Simulations of Io Plasma Torus Around Jupiter: Predictions for Lenghu Observatory

Characterizing the temporal evolution of the three‐dimensional structure of the Io plasma torus is essential to understand the dynamics of the Jovian magnetosphere. Optical imaging is a powerful tool to uncover the global torus structure. Currently, two ground‐based optical telescopes with diameters of 0.8 and 1.8 m, respectively, are under construction at the Lenghu Observatory for Planetary Science on the Tibetan Plateau of China, to systematically observe the Io plasma torus at wavelengths between 392 and 1,100 nm. These telescopes will begin to operate in the end of 2023. In order to support the inversion and scientific interpretation of the Io plasma torus images, we perform systematic simulations of the Io plasma torus in this work. First, a three‐dimensional model of electron and ion densities and electron temperature is constructed first. Then, the emissions of O+ 372.7 nm, O+ 372.9 nm, S+ 406.9 nm, S+ 671.8 nm, S+ 673.1 nm, and S++ 953.2 nm are simulated from the perspective of observing from the Earth. The simulated emission intensities and distributions are consistent with previous observations. This work provides a state‐of‐the‐art convenient tool for ground‐based telescope observation of the Io plasma torus at a specific site and time and also benefits future inversion of images to obtain physical parameters of Io plasma torus.

