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** The geometry of the LMN coordinates. (a) The Jupiter-Sun-Orbit (JSO) latitude of the magnetodisk crossings (b) The angle from the L axis to the JSO x-y plane. (c) The angle from the M axis to the JSO x-y plane. The gray dots in these panels show individual crossings, whereas the black squares and curves represent the mean value in each bin of radial distance.</figcaption></figure>

## 2.4. Field-Aligned Current Density $J_\parallel$

Using the aforementioned definitions and approximation, we can now compute the divergence of $I_\perp$, which, according to the divergence-free current condition, gives the FACs. Since a cylindrical coordinate system is adopted here, we decompose these currents into their radial ($I_r$) and azimuthal ($I_\phi$) components, as illustrated in Figure 3b. In this way, one can write that the divergence of $I$ vanishes as:

$$J_{\parallel,n} + J_{\parallel,s} = \frac{1}{r} \frac{\partial(rI_r)}{\partial r} + \frac{1}{r} \frac{\partial I_\phi}{\partial \phi}, \quad (4)$$

where $J_{\parallel,n}$ and $J_{\parallel,s}$ denote the FAC density (in $kA/R_\parallel^2$) flowing between the magnetodisk and the northern and southern ionospheres, respectively. As mentioned in the Introduction, Juno observations show that these two quantities are generally unequal (Al Saati et al., 2022; Kotsiaros et al., 2019). In the absence of direct information on their relative amplitudes in the data used for this study, we deal only with their average, $J_\parallel = \frac{1}{2}(J_{\parallel,n} + J_{\parallel,s})$. One can easily obtain $J_{\parallel,n}$ and $J_{\parallel,s}$ from $J_\parallel$ by specifying a ratio of $J_{\parallel,s}$ to $J_{\parallel,n}$.

Furthermore, for the sake of discussion, we introduce two additional variables representing the relative contributions of $I_r$ and $I_\phi$ to $J_\parallel$, $J_r = \frac{1}{2} \frac{\partial(rI_r)}{\partial r}$ and $J_\phi = \frac{1}{2} \frac{\partial I_\phi}{\partial \phi}$. However, it should be noted that $J_r$ alone does not necessarily represent currents in the field-aligned direction, as $I_r$ could divert to either the azimuthal direction or the field-aligned direction, or any arbitrary combination of them. The same applies to $J_\phi$. Nonetheless, both explanations yield the same total FACs, indicating that, from a practical standpoint, $J_r$ and $J_\phi$ can be viewed as indicators of the contributions of $I_r$ and $I_\phi$ to FACs, respectively. Hence, for simplicity, we will refer to $J_r$ and $J_\phi$ directly as FAC densities associated with $I_r$ and $I_\phi$, respectively, in what follows. However, it is important for the reader to bear in mind the potential ambiguity in this terminology.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** The height-integrated currents in the magnetodisk. (a) Height-integrated perpendicular current density in the global reference frame, with the colors representing the magnitude and the short lines giving the direction. (b) Schematics showing how to calculate the field-aligned currents from the divergence of magnetodisk currents. The global reference frame is used to present the involved quantities. (c) Height-integrated perpendicular current density as a function of System III longitude (horizontal axis) and radial distance (color codes).</figcaption></figure>

## 2.5. Mapping to Ionosphere

In order to be able to compare the FACs flowing out of the magnetodisk to their values observed in the ionosphere and polar magnetosphere by Juno, we map $J_\|$, along magnetic field lines to the ionosphere using the JRM33 model and the Connerney et al. (2020) magnetodisk model. We first calculate the System III latitude ($\lambda_{S3}$) of the footprints of the crossings. Then, we multiply $J_\|$ by a factor $\frac{B_\|}{B_n}$ to obtain the ionospheric FAC density $J_\|$, where $B_\|$ represents the magnitude of the magnetic fields at the ionosphere altitude. It is worth noting that, in order to valuably identify $J_\|$, as the ionospheric FACs, we are actually assuming that all perpendicular currents occur near the magnetodisk. This is rigorously true only to the extent that the carriers of these currents are confined to the magnetodisk: an assumption which is valid for the low energy components of magnetodisk particles but less and less so for higher energy particles. Furthermore, we would like to caution that, strictly speaking, the Connerney et al. (2020) magnetodisk model is only accurate for radial distances within ~30 $R_\j$. Despite this limitation, we choose to employ this model here due to the absence of better alternatives. However, it is important to acknowl-edge that this may introduce errors in $J_\|$, poleward of the main auroral oval, as suggested by Salveter et al. (2022) (see their Supplementary Text 1).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** The height-integrated currents in the magnetodisk. (a) Height-integrated perpendicular current density in the global reference frame, with the colors representing the magnitude and the short lines giving the direction. (b) Schematics showing how to calculate the field-aligned currents from the divergence of magnetodisk currents. The global reference frame is used to present the involved quantities. (c) Height-integrated perpendicular current density as a function of System III longitude (horizontal axis) and radial distance (color codes).</figcaption></figure>

## 2.5. Mapping to Ionosphere

In order to be able to compare the FACs flowing out of the magnetodisk to their values observed in the ionosphere and polar magnetosphere by Juno, we map $J_\parallel$ along magnetic field lines to the ionosphere using the JRM33 model and the Connerney et al. (2020) magnetodisk model. We first calculate the System III latitude ($\lambda_{S3}$) of the footprints of the crossings. Then, we multiply $J_\parallel$ by a factor $\frac{B_i}{B_n}$ to obtain the ionospheric FAC density $J_\parallel$, where $B_i$ represents the magnitude of the magnetic fields at the ionosphere altitude. It is worth noting that, in order to valuably identify $J_\parallel$, as the ionospheric FACs, we are actually assuming that all perpendicular currents occur near the magnetodisk. This is rigorously true only to the extent that the carriers of these currents are confined to the magnetodisk: an assumption which is valid for the low energy components of magnetodisk particles but less and less so for higher energy particles. Furthermore, we would like to caution that, strictly speaking, the Connerney et al. (2020) magnetodisk model is only accurate for radial distances within ~30 $R_\jmath$. Despite this limitation, we choose to employ this model here due to the absence of better alternatives. However, it is important to acknowl-edge that this may introduce errors in $J_\parallel$, poleward of the main auroral oval, as suggested by Salveter et al. (2022) (see their Supplementary Text 1).
Figure 3c displays $I_{\perp}$ as a function of the System III longitudes ($\psi_{s3}$) of the crossings (horizontal axis) and $r$ (color codes). One can see that $I_{\perp}$ is insensitive to $\psi_{s3}$ at any given $r$. Therefore, the effects of $\psi_{s3}$ can be neglected in most parts of this study. However, $\psi_{s3}$ indeed significantly affects the mapping to the ionosphere, as $\lambda_{s3}$ is not only a function solely of JSO coordinates but also of $\psi_{s3}$. The implication is that different crossings which are close to one another in JSO coordinates are taken at different time and thus different $\psi_{s3}$. Therefore, strictly speaking, there is no unique footprint latitude for $J_{\parallel}$. In order to reduce the effects of temporal variations between different crossings, $J_{\parallel}$ is computed statistically from an average of several crossings. This procedure works well for the southern ionosphere, where magnetic fields are regular. But it fails for mapping to the northern ionosphere due to the highly twisted magnetic fields there. Hence, in what follows, we only show $J_{\parallel}$ in the southern ionosphere. In addition, we note our procedure of projections may add some artificial latitude spread to the latitude profile of $J_{\parallel}$, as the FACs associated with the main aurora at different longitudes tends to map at different latitudes.

## 2.6. Error Analysis

To summarize, the determination of $I_{\perp}$ in this paper is influenced by three primary sources of errors: (a) statistical uncertainties ($\delta_s$; Section 3), (b) the approximation assuming the perpendicular currents in the magnetodisk align with the M-axis ($\delta_{a1}$; Section 2.2), and (c) the approximation assuming the M-axis aligns with the JSO x-y plan ($\delta_{a2}$; Section 2.3). By combining the three sources, we obtain the total relative errors in $I_{\perp}$ as $\delta_I = \sqrt{\delta_s^2 + \delta_{a1}^2 + \delta_{a2}^2}$. From the relevant discussions, we determine that $\delta_s \le 15\%$ (actually, $\le 18\%$ for $I_r$ and $\le 12\%$ for $I_a$, for simplicity, however, we take the average value here), $\delta_{a1} \sim 5\%$, and $\delta_{a2} \sim 12\%$. Consequently, the calculated $\delta_I \sim 20\%$, indicating the total errors in $I_{\perp}$ are about 1.3 times the statistical uncertainties. Additionally, in accordance with the formulas relating $J_{\parallel}$ with $I_{\perp}$, we find that the total errors in $J_{\parallel}$ should also be 1.3 times the statistical uncertainties. As the total errors are not significantly different from the statistical uncertainties, for simplicity, we only present the statistical uncertainties when discussing $I_{\perp}$ and $J_{\parallel}$ in the following sections. Nevertheless, obtaining the total errors is straightforward, just requiring a multiplication of the statistical uncertainties by a factor of 1.3.

# 3. Results

Now, we employ the definitions and methods introduced above to analyze the 404 magnetodisk crossings identified by Liu et al. (2021) and determine the currents threading through the magnetodisk.

## 3.1. Distributions of $I_r$ and $J_r$

Figure 4a shows the distribution of $I_r$ in the JSO x-y plane. Although there is a large scatter due to temporal variations, a trend of $I_r$ increasing at small $r$ and decreasing at large $r$ with increasing $r$ can be identified unambiguously. To focus on this trend, we group $I_r$ into several bins according to $\phi$. On the one hand, we would like to maximize the number of bins, to remove the effects of $\phi$. On the other hand, to get enough samples in each bin, the number of bins should be as small as possible. Moreover, the $\phi$ distributions of samples in each bin should be relatively uniform. The best compromise is to use three bins of $\phi$ spanning from 0 to 2 hr, from 2 to 4 hr, and from 4 to 6 hr. The three color-coded boxes in Figure 4a illustrate this division. Please note this division does not encompass all data points; those falling outside the defined boxes are not included in the following statistics presented in Figures 4b and 4c. To obtain the statistical radial profiles of $I_r$, we further divide the radial range from 20 $R_J$ to 100 $R_J$ into eight evenly spaced bins, and calculate the mean value of $I_r$ for each $r \times \phi$ bin. Standard uncertainties, which are presented in Figure 4b as error bars, are then determined using the formula, $\sqrt{\frac{\sum N (I_{r,d} - I_r)^2}{N(N-1)}}$, where $I_r$, $I_1, \dots, I_{r,N}$ represent $N$ measurements of $I_r$ in corresponding $r \times \phi$ bin and $\bar{I}_r$ the mean values.

Figure 4b shows the obtained spatial distribution of $I_r$. Inside $r = 60 R_J$, $I_r$ increases as $r$ increases regardless of $\phi$. Outside $r = 60 R_J$, $I_r$ is only available within 4 hr $< \phi < 6$ hr. There, $I_r$ shows a clear decreasing trend from $r = 60 R_J$ to $r = 80 R_J$. An increasing trend is observed again at $r > 80 R_J$. However, observations there might be contaminated by magnetopause currents. Thus, we do not discuss them further, although we still show them in the following figures for completeness.

Next, we derive $J_r$ from $I_r$ using the following numerical scheme: $J_r(r^*) = \frac{1}{2r^*} \frac{r_i I_{r,d} - r_{i-1} I_{r,d-1}}{r_i - r_{i-1}}$ (while maintaining the same $\phi$), where $r^* = \frac{r_i + r_{i-1}}{2}$, $r_i$ represents the center radial distances of the r-bins used to group $I_r$, and $I_{r,i}$ represents
Figure 3c displays $I_{\perp}$ as a function of the System III longitudes ($\psi_{s3}$) of the crossings (horizontal axis) and $r$ (color codes). One can see that $I_{\perp}$ is insensitive to $\psi_{s3}$ at any given $r$. Therefore, the effects of $\psi_{s3}$ can be neglected in most parts of this study. However, $\psi_{s3}$ indeed significantly affects the mapping to the ionosphere, as $\lambda_{s3}$ is not only a function solely of JSO coordinates but also of $\psi_{s3}$. The implication is that different crossings which are close to one another in JSO coordinates are taken at different time and thus different $\psi_{s3}$. Therefore, strictly speaking, there is no unique footprint latitude for $J_{\parallel}$. In order to reduce the effects of temporal variations between different crossings, $J_{\parallel}$ is computed statistically from an average of several crossings. This procedure works well for the southern ionosphere, where magnetic fields are regular. But it fails for mapping to the northern ionosphere due to the highly twisted magnetic fields there. Hence, in what follows, we only show $J_{\parallel}$ in the southern ionosphere. In addition, we note our procedure of projections may add some artificial latitude spread to the latitude profile of $J_{\parallel}$, as the FACs associated with the main aurora at different longitudes tends to map at different latitudes.

## 2.6. Error Analysis

To summarize, the determination of $I_{\perp}$ in this paper is influenced by three primary sources of errors: (a) statistical uncertainties ($\delta_s$; Section 3), (b) the approximation assuming the perpendicular currents in the magnetodisk align with the M-axis ($\delta_{a1}$; Section 2.2), and (c) the approximation assuming the M-axis aligns with the JSO x-y plan ($\delta_{a2}$; Section 2.3). By combining the three sources, we obtain the total relative errors in $I_{\perp}$ as $\delta_I = \sqrt{\delta_s^2 + \delta_{a1}^2 + \delta_{a2}^2}$. From the relevant discussions, we determine that $\delta_s \le 15\%$ (actually, $\le 18\%$ for $I_r$ and $\le 12\%$ for $I_a$, for simplicity, however, we take the average value here), $\delta_{a1} \sim 5\%$, and $\delta_{a2} \sim 12\%$. Consequently, the calculated $\delta_I \sim 20\%$, indicating the total errors in $I_{\perp}$ are about 1.3 times the statistical uncertainties. Additionally, in accordance with the formulas relating $J_{\parallel}$ with $I_{\perp}$, we find that the total errors in $J_{\parallel}$ should also be 1.3 times the statistical uncertainties. As the total errors are not significantly different from the statistical uncertainties, for simplicity, we only present the statistical uncertainties when discussing $I_{\perp}$ and $J_{\parallel}$ in the following sections. Nevertheless, obtaining the total errors is straightforward, just requiring a multiplication of the statistical uncertainties by a factor of 1.3.

# 3. Results

Now, we employ the definitions and methods introduced above to analyze the 404 magnetodisk crossings identified by Liu et al. (2021) and determine the currents threading through the magnetodisk.

## 3.1. Distributions of $I_r$ and $J_r$

Figure 4a shows the distribution of $I_r$ in the JSO x-y plane. Although there is a large scatter due to temporal variations, a trend of $I_r$ increasing at small $r$ and decreasing at large $r$ with increasing $r$ can be identified unambiguously. To focus on this trend, we group $I_r$ into several bins according to $\phi$. On the one hand, we would like to maximize the number of bins, to remove the effects of $\phi$. On the other hand, to get enough samples in each bin, the number of bins should be as small as possible. Moreover, the $\phi$ distributions of samples in each bin should be relatively uniform. The best compromise is to use three bins of $\phi$ spanning from 0 to 2 hr, from 2 to 4 hr, and from 4 to 6 hr. The three color-coded boxes in Figure 4a illustrate this division. Please note this division does not encompass all data points; those falling outside the defined boxes are not included in the following statistics presented in Figures 4b and 4c. To obtain the statistical radial profiles of $I_r$, we further divide the radial range from 20 $R_J$ to 100 $R_J$ into eight evenly spaced bins, and calculate the mean value of $I_r$ for each $r \times \phi$ bin. Standard uncertainties, which are presented in Figure 4b as error bars, are then determined using the formula, $\sqrt{\frac{\sum N (I_{r,d} - I_r)^2}{N(N-1)}}$, where $I_r$, $I_1, \dots, I_{r,N}$ represent $N$ measurements of $I_r$ in corresponding $r \times \phi$ bin and $\bar{I}_r$ the mean values.