The IPT surrounds Io's orbit (5.9 R j , R j is Jupiter's radius, 1 R j = 71,490 km).The Jupiter's magnetosphere is relatively complex and not strictly a dipolar one (Zhang et al., 2021).But in the vicinity of the IPT, for low-precision observations, it can be approximated as a dipole field (Hill et al., 1974).Ions injected into the Jovian magnetosphere oscillate along magnetic field lines at about an equilibrium position-the centrifugal equator.Equilibrium state distributed along the field line is related to its temperature, density, etc.This equilibrium position is determined by the balance between the magnetic mirror force (with possible temperature anisotropy), the centrifugal force, and the ambipolar electric field force.These equilibrium positions are located on a surface called centrifugal symmetric surface.It is located two-thirds of the way to the magnetic equator from the rotational equator.On the Jupiter, the magnetic axis is tilted 9.6° from the rotational axis, meaning that the centrifugal axis defining the plane of the IPT is 6.4° from the rotational axis and 3.2° from the magnetic axis (P.Phipps & Bagenal, 2021;Thomas et al., 2004).
There are two main methods to observe the IPT, one is in situ satellite measurements, such as those measurements on Voyager 1 and Galileo, and the other is remote sensing observations.In situ measurements provide detailed information on the plasma parameters (density and temperature) in the IPT, while the remote sensing could capture the global view.The remote sensing observations are divided into optical (from millimeter to optical to UV) observations and radio observations according to the bands used.The first systematic observation of IPT was made by the ultraviolet spectrometer (UVS) on Voyager 1 (Broadfoot et al., 1979).Through the in situ data of Voyager 1 in the IPT, the primary ionic composition of the torus: S + , S ++ , O + , O ++ , SO 2 + and their temperature and density distributions were first uncovered (Bagenal & Sullivan, 1981;Bagenal et al., 1980Bagenal et al., , 1985)).Schneider and Thomas each compared ground-based optical images with Voyager 1 observations, highlighting inconsistencies and variability in torus conditions (Schneider & Trauger, 1995;Thomas, 1992).Eighty images of 673.1 nm emissions were analyzed by Schneider who found interesting structural characteristics along radial, local time, latitudinal, and longitudinal axes (Schneider & Trauger, 1995).The IPT observed by Galileo appears to be different from the torus observed by Voyager 1, the density was enhanced by a factor 2 between 7.8 and 5.9 R j (Bagenal et al., 1997).Kuppers reported the discovery of singly ionized chlorine in the IPT through the detection of emission at 857.9 nm (Kuppers & Schneider, 2000).During the IPT crossings by the Galileo spacecraft, using the far ultraviolet (FUV) images and long-slit spectral scans of the dawn ansae of the torus by Hubble Space Telescope (HST), the distribution and variation of the abundances of the sulfur ions at three charged states were determined (Herbert et al., 2003).In the Jovian magnetosphere, long-term optical observations of the IPT between 1997 and 2000 provided valuable information on the plasma environment and indicated that the plasma torus underwent systematic long-term variations, indicating that Io's volcanic activity has been reducing over the years.At the same time, the electron density in Jupiter's middle and outer magnetosphere also decreased during this period (Nozawa et al., 2005).Sporadic enhancement during the period was shown to be related to solar wind disturbances (Nozawa et al., 2006).Recently, the Japan Aerospace Exploration Agency's (JAXA) Hisaki spacecraft orbiting around the Earth gathered more information on the IPT.The EUV spectral range of Hisaki satellite is mainly 53-147 nm (Murakami et al., 2016;Yoshikawa et al., 2014;Yoshioka et al., 2013).Using Hisaki data, the temporal variation and spatial structure of superthermal electrons were explored.During the volcanic period, the mass input of the plasma environment around Jupiter increased by a factor of 5, and after the onset of volcanism, the hot electron fraction increased by a factor of 3.8, supporting the fact that volcanic activity can lead to an increase in the mass loading of the magnetosphere (Hikida et al., 2020).Using the latest total electron content data retrieved from the radio occultation observations on Juno spacecraft, the electron density profiles of the IPT were greatly improved (P. H. Phipps & Withers, 2017;P. H. Phipps et al., 2018P. H. Phipps et al., , 2019P. H. Phipps et al., , 2021)).To complement the observations in the visible light band, ground-based observations of the IPT were conducted with the 3.5 m telescope at Apache Point Observatory to complement Hisaki's ultraviolet observations (Schmidt et al., 2018).
Nevertheless, the IPT observations are far from enough, especially in the visible light, to fully understand its physical process.And the study of the IPT is of great significance to the research of Jupiter's magnetospheric dynamics, because it is the main source of material in Jupiter's magnetosphere, and its structure and behavior are key to know how mass, momentum, and energy are circulated within its rotation-dominated magnetosphere (Bagenal & Delamere, 2011).In order to support the observations of the Jupiter system within Planetary Exploration of China, the Institute of Geology and Geophysics, at the Chinese Academy of Sciences (IGGCAS) established the Lenghu Observatory for Planetary Science (LOPS).Benefiting from the high-quality optical observation conditioning on the Saishiteng Mountain, Lenghu, China (Deng et al., 2021), two optical telescopes are currently under construction (He et al., 2021).The first telescope is the Planetary Atmospheric Spectrum Telescope (PAST) with a diameter of 0.8 m, a field of view of 15′, an angular resolution of 0.5″, and an operation wavelength range of 280-680 nm (seven UV and four visible bands).The PAST is equipped with a Jovian coronagraph, which can shade the strong emission of the planet Jupiter and observe the weak atmosphere and plasma around Jupiter.The second telescope is the Jupiter internal structure and Io geological activity observation telescope (TINTIN).It is a high-resolution spectral imaging telescope with an aperture of 1.8 m and a spectral range of 392-1,100 nm.The core objective of the telescope is to monitor the atmospheric escape caused by Io's volcanic activity and evolution of the IPT.The telescope will also be equipped with a coronagraph with a pixel resolution of 0.25″.The combination of PAST and TINTIN telescopes will complete the multiscale monitoring from the geological activities of Io to the IPT in Jupiter space for the first time, which is important to understand the coupling between the geological activities of the planetary system and the space environment.
A state-of-the-art IPT emission model is crucial for comprehending observations of the IPT, whether conducted from ground-based or space platforms.In this paper, we will establish a spectral emission model for the IPT.We define a static physical model and calculate the spectral emission intensity.A simulation model is built to obtain a spectral image at a given time and location.The motivation of this paper is to establish a simplified empirical model of optical emissions.Therefore, the longitudinal variations are not considered.