Figure 4b shows the obtained spatial distribution of $I_r$. Inside $r = 60 R_J$, $I_r$ increases as $r$ increases regardless of $\phi$. Outside $r = 60 R_J$, $I_r$ is only available within 4 hr $< \phi < 6$ hr. There, $I_r$ shows a clear decreasing trend from $r = 60 R_J$ to $r = 80 R_J$. An increasing trend is observed again at $r > 80 R_J$. However, observations there might be contaminated by magnetopause currents. Thus, we do not discuss them further, although we still show them in the following figures for completeness.

Next, we derive $J_r$ from $I_r$ using the following numerical scheme: $J_r(r^*) = \frac{1}{2r^*} \frac{r_i I_{r,d} - r_{i-1} I_{r,d-1}}{r_i - r_{i-1}}$ (while maintaining the same $\phi$), where $r^* = \frac{r_i + r_{i-1}}{2}$, $r_i$ represents the center radial distances of the r-bins used to group $I_r$, and $I_{r,i}$ represents
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Height-integrated perpendicular current density and its divergence. (a) The height-integrated radial current density $I_r$. (b) $I_r$ in three different local time bins. (c) The radial gradient of $I_r$. Panels (d)–(f) similar to panels (a)–(c), but showing the height-integrated azimuthal current density $I_\theta$. Error bars here represent standard uncertainty.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Height-integrated perpendicular current density and its divergence. (a) The height-integrated radial current density $I_r$. (b) $I_r$ in three different local time bins. (c) The radial gradient of $I_r$. Panels (d)–(f) similar to panels (a)–(c), but showing the height-integrated azimuthal current density $I_\theta$. Error bars here represent standard uncertainty.</figcaption></figure>
corresponding mean values of $I_r$. Moreover, standard uncertainties are calculated using standard error propagation analysis applied to this numerical scheme. Figure 4c shows the obtained $J_r$, with positive and negative values indicating FACs flowing into and out of the magnetodisk (i.e., out of and into the ionospheres), respectively. Inside $r = 80 R_j$, the overall pattern of $J_r$ agrees well with the axisymmetric corotation enforcement model. Namely, at small $r$, $J_r$ is positive and flows into the magnetodisk, whereas at larger $r$, $J_r$ becomes negative and flows out of the magnetodisk. However, in contrast to this model, the total into-magnetodisk and out-of-magnetodisk FACs per radian of azimuth are highly imbalanced, with the former and latter being 25.9 ± 6.1 and 2.9 ± 5.2 MA/rad, respectively. This observation indicates that currents either off the meridian plane or beyond the radial extent considered here must be involved to reach closure. The subsequent observations presented below provide evidence supporting the former as a plausible explanation, although we cannot completely dismiss the latter due to the limitations in Juno observations' coverage.

## 3.2. Distributions of $I_a$ and $J_a$

Figures 4d–4f process and present $I_a$ and $J_a$ in a similar format as Figures 4a–4c. However, in this case, the radial range is divided into four bins (25–40 $R_j$, 40–60 $R_j$, 60–80 $R_j$ and 80–100 $R_j$), while the local-time range from $\frac{5}{6}$ hr to $5\frac{5}{6}$ hr is evenly divided into five bins. By comparing Figures 4a and 4d, we find that the magnitude of $I_a$ ($\sim 10^3$ kA/$R_j$) is about one order of magnitude larger than $I_r$ ($\sim 10^2$ kA/$R_j$), indicating $I_a$ is the dominant component in terms of magnitude. Moreover, $I_a$ has a spatial distribution similar to $I_\perp$. It also decreases as $r$ and $\phi$ increase. The dependence on $r$ and $\phi$ can be seen more quantitatively in Figure 4e, which shows $I_a$ as a function of $\phi$ in four $r$ bins.

The dependence of $I_a$ on $\phi$ indicates the existence of nonzero $J_a$. Figure 4f displays $J_a$ at different $r$. For the sake of presentation, this panel is divided into two sub-panels, with the top and bottom sub-panels showing $J_a$ outside and inside $r = 40 R_j$, respectively. Two features are noted. First, $J_a$ is negative regardless of $r$, indicating a FAC flowing out of the magnetodisk. Second, the magnitude of $J_a$ decreases sharply with increasing $r$. Consequently, $J_a$ is about twice the magnitude of $J_r$ within $20 R_j < r < 40 R_j$, but becomes secondary at larger $r$, though $|J_r|$ itself also decreases as $r$ increases.

## 3.3. Total FAC Density $J_\parallel$

Next, we combine $J_r$ and $J_a$ together to obtain $J_\parallel$. When calculating $J_r$ and $J_a$, the coordinate space of interest ([20–100] $R_j$)×[0, 6] hr) is divided into $r \times \phi$ bins with different manners ($7 \times 3$ for $J_r$ and $4 \times 4$ for $J_a$). To compute $J_\parallel$, we first re-divide the whole space into $16 \times 12$ bins, then linearly interpolate $J_r$ and $J_a$ onto the new grids, and finally add them up. Figure 5a shows $J_\parallel$ in the JSO x-y plane, with the warm and cool colors representing $J_\parallel$ flowing from the conjugate ionospheres into the magnetodisk and from the magnetodisk into the conjugate ionospheres, respectively.

The local time coverage is highly limited by the geometry of Juno orbits. Hence, here we primarily focus on the radial distributions. Figure 5b shows $J_\parallel$ as a function of $r$ within the 3.5 hr $< \phi < 4.5$ hr sector, where the whole radial extent from 20 $R_j$ to 80 $R_j$ is well covered by Juno. In terms of the sign of $J_\parallel$, the magnetodisk can be divided into three subregions:

1. 20–40 $R_j$: $J_\parallel < 0$. $J_a$ is dominant in this subregion, although $J_r$ reaches its most positive value there.

2. 40–60 $R_j$: $J_\parallel > 0$. $J_r$ and $J_a$ are positive and negative, respectively. $J_r$ is the dominant component in terms of magnitude in this subregion.

3. 60–80 $R_j$: $J_\parallel < 0$. Both $J_r$ and $J_a$ are negative there.

Interestingly, we note that Szalay et al. (2017) concluded to the existence of a similar three-sub-regions structure, based on plasma data taken by Juno/Jovian Auroral Distributions Experiment (JADE) (McComas et al., 2017) during the first science peri-jove of Juno.

Figure 5b shows that the magnitude of $J_\parallel$ is about a few kA/$R_j^2$ in general. To better capture the global balance of FACs, we calculate the total into-magnetodisk ($I_{\parallel,+}$) and out-of-magnetodisk ($I_{\parallel,-}$) FACs per radian of azimuth by integrating $J_\parallel$ over corresponding radial extent. The results are $I_{\parallel,+} = 6.8 \pm 3.2$ MA/rad and $I_{\parallel,-} = 10.4 \pm 4.3$ MA/rad. Therefore, the total into-magnetodisk FACs are approximately balanced by the total out-of-magnetodisk FACs. There are no net FACs ($I_{\parallel,+} - I_{\parallel,-} = -3.6 \pm 5.4$ MA/rad) within the error range, which also implies that the divergence of radial magnetodisk currents is well balanced by that of azimuthal currents.
corresponding mean values of $I_r$. Moreover, standard uncertainties are calculated using standard error propagation analysis applied to this numerical scheme. Figure 4c shows the obtained $J_r$, with positive and negative values indicating FACs flowing into and out of the magnetodisk (i.e., out of and into the ionospheres), respectively. Inside $r = 80~R_J$, the overall pattern of $J_r$ agrees well with the axisymmetric corotation enforcement model. Namely, at small $r$, $J_r$ is positive and flows into the magnetodisk, whereas at larger $r$, $J_r$ becomes negative and flows out of the magnetodisk. However, in contrast to this model, the total into-magnetodisk and out-of-magnetodisk FACs per radian of azimuth are highly imbalanced, with the former and latter being 25.9 ± 6.1 and 2.9 ± 5.2 MA/rad, respectively. This observation indicates that currents either off the meridian plane or beyond the radial extent considered here must be involved to reach closure. The subsequent observations presented below provide evidence supporting the former as a plausible explanation, although we cannot completely dismiss the latter due to the limitations in Juno observations' coverage.

## 3.2. Distributions of $I_a$ and $J_a$

Figures 4d–4f process and present $I_a$ and $J_a$ in a similar format as Figures 4a–4c. However, in this case, the radial range is divided into four bins (25–40 $R_J$, 40–60 $R_J$, 60–80 $R_J$ and 80–100 $R_J$), while the local-time range from $\frac{5}{6}$ hr to $5\frac{5}{6}$ hr is evenly divided into five bins. By comparing Figures 4a and 4d, we find that the magnitude of $I_a$ (~10³ kA/$R_J$) is about one order of magnitude larger than $I_r$ (~10² kA/$R_J$), indicating $I_a$ is the dominant component in terms of magnitude. Moreover, $I_a$ has a spatial distribution similar to $I_\perp$. It also decreases as $r$ and $\phi$ increase. The dependence on $r$ and $\phi$ can be seen more quantitatively in Figure 4e, which shows $I_a$ as a function of $\phi$ in four $r$ bins.

The dependence of $I_a$ on $\phi$ indicates the existence of nonzero $J_a$. Figure 4f displays $J_a$ at different $r$. For the sake of presentation, this panel is divided into two sub-panels, with the top and bottom sub-panels showing $J_a$ outside and inside $r = 40~R_J$, respectively. Two features are noted. First, $J_a$ is negative regardless of $r$, indicating a FAC flowing out of the magnetodisk. Second, the magnitude of $J_a$ decreases sharply with increasing $r$. Consequently, $J_a$ is about twice the magnitude of $J_r$ within $20~R_J < r < 40~R_J$, but becomes secondary at larger $r$, though $|J_r|$ itself also decreases as $r$ increases.

## 3.3. Total FAC Density $J_\parallel$

Next, we combine $J_r$ and $J_a$ together to obtain $J_\parallel$. When calculating $J_r$ and $J_a$, the coordinate space of interest ([20–100] $R_J$)×[0, 6] hr) is divided into $r \times \phi$ bins with different manners ($7 \times 3$ for $J_r$ and $4 \times 4$ for $J_a$). To compute $J_\parallel$, we first re-divide the whole space into 16 × 12 bins, then linearly interpolate $J_r$ and $J_a$ onto the new grids, and finally add them up. Figure 5a shows $J_\parallel$ in the JSO x-y plane, with the warm and cool colors representing $J_\parallel$ flowing from the conjugate ionospheres into the magnetodisk and from the magnetodisk into the conjugate ionospheres, respectively.

The local time coverage is highly limited by the geometry of Juno orbits. Hence, here we primarily focus on the radial distributions. Figure 5b shows $J_\parallel$ as a function of $r$ within the 3.5 hr $< \phi < 4.5$ hr sector, where the whole radial extent from 20 $R_J$ to 80 $R_J$ is well covered by Juno. In terms of the sign of $J_\parallel$, the magnetodisk can be divided into three subregions:

1. 20–40 $R_J$: $J_\parallel < 0$. $J_a$ is dominant in this subregion, although $J_r$ reaches its most positive value there.

2. 40–60 $R_J$: $J_\parallel > 0$. $J_r$ and $J_a$ are positive and negative, respectively. $J_r$ is the dominant component in terms of magnitude in this subregion.

3. 60–80 $R_J$: $J_\parallel < 0$. Both $J_r$ and $J_a$ are negative there.

Interestingly, we note that Szalay et al. (2017) concluded to the existence of a similar three-sub-regions structure, based on plasma data taken by Juno/Jovian Auroral Distributions Experiment (JADE) (McComas et al., 2017) during the first science peri-jove of Juno.

Figure 5b shows that the magnitude of $J_\parallel$ is about a few kA/$R_J^2$ in general. To better capture the global balance of FACs, we calculate the total into-magnetodisk ($I_{\parallel,+}$) and out-of-magnetodisk ($I_{\parallel,-}$) FACs per radian of azimuth by integrating $J_\parallel$ over corresponding radial extent. The results are $I_{\parallel,+} = 6.8 \pm 3.2$ MA/rad and $I_{\parallel,-} = 10.4 \pm 4.3$ MA/rad. Therefore, the total into-magnetodisk FACs are approximately balanced by the total out-of-magnetodisk FACs. There are no net FACs ($I_{\parallel,+} - I_{\parallel,-} = -3.6 \pm 5.4$ MA/rad) within the error range, which also implies that the divergence of radial magnetodisk currents is well balanced by that of azimuthal currents.
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Field-aligned current (FAC) density $J_\|$. (a) The Jupiter-Sun-Orbit x-y plane distribution of $J_\|$. Positive (warm color) and negative (cool color) values represent $J_\|$ flowing into the magnetodisk (out of the ionosphere) and out of the magnetodisk (into the ionosphere), respectively. (b) $J_\|$ within 3.5 hr < local time < 4.5 hr, as a function of the radial distance to Jupiter. (c) Similar to panel b but shows $J_\|$ mapped to the southern ionosphere. Shadowed areas in panels b and c mark the regions of positive (upward) FACs. Error bars here represent standard uncertainty.</figcaption></figure>

3.4. Ionospheric FAC Density $J_{\parallel,i}$

Finally, we map $J_\|$ to the southern ionosphere using the method described in Section 2.5. Figure 5c shows the results. The most notable feature is the positive $J_{\parallel,i}$ spanning from the ~ -70° latitude to the ~ -78° latitude. As suggested by previous observations (e.g., Grodent et al., 2003), this latitude range corresponds to the main auroral emissions. Theoretical considerations proposed before the arrival of Juno generally attribute the main auroral emission to upward FACs (e.g., Cowley & Bunce, 2001; Hill, 2001). Our results based on equatorial observations thus confirm this suggestion and provide the equatorial location corresponding to the main auroral emission, that is, ~40 $R_j < r < 60 R_j$.

However, recent observations from Juno over Jupiter's polar regions have provided a more complex picture. In particular, they reveal that the main auroral emissions can occur both in the regions of upward and downward FACs (e.g., Mauk et al., 2020; Sulaiman et al., 2022). This finding contrasts with ours presented in Figure 5c. Although we currently lack conclusive evidence to address this discrepancy, we suggest three potential explanations. First, it is noted that Juno's polar observations are typically based on individual crossings of the main auroral emissions, whereas our results are derived from the combination of all available data. Thus, the signature of downward FACs may be blurred in our analysis if the locations of downward and upward FACs vary over time and the magnitude of downward FACs is smaller than that of upward FACs (e.g., Al Saati et al., 2022; Sulaiman et al., 2022). Second, Juno's polar and equatorial observations are conducted at different local times. Thus, the observed discrepancy may be attributed to local time asymmetries. Finally, studies conducted on Earth FACs suggest that a large-scale FAC extending from the equator to low-altitude regions could fragment into several filamentary localized FACs with different orientations (e.g., Consolini et al., 2020; Golovchanskaya et al., 2006). This mechanism could explain the observed discrepancy; however, we cannot confirm its applicability to Jupiter at present.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Field-aligned current (FAC) density $J_\|$. (a) The Jupiter-Sun-Orbit x-y plane distribution of $J_\|$. Positive (warm color) and negative (cool color) values represent $J_\|$ flowing into the magnetodisk (out of the ionosphere) and out of the magnetodisk (into the ionosphere), respectively. (b) $J_\|$ within 3.5 hr < local time < 4.5 hr, as a function of the radial distance to Jupiter. (c) Similar to panel b but shows $J_\|$ mapped to the southern ionosphere. Shadowed areas in panels b and c mark the regions of positive (upward) FACs. Error bars here represent standard uncertainty.</figcaption></figure>

3.4. Ionospheric FAC Density $J_{\parallel,i}$

Finally, we map $J_\|$ to the southern ionosphere using the method described in Section 2.5. Figure 5c shows the results. The most notable feature is the positive $J_{\parallel,i}$ spanning from the ~ -70° latitude to the ~ -78° latitude. As suggested by previous observations (e.g., Grodent et al., 2003), this latitude range corresponds to the main auroral emissions. Theoretical considerations proposed before the arrival of Juno generally attribute the main auroral emission to upward FACs (e.g., Cowley & Bunce, 2001; Hill, 2001). Our results based on equatorial observations thus confirm this suggestion and provide the equatorial location corresponding to the main auroral emission, that is, ~40 $R_j < r < 60 R_j$.