Emission in IPT
The IPT is mainly divided into three parts, namely the cold torus, ribbon, and warm torus (see review by Bagenal & Dols, 2020).The cold torus is a collection of compact cold plasma, the density of the electron is about 1,000 cm −3 , the primary ions are S + , and the temperature of the electrons and ions are ∼1 eV.The ribbon region is the brightest in ground-based observations, and the composition of ribbon is similar to that of the cold torus, it may be derived from the ribbon by inward transport (Herbert et al., 2008).In the warm torus, the electron density is about 2,000 cm −3 , the primary ions are S ++ and O + , and the temperature of the electrons and ions are ∼5 eV and ∼100 eV, respectively.
The radiation mechanism of the IPT is that the electrons collide with corresponding ions to excite an energy level transition, thus scattering electrons.In total, the IPT radiates roughly 1 TW of power (1 TW = 10 12 W).Since electrons lose energy by collisional excitation of radiative transitions in ions, the torus accumulates more than 2 TW of energy in total (Steffl, 2005).The main means of removing energy from the torus is through radiation.Roughly, the total radiated energy is emitted in the EUV region and visible wavelengths of the spectrum.Ground-based spectroscopy and narrowband imaging can detect emissions from all three primary species of Io's inner plasma torus at visible wavelengths: S + , S ++ , and O + .The emissions of O + 372.7 nm, O + 372.9 nm, S + 406.9 nm, S + 671.8 nm, S + 673.1 nm, and S ++ 953.2 nm are the most intense band in the visible light.
In order to simulate the emission spectra of the IPT, we developed a torus emission model.The model calculates the spectral emission intensity for a given emission line.The brightness is given by (Shemansky, 1980;Shemansky & Smith, 1981) where A ji is the Einstein coefficient for spontaneous emission, f j is the fraction of ions, T e is the electron temperature, n e is the electron density, and n i is the density of ion species responsible for the emission.The unit of light intensity is Rayleigh (1 Rayleigh = 10 6 /4π photon cm −2 s −1 sr −1 ).The atomic data in this work are all calculated by the ChiantiPy (version 0.11.0)-atomicreaction and emission data base.With CHIANTI, optically thin spectra of astrophysical objects can be calculated and spectroscopic plasma diagnostics can be performed on astrophysical spectra.The database includes atomic energy levels, wavelengths, radiative transition probabilities, collision excitation rate coefficients, ionization, and recombination rate coefficients, as well as data to calculate free-free, free-bound, and two-photon continuum emission (Landi et al., 2013).Specific band transitions, i, j, and A ji values used in this study are shown in Table 1.

Electron Density and Temperature
Phipps used Juno measurements of radio occultations of the IPT to develop an electron density model, hereafter referred as Phipps2017 model (P.H. Phipps & Withers, 2017; P. H. Phipps et al., 2019).The Phipps2017 model is shown in Figure 1a and characterizes the IPT using four functions, two for warm torus, one for cold torus, and one for ribbon.It was compiled from the radio occultations of the IPT by the Juno spacecraft, and the equations are as follows (P.H. Phipps & Withers, 2017;P. H. Phipps et al., 2019): where R is distance away from the center of Jupiter in the equatorial plane, H is the scale height, and z is the distance away from the plane of the centrifugal equator.The density distribution is a symmetrical distribution about the centrifugal plane.N 1 , N 2 , N 3 , and N 4 correspond to the peak densities of the cold torus, ribbon, warm torus, and extended torus, respectively.C 1 , C 2 , C 3 , and C 4 are the central locations of the cold torus, ribbon, warm torus, and extended torus, respectively.W 1 , W 2 , W 3 , and W 4 are the radial widths of the cold torus, ribbon, warm torus, and extended torus, respectively.These input parameters are shown in Table 2.
The electron and ion temperature model uses the Voyager-based model of Bagenal (1994), shown in Figure 1b.