However, recent observations from Juno over Jupiter's polar regions have provided a more complex picture. In particular, they reveal that the main auroral emissions can occur both in the regions of upward and downward FACs (e.g., Mauk et al., 2020; Sulaiman et al., 2022). This finding contrasts with ours presented in Figure 5c. Although we currently lack conclusive evidence to address this discrepancy, we suggest three potential explanations. First, it is noted that Juno's polar observations are typically based on individual crossings of the main auroral emissions, whereas our results are derived from the combination of all available data. Thus, the signature of downward FACs may be blurred in our analysis if the locations of downward and upward FACs vary over time and the magnitude of downward FACs is smaller than that of upward FACs (e.g., Al Saati et al., 2022; Sulaiman et al., 2022). Second, Juno's polar and equatorial observations are conducted at different local times. Thus, the observed discrepancy may be attributed to local time asymmetries. Finally, studies conducted on Earth FACs suggest that a large-scale FAC extending from the equator to low-altitude regions could fragment into several filamentary localized FACs with different orientations (e.g., Consolini et al., 2020; Golovchanskaya et al., 2006). This mechanism could explain the observed discrepancy; however, we cannot confirm its applicability to Jupiter at present.
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Radial mass transport rate. The gray dots show flow speed obtained by Kim et al. (2020) based on Juno/Jovian Auroral Distributions Experiment ion observations. The dashed line shows rigid corotation speed. The three solid curves show the flow speed derived from Equation 5, with the red, black and blue curves corresponding to the radial mass transport rate of 1,000, 1,500, and 2000 kg/s, respectively.</figcaption></figure>

# 4. Discussion

In this section we discuss our calculations of the different current systems threading the Jovian magnetodisk in the midnight-to-dawn sector in the light of their implication on global radial mass transport in the disk, and compare them with estimates of these current systems based on previous observations. Some implications of our results on our current understanding of MIT coupling at Jupiter are drawn.

## 4.1. Radial Mass Transport

As suggested by corotation-enforcement models (Cowley & Bunce, 2001; Hill, 1979; Vasyliunas, 1983), $I_r$ results from the balance of torques associated with radial currents in the equatorial plane and latitudinal currents in the ionosphere. In the equatorial plane, the electrodynamic torque exerted by the $J \times B$ force balances the net transport of angular momentum carried by radial plasma motions, which can be written as (also see Ray et al. (2014))

$$ \dot{M} \frac{d}{dr} (r^2 \omega) = 2\pi r^2 I_r B_n, \qquad (5) $$

where $\omega$ represents the angular velocity and $\dot{M}$ denotes the radial mass transport rate. We note $I_r$ has been estimated in this study, while $B_n$ has been modeled by Liu et al. (2021) as $B_n = -2.3 \times 10^4 r^{-2.58}$ nT. Therefore one can obtain either $\omega$ or $\dot{M}$ by specifying the other quantity. Here, we choose to derive $\dot{M}$ from previous observations of $\omega$.

The gray dots in Figure 6 show the flow speed derived from Juno/JADE ion measurements by Kim et al. (2020) (their Figure 6). The solid curves display the quantity $V_f = r\omega$ derived from Equation 5, or more explicitly,

$$ V_f = \frac{r_0^2}{r} \Omega_J + \frac{1}{r} \frac{2\pi}{\dot{M}} \int_{r_0}^{r} r^2 I_r B_n dr, \qquad (6) $$

where $\Omega_J$ is Jupiter's angular velocity ($1.7735 \times 10^{-4}$ rad/s) and $r_0$ is taken as 15 $R_J$, a radial distance where the magnetodisk is assumed to be in rigid corotation with the planet. One can see that the black curve corresponding to $\dot{M} = 1500$ kg/s approximately represents the median levels of the flow speed, whereas the red curve corresponding to $\dot{M} = 2000$ kg/s and the blue curve corresponding to $\dot{M} = 1000$ kg/s fit the upper and lower envelopes, respectively. From Figure 6, we conclude that a radial mass transport rate of ~1,500 kg/s matches Juno observations of the magnetodisk currents and flow speed best.

However, it might be noted the average pattern of the flow speed obtained by Kim et al. (2020) does not precisely align with the curves. In addition to temporal variations, this deviation may suggest the presence of processes that are not captured by Equation 6, including azimuthally asymmetric transportation, the existence of mass sources or sinks, and non-steady-state flow dynamics. Future investigations, particularly those integrating data from JADE, Jupiter Energetic Particle Detector Instruments (JEDI), and MAG onboard Juno, might further address this issue quantitatively.
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Radial mass transport rate. The gray dots show flow speed obtained by Kim et al. (2020) based on Juno/Jovian Auroral Distributions Experiment ion observations. The dashed line shows rigid corotation speed. The three solid curves show the flow speed derived from Equation 5, with the red, black and blue curves corresponding to the radial mass transport rate of 1,000, 1,500, and 2000 kg/s, respectively.</figcaption></figure>

# 4. Discussion

In this section we discuss our calculations of the different current systems threading the Jovian magnetodisk in the midnight-to-dawn sector in the light of their implication on global radial mass transport in the disk, and compare them with estimates of these current systems based on previous observations. Some implications of our results on our current understanding of MIT coupling at Jupiter are drawn.

## 4.1. Radial Mass Transport

As suggested by corotation-enforcement models (Cowley & Bunce, 2001; Hill, 1979; Vasyliunas, 1983), $I_r$ results from the balance of torques associated with radial currents in the equatorial plane and latitudinal currents in the ionosphere. In the equatorial plane, the electrodynamic torque exerted by the $J \times B$ force balances the net transport of angular momentum carried by radial plasma motions, which can be written as (also see Ray et al. (2014))

$$ \dot{M} \frac{d}{dr} (r^2 \omega) = 2\pi r^2 I_r B_n, \qquad (5) $$

where $\omega$ represents the angular velocity and $\dot{M}$ denotes the radial mass transport rate. We note $I_r$ has been estimated in this study, while $B_n$ has been modeled by Liu et al. (2021) as $B_n = -2.3 \times 10^4 r^{-2.58}$ nT. Therefore one can obtain either $\omega$ or $\dot{M}$ by specifying the other quantity. Here, we choose to derive $\dot{M}$ from previous observations of $\omega$.

The gray dots in Figure 6 show the flow speed derived from Juno/JADE ion measurements by Kim et al. (2020) (their Figure 6). The solid curves display the quantity $V_f = r\omega$ derived from Equation 5, or more explicitly,

$$ V_f = \frac{r_0^2}{r} \Omega_J + \frac{1}{r} \frac{2\pi}{\dot{M}} \int_{r_0}^{r} r^2 I_r B_n dr, \qquad (6) $$

where $\Omega_J$ is Jupiter's angular velocity ($1.7735 \times 10^{-4}$ rad/s) and $r_0$ is taken as 15 $R_J$, a radial distance where the magnetodisk is assumed to be in rigid corotation with the planet. One can see that the black curve corresponding to $\dot{M} = 1500$ kg/s approximately represents the median levels of the flow speed, whereas the red curve corresponding to $\dot{M} = 2000$ kg/s and the blue curve corresponding to $\dot{M} = 1000$ kg/s fit the upper and lower envelopes, respectively. From Figure 6, we conclude that a radial mass transport rate of ~1,500 kg/s matches Juno observations of the magnetodisk currents and flow speed best.

However, it might be noted the average pattern of the flow speed obtained by Kim et al. (2020) does not precisely align with the curves. In addition to temporal variations, this deviation may suggest the presence of processes that are not captured by Equation 6, including azimuthally asymmetric transportation, the existence of mass sources or sinks, and non-steady-state flow dynamics. Future investigations, particularly those integrating data from JADE, Jupiter Energetic Particle Detector Instruments (JEDI), and MAG onboard Juno, might further address this issue quantitatively.
## 4.2. Comparison With Previous Magnetodisk Current Observations

In light of their importance, electric currents in Jupiter's MIT coupling system have for two decades been broadly studied. In this subsection, we compare our results with three previous representative studies also based on magnetodisk observations: Khurana (2001), Ray et al. (2014), and Lorch et al. (2020). The first two works were based on Galileo data, whereas the third one included all Jovian missions and flybys before July 2018, including an early set of Juno orbits.

The radial profiles of $I_r$ obtained by the three studies and ours show similar unimodal structures, although the detailed location of the peak is somewhat different (ranging from $30 R_J$ to $60 R_J$). Besides, Khurana (2001), Lorch et al. (2020) and our study (also Nichols and Cowley (2022) who showed $I_r$ in some particular cases) obtain similar magnitude of $I_r$. For example, all these studies find $I_r$ of about 500 kA/$R_J$ at $r \sim 50 R_J$, $\phi \sim 6$ hr. However, the value of $I_r$ given by Ray et al. (2014) is only about half of ours. This difference might be explained by the radial mass transport rate ($\sim 1,000$ kg/s) used by Ray et al. (2014) to compute $I_\perp$, which is smaller than the value inferred from our observations ($\sim 1,500$ kg/s).

Regarding $J_r$, the results obtained by our study are slightly different from the three previous papers. We find that $J_r$ is negative within $60 R_J < r < 80 R_J$, while they showed a positive $J_r$ at all $r$ in the midnight-to-dawn sector. However, the differences are small, as all four papers show $|J_r|$ within $60 R_J < r < 80 R_J$ is close to zero.

Khurana (2001), Ray et al. (2014) and our study all investigated $J_a$ and found that it flows from the magnetodisk into the ionosphere in the midnight-to-dawn sector. Our results especially highlight the effects of $J_a$ at small $r$. Our Figure 5 shows that $J_a$ dominates $J_\parallel$ within $20 R_J < r < 40 R_J$, and that the latter is directed from the magnetodisk to the ionosphere there. In contrast, Khurana (2001) and found that $J_\parallel$ flows into the magnetodisk at all $r$. Consequently, in our picture, the into-magnetodisk FACs are roughly balanced by the out-of-magnetodisk FACs within the midnight-to-dawn sector, whereas Khurana (2001) and Lorch et al. (2020) required out-of-magnetodisk FACs at other local time (e.g., duskside) to close the into-magnetodisk FACs in the midnight-to-dawn sector.

## 4.3. Comparison With Juno Polar Observations

Finally, we compare our results with Juno observations of FACs over Jupiter's polar regions. Interestingly, the magnitude of $J_{\parallel,i}$ obtained in our study based on magnetodisk measurements is very close to those inferred from Juno polar measurements. Kotsiaros et al. (2019) analyzed magnetic field variations detected during Juno transits through polar regions. They estimated a total downward FAC integrated over azimuth of $\sim 58$ MA in the southern hemisphere and $\sim 24$ MA in the northern hemisphere, corresponding to a north-south averaged current density of $\sim 6.5$ MA/rad that roughly agrees with ours ($I_{\parallel,-} = 10.4 \pm 4.3$ MA/rad).

By combining Juno multi-instrument data and modeling tools, Wang et al. (2021) and Al Saati et al. (2022) surveyed FACs and their other defined “MIT coupling Key Parameters” comprehensively during Juno magnetic footprint traversals of the main auroral emission. They found peak values of FACs (both upward and downward) in the northern and southern hemispheres of about 1 and $2 \mu A/m^2$, respectively. These results are comparable with our results shown in Figure 5c. In addition, assuming longitudinal homogeneity of currents for simplicity, Wang et al. (2021) estimated from the perijove 3 flyby that the total FAC entering/leaving the southern hemisphere is close to $\sim 66$ MA, also consistent with our estimates.

However, two significant differences appear between our equatorial and these previous polar observations. First, the latter generally found a two-subregion structure with an upward FAC on the equatorward side and a downward FAC on the poleward side, except for a minor fraction of northern flybys for which Al Saati et al. (2022) observed the opposite trend. In contrast, our study finds an additional downward FAC on the equatorward side of the upward FAC. The absence of this additional downward FAC in polar observations might be explained by the different ranges of local time covered by Juno equatorial observations (the midnight to dawn quadrant) and polar observations (noon-dusk quadrant in the southern hemisphere, 15 to 21 LT for the northern hemisphere), as shown by Figure 11 of Al Saati et al. (2022).

Another difference appears between the latitudinal width of the main region of upward currents estimated from the different studies: Figure 6 of Al Saati et al. (2022) shows that it is on the order of 2° at most for the southern hemisphere, while in our study (Figure 5c), the full width at half maximum of our FACs projected on the southern hemisphere is on the order of 5°. This may be due to the LT variations in latitudinal width of the main auroral
## 4.2. Comparison With Previous Magnetodisk Current Observations

In light of their importance, electric currents in Jupiter's MIT coupling system have for two decades been broadly studied. In this subsection, we compare our results with three previous representative studies also based on magnetodisk observations: Khurana (2001), Ray et al. (2014), and Lorch et al. (2020). The first two works were based on Galileo data, whereas the third one included all Jovian missions and flybys before July 2018, including an early set of Juno orbits.

The radial profiles of $I_r$ obtained by the three studies and ours show similar unimodal structures, although the detailed location of the peak is somewhat different (ranging from $30 R_J$ to $60 R_J$). Besides, Khurana (2001), Lorch et al. (2020) and our study (also Nichols and Cowley (2022) who showed $I_r$ in some particular cases) obtain similar magnitude of $I_r$. For example, all these studies find $I_r$ of about 500 kA/$R_J$ at $r \sim 50 R_J$, $\phi \sim 6$ hr. However, the value of $I_r$ given by Ray et al. (2014) is only about half of ours. This difference might be explained by the radial mass transport rate (~1,000 kg/s) used by Ray et al. (2014) to compute $I_\perp$, which is smaller than the value inferred from our observations (~1,500 kg/s).

Regarding $J_r$, the results obtained by our study are slightly different from the three previous papers. We find that $J_r$ is negative within $60 R_J < r < 80 R_J$, while they showed a positive $J_r$ at all $r$ in the midnight-to-dawn sector. However, the differences are small, as all four papers show $|J_r|$ within $60 R_J < r < 80 R_J$ is close to zero.

Khurana (2001), Ray et al. (2014) and our study all investigated $J_a$ and found that it flows from the magnetodisk into the ionosphere in the midnight-to-dawn sector. Our results especially highlight the effects of $J_a$ at small $r$. Our Figure 5 shows that $J_a$ dominates $J_\parallel$ within $20 R_J < r < 40 R_J$, and that the latter is directed from the magnetodisk to the ionosphere there. In contrast, Khurana (2001) and found that $J_\parallel$ flows into the magnetodisk at all $r$. Consequently, in our picture, the into-magnetodisk FACs are roughly balanced by the out-of-magnetodisk FACs within the midnight-to-dawn sector, whereas Khurana (2001) and Lorch et al. (2020) required out-of-magnetodisk FACs at other local time (e.g., duskside) to close the into-magnetodisk FACs in the midnight-to-dawn sector.