Ion Density
Bagenal (1994) established the one-dimensional ion density model in the centrifugal equator using the O4 magnetic field (Acuna et al., 1983) with current sheet based on the Voyager 1 observations.In order to extend the ion density from one dimension to two dimensions, Bagenal made the following assumptions (Bagenal & Sullivan, 1981): 1.The full system is taken to be in a steady state, as diffusion typically takes several days, and bounce periods for cold heavy ions range from seconds to several hours.Ion Wavelength (nm) Transition i j A ij S + 673.1 3s 2 3p 3 4S 3/2 -3s 2 3p 3 2D 3/2 1 2 6.320e−04 S + 671.8 3s 2 3p 3 4S 3/2 -3s 2 3p 3 2D 5/2 1 3 2.195e−04 S + 406.9 3s 2 3p 3 4S 3/2 -3s 2 3p 3 2D 2. Since Coulomb collisions are relatively infrequent except in the coldest and densest parts of the torus, Coulomb forces have also been ignored.3. The two components that the major thermal electrons and the minor hot electrons are considered separately, and any coupling between them is minimal.4. Furthermore, any particles lost to Jupiter's ionosphere as a result of precipitation are also ignored in this steady-state model.
Under the above assumptions and considering the balance of centrifugal force and electric field force along the field line, the effect of gravity and magnetic mirror force is ignored, because it is known that gravity and magnetic mirror force are far smaller than centrifugal force and electric field force.Bagenal (1994) obtained the formula for the change of particles along the magnetic field line (hereafter referred as Bagenal1994 model).For electrons: and for ions: where q is the electron charge, k is the Boltzmann constant, T i is the ion temperature, Φ is the electric potential, m i is the ion mass, r denotes the radial distance, θ represents the magnetic latitudes, α is the angle that the centrifugal symmetry surface inclined to the magnetic equatorial plane, Z is the ion charge state, and Ω is the rotation rate of Jupiter.The potential difference in Equations 3 and 4 is expressed as where s 0 represents the particle density and electrostatic potential of centrifugal equatorial, s means the density and electrostatic potential of a given position along the magnetic field in the iteration process.The effective ion mass (m + ) is defined as where m e is the electron density, m j , n j , Z j , and C j (=T e /T j ) are the mass, number density, charge state, and temperature ratio for the jth ion, respectively.
Using the electron density model of Phipps and the one-dimensional ion distribution obtained by Bagenal, the two-dimensional ion density distribution in System III coordinate system is obtained through two-dimensional extension as shown in Figure 2.
The electrons exhibit limited susceptibility to centrifugal forces due to their relatively low mass, thereby experiencing predominant restraint arising from electrostatic interactions with ions.Ions possessing reduced mass and elevated charge states manifest heightened susceptibility to displacement from the centrifugal equatorial plane in conjunction with electrons.Consequently, their density profile along the magnetic field lines exhibits an enlarged effective scale height (Bagenal, 1994).The dominant ion (e.g., S + in the cold torus) dominates the determination of the ambipolar electric potential.Lighter ions (e.g., O + ) or ions with a higher charge state (e.g., S ++ ) will be pulled away from the equator by this electric potential.Bagenal and Sullivan (1981) showed how this leads to two peaks of O ++ above and below the centrifugal equator in the cold torus.
Compared with the Bagenal1994 model, the two-dimensional ion density obtained by this model is slightly different.This is because we adopted different electron density model and magnetic field model.The ion density is more discretely distributed along the magnetic field lines.

Three-Dimensional Distribution
Having obtained the density distribution in the two-dimensional meridian plane in the previous section, we need to extend the two-dimensional density to the entire space of Jupiter.The actual situation of the IPT is complicated, however, and is limited by current global observation of the IPT.The motivation of this paper is to establish a simplified empirical model of optical emissions in the IPT.Therefore, the longitudinal variations are not considered.So first, we have to obtained the intersection line between each meridian plane and the centrifugal equatorial plane, and the three-dimensional space construction is shown in Figure 3.Then, the intersection line is taken as the equilibrium point, and it is extended southward and northward along the magnetic field line.
The state-of-the-art magnetic field model of the Juno reference model through Perijove 33 (JRM33; Connerney et al., 2022) is used to trace the field lines during above calculations (James et al., 2023).For the Bagenal1994 model, the simulation range in the radial direction of Jupiter is 5-10 R j , which is roughly in line with the range of the electron model of Phipps2017.As for the simulation range in the latitude direction, the electron density from Phipps2017 model tends to zero at the position of 2 R j off the equator.Since the mass of electrons is much smaller than that of ions, the degree of dispersion distribution of ions along magnetic field lines is always smaller than that of electrons.Therefore, the density of ions and electrons is within 2 R j in the simulated latitudinal direction, and the converted latitude angle is about 25°.The precision in the longitudinal direction is 0.1 radians.Figure 4 shows the distributions of the ion and electron densities obtained in the magnetic equatorial plane.The particle densities are rotationally symmetric in the centrifugal equatorial plane, while they are asymmetric in the magnetic equatorial plane, with the peak densities at the direction of the intersection line between the magnetic equatorial plane and the centrifugal symmetry plane.At the same time, from Figure 4, we can also see that S + ions and electrons are mainly concentrated in 5-5.5 R j , S ++ and O + ions are mainly concentrated around 6 R j , S +++ ions are mainly concentrated in the 6-7 R j region, and O ++ ions are mainly concentrated in 7-8 R j consistent with physical chemistry models.As Jupiter rotates around its axis of rotation, we can see periodic oscillations of the IPT due to the angle between the torus and the equatorial plane of rotation.