## 4.3. Comparison With Juno Polar Observations

Finally, we compare our results with Juno observations of FACs over Jupiter's polar regions. Interestingly, the magnitude of $J_{\parallel,i}$ obtained in our study based on magnetodisk measurements is very close to those inferred from Juno polar measurements. Kotsiaros et al. (2019) analyzed magnetic field variations detected during Juno transits through polar regions. They estimated a total downward FAC integrated over azimuth of ~58 MA in the southern hemisphere and ~24 MA in the northern hemisphere, corresponding to a north-south averaged current density of ~6.5 MA/rad that roughly agrees with ours ($I_{\parallel,-} = 10.4 \pm 4.3$ MA/rad).

By combining Juno multi-instrument data and modeling tools, Wang et al. (2021) and Al Saati et al. (2022) surveyed FACs and their other defined “MIT coupling Key Parameters” comprehensively during Juno magnetic footprint traversals of the main auroral emission. They found peak values of FACs (both upward and downward) in the northern and southern hemispheres of about 1 and 2 µA/m², respectively. These results are comparable with our results shown in Figure 5c. In addition, assuming longitudinal homogeneity of currents for simplicity, Wang et al. (2021) estimated from the perijove 3 flyby that the total FAC entering/leaving the southern hemisphere is close to ~66 MA, also consistent with our estimates.

However, two significant differences appear between our equatorial and these previous polar observations. First, the latter generally found a two-subregion structure with an upward FAC on the equatorward side and a downward FAC on the poleward side, except for a minor fraction of northern flybys for which Al Saati et al. (2022) observed the opposite trend. In contrast, our study finds an additional downward FAC on the equatorward side of the upward FAC. The absence of this additional downward FAC in polar observations might be explained by the different ranges of local time covered by Juno equatorial observations (the midnight to dawn quadrant) and polar observations (noon-dusk quadrant in the southern hemisphere, 15 to 21 LT for the northern hemisphere), as shown by Figure 11 of Al Saati et al. (2022).

Another difference appears between the latitudinal width of the main region of upward currents estimated from the different studies: Figure 6 of Al Saati et al. (2022) shows that it is on the order of 2° at most for the southern hemisphere, while in our study (Figure 5c), the full width at half maximum of our FACs projected on the southern hemisphere is on the order of 5°. This may be due to the LT variations in latitudinal width of the main auroral
emission, or possibly to the slight dispersion in latitude produced by our projections of magnetodisk crossings at different longitudes (see our discussion in Section 2.4). To resolve this discrepancy, future observations of polar and equatorial currents covering the same local times will be critical.

**5. Summary**

The main focus of this paper is the determination of electric currents in Jupiter's magnetodisk in the midnight-to-dawn sector. Based on Juno observations of 404 magnetodisk crossings, we first established the spatial distribution of the height-integrated perpendicular current density $I_{\perp}$ in the magnetodisk. Then, we decomposed $I_{\perp}$ into its radial ($I_r$) and azimuthal ($I_{\phi}$) components, and calculated from their divergence their respective contributions $J_r$ and $J_{\phi}$ to the total FAC densities ($J_{\parallel} = J_r + J_{\phi}$) connecting the magnetodisk to the two conjugate ionospheres. This led us to the following main findings:

1. $I_{\phi}$ decreases from ~2000 kA/R$_{J}$ at $r \sim 20 R_{J}$ to ~400 kA/R$_{J}$ at $r \sim 100 R_{J}$, whereas $I_{r}$ is ~10$^{2}$ kA/R$_{J}$ at all $r$.

2. $J_r$ flows into and out of the magnetodisk inside and outside of $r = 60 R_J$, respectively. After integrating $J_r$ over the corresponding radial extent, the total into-magnetodisk currents (25.9 ± 6.1 MA/rad) are found to be significantly larger than the total out-of-magnetodisk currents (2.9 ± 5.2 MA/rad).

3. Within the local time range covered, $I_{\phi}$ decreases with increasing $\phi$, leading to a $J_{\phi}$ flowing out of the magnetodisk at all $r$, thus breaking the local time symmetry of the magnetosphere in this local time quadrant.

4. $J_{\parallel}$ flows out of the magnetodisk (~10 kA/R$_{J}^{2}$) inside $r = 20 R_J$ into the magnetodisk (~4 kA/R$_{J}^{2}$) between 40 $R_J$ and 60 $R_J$, and again out of the magnetodisk (~1.5 kA/R$_{J}^{2}$) outside of 60 $R_J$. The total FACs in and out of the magnetodisk nearly exactly balance, within the error range, after integrating $J_{\parallel}$ over the whole domain of study.

5. Using the estimates of $I_r$ from this study and radial profiles of the magnetic field $B_n$ orthogonal to the magnetodisk and of the plasma rotation rate $\omega$ obtained in previous studies, we have been able to estimate that the radial mass transport rate in the magnetodisk is close to ~1,500 kg/s.

**Data Availability Statement**

The authors acknowledge the use of NASA Planetary Plasma Interactions Node for obtaining the Juno/MAG data (https://pds-ppi.igpp.ucla.edu/search/view/?f=yes&id=pds://PPI/JNO-J-3-FGM-CAL-V1.0/DATA; also see Connerney (2017)). The statistical data sets can be found in Liu et al. (2021).

**References**

Al Saati, S., Clément, N., Blanc, M., Wang, Y., André, N., Louis, C., et al. (2022). Magnetosphere-ionosphere-thermosphere coupling study at Jupiter based on Juno first 30 orbits and modelling tools. *Journal of Geophysical Research: Space Physics*, 127(10), e2022JA030586. https://doi.org/10.1029/2022JA030586

Arridge, C., Kane, M., Sergis, N., Khurana, K., & Jackman, C. (2016). Sources of local time asymmetries in magnetodiscs. In *The magnetodiscs and aurorae of giant planets* (pp. 301–333). Springer.

Bagenal, F., Adriani, A., Allegrini, F., Bolton, S., Bonfond, B., Bunce, E., et al. (2017). Magnetospheric science objectives of the Juno mission. *Space Science Reviews*, 213(1), 219–287. https://doi.org/10.1007/s11214-014-0036-8

Bonfond, B., Yao, Z., & Grodent, D. (2020). Six pieces of evidence against the corotation enforcement theory to explain the main aurora at Jupiter. *Journal of Geophysical Research: Space Physics*, 125(11), e2020JA028152. https://doi.org/10.1029/2020JA028152

Caudal, G. (1986). A self-consistent model of Jupiter's magnetodisc including the effects of centrifugal force and pressure. *Journal of Geophysical Research*, 91(A4), 4201–4221. https://doi.org/10.1029/91A404201

Connerney, J., Benn, M., Bjarno, J., Denver, T., Espley, J., Jorgensen, J., et al. (2017). The Juno magnetic field investigation. *Space Science Reviews*, 213(1), 39–138. https://doi.org/10.1007/s11214-017-0334-z

Connerney, J., Timmins, S., Herceg, M., & Joergensen, J. (2020). A Jovian magnetodisc model for the Juno era. *Journal of Geophysical Research: Space Physics*, 125(10), e2020JA028138. https://doi.org/10.1029/2020JA028138

Connerney, J. E. P. (2017). Juno fluxgate magnetometer calibrated data v1.0 [Dataset]. NASA Planetary Data System. https://doi.org/10.17189/1519711

Consolini, G., De Michelis, P., Alberti, T., Giannattasio, F., Coco, I., Tozzi, R., & Chang, T. (2020). On the multifractal features of low-frequency magnetic field fluctuations in the field-aligned current ionospheric polar regions: Swarm observations. *Journal of Geophysical Research: Space Physics*, 125(5), e2019JA027429. https://doi.org/10.1029/2019JA027429

Cowley, S., & Bunce, E. (2001). Origin of the main auroral oval in Jupiter's coupled magnetosphere-ionosphere system. *Planetary and Space Science*, 49(10–11), 1067–1088. https://doi.org/10.1016/S0032-0633(00)00167-7

Delamere, P., & Bagenal, F. (2010). Solar wind interaction with Jupiter's magnetosphere. *Journal of Geophysical Research*, 115(A10), 10170–10199. https://doi.org/10.1029/2010JA015347

Delamere, P., Bagenal, F., & Steffl, A. (2005). Radial variations in the Io plasma torus during the Cassini era. *Journal of Geophysical Research*, 110(A12), A12223. https://doi.org/10.1029/2005JA011251

**Acknowledgments**

This work was supported by the National Natural Science Foundation of China 42230202 (Q.G.Z), the Major Project of Chinese National Programs for Fundamental Research and Development 2021YFA0718600 (Q.G.Z.), and the China Space Agency project D020301 (Q.G.Z). Michel Blanc expresses his sincere thanks to CNES and to the National Planetology Program of CNRS/INSU for their support to this research. The authors are very grateful to NASA and to the contributing institutions that have made the Juno mission possible, and to all institutions supporting the development, operation and data analysis of the Juno/MAG instruments. Our special thanks to Dr. John E. Connerney, Principal Investigator of the MAG experiment and to the MAG team for providing data critical to this study.
emission, or possibly to the slight dispersion in latitude produced by our projections of magnetodisk crossings at different longitudes (see our discussion in Section 2.4). To resolve this discrepancy, future observations of polar and equatorial currents covering the same local times will be critical.

**5. Summary**

The main focus of this paper is the determination of electric currents in Jupiter's magnetodisk in the midnight-to-dawn sector. Based on Juno observations of 404 magnetodisk crossings, we first established the spatial distribution of the height-integrated perpendicular current density $I_\perp$ in the magnetodisk. Then, we decomposed $I_\perp$ into its radial ($I_r$) and azimuthal ($I_\phi$) components, and calculated from their divergence their respective contributions $J_r$ and $J_\phi$ to the total FAC densities ($J_\parallel = J_r + J_\phi$) connecting the magnetodisk to the two conjugate ionospheres. This led us to the following main findings:

1. $I_\phi$ decreases from ~2000 kA/R$_J$ at $r \sim 20 R_J$ to ~400 kA/R$_J$ at $r \sim 100 R_J$, whereas $I_r$ is ~10² kA/R$_J$ at all $r$.

2. $J_r$ flows into and out of the magnetodisk inside and outside of $r = 60 R_J$, respectively. After integrating $J_r$ over the corresponding radial extent, the total into-magnetodisk currents (25.9 ± 6.1 MA/rad) are found to be significantly larger than the total out-of-magnetodisk currents (2.9 ± 5.2 MA/rad).

3. Within the local time range covered, $I_\phi$ decreases with increasing $\phi$, leading to a $J_\phi$ flowing out of the magnetodisk at all $r$, thus breaking the local time symmetry of the magnetosphere in this local time quadrant.

4. $J_\parallel$ flows out of the magnetodisk (~10 kA/R$_J^2$) inside $r = 20 R_J$ into the magnetodisk (~4 kA/R$_J^2$) between 40 $R_J$ and 60 $R_J$, and again out of the magnetodisk (~1.5 kA/R$_J^2$) outside of 60 $R_J$. The total FACs in and out of the magnetodisk nearly exactly balance, within the error range, after integrating $J_\parallel$ over the whole domain of study.

5. Using the estimates of $I_r$ from this study and radial profiles of the magnetic field $B_n$ orthogonal to the magnetodisk and of the plasma rotation rate $\omega$ obtained in previous studies, we have been able to estimate that the radial mass transport rate in the magnetodisk is close to ~1,500 kg/s.

**Data Availability Statement**

The authors acknowledge the use of NASA Planetary Plasma Interactions Node for obtaining the Juno/MAG data (https://pds-ppi.igpp.ucla.edu/search/view/?f=yes&id=pds://PPI/JNO-J-3-FGM-CAL-V1.0/DATA; also see Connerney (2017)). The statistical data sets can be found in Liu et al. (2021).

**References**

Al Saati, S., Clément, N., Blanc, M., Wang, Y., André, N., Louis, C., et al. (2022). Magnetosphere-ionosphere-thermosphere coupling study at Jupiter based on Juno first 30 orbits and modelling tools. *Journal of Geophysical Research: Space Physics*, 127(10), e2022JA030586. https://doi.org/10.1029/2022JA030586

Arridge, C., Kane, M., Sergis, N., Khurana, K., & Jackman, C. (2016). Sources of local time asymmetries in magnetodiscs. In *The magnetodiscs and aurorae of giant planets* (pp. 301–333). Springer.

Bagenal, F., Adriani, A., Allegrini, F., Bolton, S., Bonfond, B., Bunce, E., et al. (2017). Magnetospheric science objectives of the Juno mission. *Space Science Reviews*, 213(1), 219–287. https://doi.org/10.1007/s11214-014-0036-8

Bonfond, B., Yao, Z., & Grodent, D. (2020). Six pieces of evidence against the corotation enforcement theory to explain the main aurora at Jupiter. *Journal of Geophysical Research: Space Physics*, 125(11), e2020JA028152. https://doi.org/10.1029/2020JA028152

Caudal, G. (1986). A self-consistent model of Jupiter's magnetodisc including the effects of centrifugal force and pressure. *Journal of Geophysical Research*, 91(A4), 4201–4221. https://doi.org/10.1029/91A404201

Connerney, J., Benn, M., Bjarno, J., Denver, T., Espley, J., Jorgensen, J., et al. (2017). The Juno magnetic field investigation. *Space Science Reviews*, 213(1), 39–138. https://doi.org/10.1007/s11214-017-0334-z

Connerney, J., Timmins, S., Herceg, M., & Joergensen, J. (2020). A Jovian magnetodisc model for the Juno era. *Journal of Geophysical Research: Space Physics*, 125(10), e2020JA028138. https://doi.org/10.1029/2020JA028138

Connerney, J. E. P. (2017). Juno fluxgate magnetometer calibrated data v1.0 [Dataset]. NASA Planetary Data System. https://doi.org/10.17189/1519711

Consolini, G., De Michelis, P., Alberti, T., Giannattasio, F., Coco, I., Tozzi, R., & Chang, T. (2020). On the multifractal features of low-frequency magnetic field fluctuations in the field-aligned current ionospheric polar regions: Swarm observations. *Journal of Geophysical Research: Space Physics*, 125(5), e2019JA027429. https://doi.org/10.1029/2019JA027429

Cowley, S., & Bunce, E. (2001). Origin of the main auroral oval in Jupiter's coupled magnetosphere-ionosphere system. *Planetary and Space Science*, 49(10–11), 1067–1088. https://doi.org/10.1016/S0032-0633(00)00167-7

Delamere, P., & Bagenal, F. (2010). Solar wind interaction with Jupiter's magnetosphere. *Journal of Geophysical Research*, 115(A10), 10170–10199. https://doi.org/10.1029/2010JA015347

Delamere, P., Bagenal, F., & Steffl, A. (2005). Radial variations in the Io plasma torus during the Cassini era. *Journal of Geophysical Research*, 110(A12), A12223. https://doi.org/10.1029/2005JA011251

**Acknowledgments**

This work was supported by the National Natural Science Foundation of China 42230202 (Q.G.Z.), the Major Project of Chinese National Programs for Fundamental Research and Development 2021YFA0718600 (Q.G.Z.), and the China Space Agency project D020301 (Q.G.Z). Michel Blanc expresses his sincere thanks to CNES and to the National Planetology Program of CNRS/INSU for their support to this research. The authors are very grateful to NASA and to the contributing institutions that have made the Juno mission possible, and to all institutions supporting the development, operation and data analysis of the Juno/MAG instruments. Our special thanks to Dr. John E. Connerney, Principal Investigator of the MAG experiment and to the MAG team for providing data critical to this study.
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