Emission Integration
Having obtained the three-dimensional distributions of the quantities in Equation 1, a line-of-sight (LOS) integration procedure is then designed to obtain the two-dimensional images of the IPT in the perspective of a ground-based telescope at LOPS based on a telescope coordinate system (TCS).In the TCS, the projection plane of the simulated image is perpendicular to the Lenghu-Jupiter line (Z TCS axis, pointing from telescope to Jupiter's center, which is also the optical axis of the telescope).The X TCS (vertical in the image) and Y TCS (horizontal in the image) axes are defined in the following manner.To ensure that the rotation axis of Jupiter is always in the vertical direction of the image, the Y TCS axis is defined as the product between Z-axis and Jupiter's rotation axis, and finally the X TCS axis is determined according to the right-hand law.A series of coordinate system transformations are then required for the LOS integration.Before doing this, a local horizontal coordinate system (LHCS) is set up.In LHCS, the Z LHCS axis points toward the local zenith, the Y LHCS axis points toward the north in the local meridian plane and is perpendicular to the Z LHCS axis, and the X LHCS axis completes the right-handed orthogonal set.The schematic diagram of coordinate system (TCS and LHCS) is shown in Figure 5a.Based on the geographic longitude and latitude of the telescope at LOPS, a transformation matrix between the IAU-EARTH and the LHCS can be determined.Then, the transformation between IAU-JUPITER (equal to right-handed System III) and IAU-EARTH coordinate systems can be determined based on planetary ephemeris (Shi et al., 2021).Finally, we can obtain the transformation matrices among IAU-JUPITER, IAU-EARTH, LHCS, and TCS.
The imaging region in the TCS is −4 R j to 4 R j along X TCS axis, −7 R j to 7 R j along Y TCS axis, and −10 R j to 10 R j along Z TCS axis, respectively, with a spatial resolution of 0.1 R j in the xy plane of TCS and a integration step size of 0.1 R j along the LOS.For each pixel in the xy plane of TCS, the vector of LOS can be determined according The dark orange sphere is Jupiter.The blue plane is centrifugal symmetry surface, and the yellow plane is magnetic equatorial plane.The red straight line is the magnetic axis, and the red curve is the magnetic field line.The red arrow represents that the point on the white straight line is taken as the point of known density and is superposed to the south and north along the magnetic field line.The same calculation process can be applied on arbitrary meridian plane.
to the coordinates of X TCS and Y TCS .Then, the LOS vector can be transformed into IAU-JUPITER and finally to Jupiter's centrifugal equator coordinate system and Jupiter's magnetic coordinate system, in which the ion and electron densities, temperatures, and corresponding values of A ji and f j can be calculated with the methods introduced in previous sections.The calculation process is shown in Figure 5b.

Simulation Results
In this section, we present the simulation results of the IPT at different wavelengths and compare with observations.For each simulation, once the time, geographic information of the site, and the wavelength of the emission are set, an image of the IPT can be obtained through the steps described in above sections.Figure 6 shows the IPT images at six wavelengths at 00:00:00 UT on 1 January 2022 simulated at Lenghu site.At various wavelengths from S + , we can observe a clear annular structure with two peaks on each side of the torus.This is due to the density of S + presenting two peaks.However, in the bands from S ++ and O + , the annular structure is not prominent, which is likely caused by the different degrees of ion distribution along the magnetic field lines in space.Nevertheless, in all bands, the maximum intensity occurs on the dawn and dusk sides.The highest radiation intensity occurs in the 673.1 nm (Figure 6e) from the S + , followed by the 671.8 nm (Figure 6f).
In order to evaluate the accuracy of the model, we compared the calculation results of the model with Catalina telescope observations on 3-5 February 1991.We simulated the IPT images at times listed in Table 3 and calculated the average radial profiles as shown in Figure 7 (Schneider & Trauger, 1995).In comparison with the observational data from Schneider, the positions of the ansae on the dusk and dawn sides correspond well, which may be attributed to the good correction effect of the newer magnetic field model (JRM33) used in the model for the positions of the ansae.However, the dawn and dusk asymmetry of the intensity is not well described, because our model does not consider the existence of the dawn .9nm, from S + at (c) 406.9 nm, (d) 671.8 nm and (e) 673.1 nm, and from S ++ at (f) 406.9 nm.Note that positive R j in the horizontal direction denotes the dusk side, while negative R j denotes the dawn side.All the following images are drawn in this manner.
to dusk electric field.The present study has not taken into account the diurnal electric field, as it constitutes a temporally varying quantity.In subsequent investigations, endeavors can be made to quantitatively reconcile the model that neglects the diurnal electric field with empirically observed outcomes, thus facilitating an inquiry into the magnitude and orientation of the diurnal electric field.
In order to further qualitatively verify the performance of the newly constructed IPT emission model at different phases of Jupiter rotation, the simulated images are compared with real-time images taken by the Tohoku 60-cm telescope at Haleakala Observatory in Hawaii on 14 June 2020.The telescope was equipped with a digital micromirror device (DMD) coronagraph to observe S + emissions at 671.6 and 673.1 nm from the IPT since 2018.The DMD occultation reduced the light from the disk of Jupiter and Galilean moons by 2.6 × 10 −3 (Kagitani et al., 2020).The comparisons are shown in Figure 8.During the period from 09:30 to 14:30 UT, Jupiter rotated about a half cycle and the shape of IPT as viewed from the Earth changed from flattened to ellipse.As the centrifugal symmetry surface rotates with Jupiter and contains the Earth-Jupiter line, the IPT becomes a line due to the projection effect.The simulated shapes of the IPT are not strictly the same as those observed by the Tohoku 60-cm telescope, possibly because the IPT is not always strictly aligned with the centrifugal symmetric surface.
Due to the impact of other moons in the observed images, it is hard to quantitatively compare the emission intensity.We just quantitatively compared the structure of the IPT, including the peak locations in the dawn (L dawn ) and dusk (L dusk ) and the tilt angle of the torus as listed in Table 4. Generally, the model consistent well with the observations.If further dynamic model of the IPT plasmas could be available in future, the IPT emission model can be used to simulate the dynamic evolution of the IPT.

Conclusion and Discussion
In this paper, a static empirical model of the IPT was established to calculate the three-dimensional density and temperature for ions and electrons in the IPT.The IPT model was then used to simulate the emission intensity distributions and temporal evolutions of different ion spices in perspectives of ground-based telescopes.The simulated emission intensity distributions are in good agreement with ground-based telescope observations.Since the IPT model is symmetric about the centrifugal surface, the east-west asymmetry of the IPT was not well depicted as observed by telescopes.Nevertheless, this work provided a convenient tool for fast simulation of the emission distribution of the IPT and could well guide ground-based telescope observations.This model can also allow the inversion of the IPT images observed by telescopes in the future.
In comparison to Colorado Io Torus Emissions Package (CITEP; Taylor et al., 1995), our model incorporates the latest electron density and magnetic field data, both derived from Juno observations, and utilizes the most up-to-date atomic database sourced from the widely recognized CHIANTI database.The absolute emission intensity relies heavily on the volume emission rate, as provided by the atomic database, electron temperature, and density, while the two-dimensional emission distribution is predominantly influenced by factors such as the magnetic field model, ion composition, temperature, and their longitudinal distribution.Employing the most recent data for these variables has notably improved our model's performance, leading to better alignment with observations.In the near future, we firmly believe that our new model, with the aid of the latest computational resources and machine learning techniques, coupled with high-quality observational data of sufficient resolution in future, has the potential to derive the longitudinal distribution of temperature and density for specific ions from LOS-integrated 2D images, to achieve image inversion in future studies.Furthermore, we are exploring the integration of artificial intelligence algorithms into our model to achieve higher efficiency.At the same time, we will have two optical telescopes that can observe IPT, including PAST (low resolution and large field of view, currently under commissioning) and TINTIN (high resolution and small field of view, begins to operate in the late 2024).The PAST can observe not only the IPT at 673.1 nm but also the Jovian neutral nebula at specific wavelengths (such as 630.0 and 589.3 nm).The combination of PAST and TINTIN could provide long-term monitoring of the IPT and neutral nebula to investigate their evolutions at different time scales.At the same time, there is a midinfrared solar telescope on the Saishiteng Mountain in Lenghu, which can observe the eruption of Io's volcanoes.The joint observation of the three telescopes will establish the complete mass and energy transportation chain from the eruption of Io's volcanoes to the escape of the atmosphere and then to the formation of the plasma surrounding Jupiter.This will complete the multiscale monitoring from the geological activities of Io to plasma environment in Jupiter's space and promote the understanding of the coupling process between the geological activities of Io and Jupiter's space environment.3. The blue line is the spectral image taken by the telescope (Schneider & Trauger, 1995), while the yellow line is the result of this model.

Figure 1 .
Figure 1.(a) The density model of the Io plasma torus from P. H. Phipps and Withers (2017) and (b) the electron and ion temperature from Bagenal (1994).

Figure 3 .
Figure3.Schematic diagram of 3D space expansion.The dark orange sphere is Jupiter.The blue plane is centrifugal symmetry surface, and the yellow plane is magnetic equatorial plane.The red straight line is the magnetic axis, and the red curve is the magnetic field line.The red arrow represents that the point on the white straight line is taken as the point of known density and is superposed to the south and north along the magnetic field line.The same calculation process can be applied on arbitrary meridian plane.

Figure 5 .
Figure 5. (a) Illustration of the telescope coordinate system (TCS) and local horizontal coordinate system (LHCS), Z IAU_J is the Z axis direction of IAU-JUPITER coordinate system and also the direction of Jupiter's rotation axis.Blue dotted line plane perpendicular to Z TCS (Lenghu-Jupiter line), Y TCS is the projection of Z axis direction of IAU-JUPITER coordinate system (Jupiter's rotation axis) on this plane.(b) The schematic diagram of spectral emission model.The red, blue sphere represent Jupiter and Earth.The black spot on the Earth is the location of the Lenghu.The ring represents the Io plasma torus.The plane in the figure passes through the center of Jupiter and is perpendicular to the Lenghu-Jupiter center line.

Figure 6 .
Figure6.The spectral image obtained by the model for the viewing geometry corresponding to 00:00:00 on 1 January 2022.The X-axis is the centrifugal distance, and the Y-axis is the vertical height from the centrifugal plane.Shown above are from O + at (a) 372.7 nm and (b) 372.9 nm, from S + at (c) 406.9 nm, (d) 671.8 nm and (e) 673.1 nm, and from S ++ at (f) 406.9 nm.Note that positive R j in the horizontal direction denotes the dusk side, while negative R j denotes the dawn side.All the following images are drawn in this manner.

Figure 7 .
Figure 7.The average radial profiles of the torus at 673.1 nm.Selected time is shown in Table3.The blue line is the spectral image taken by the telescope(Schneider & Trauger, 1995), while the yellow line is the result of this model.

Figure 8 .
Figure 8.Comparison between telescope observation data and simulation results at 673.1 nm emission line on 14 June 2020.The images observed by the Tohoku 60-cm telescope are shown in the left panels (Kagitani et al., 2020) and the corresponding simulated images are shown in the right panels.In all the images, Jupiter is located at the center with the rotation axis in the vertical direction.

Table 2 Input
Phipps et al., 2019)lectron Density Model (P.H.Phipps et al., 2019) Tick means to calculate the value of dawn or dusk side at this time.

Table 3
Input Time

Table 4
Morphological Comparison Between Model and Observation