Simulating Compressive Stream Interaction Regions during Parker Solar Probe’s First Perihelion Using Stream-aligned Magnetohydrodynamics

We used the stream-aligned magnetohydrodynamics (SA-MHD) model to simulate Carrington rotation 2210, which contains Parker Solar Probe’s (PSP) first perihelion at 36.5 R ⊙ on 2018 November 6, to provide context to the in situ PSP observations by FIELDS and SWEAP. The SA-MHD model aligns the magnetic field with the velocity vector at each point, thereby allowing for clear connectivity between the spacecraft and the source regions on the Sun, without unphysical magnetic field structures. During this Carrington rotation, two stream interaction regions (SIRs) form, due to the deep solar minimum. We include the energy partitioning of the parallel and perpendicular ions and the isotropic electrons to investigate the temperature anisotropy through the compression regions to better understand the wave energy amplification and proton thermal energy partitioning in a global context. Overall, we found good agreement in all in situ plasma parameters between the SA-MHD results and the observations at PSP, STEREO-A, and Earth, including at PSP’s perihelion and through the compression region of the SIRs. In the typical solar wind, the parallel proton temperature is preferentially heated, except in the SIR, where there is an enhancement in the perpendicular proton temperature. This is further showcased in the ion cyclotron relaxation time, which shows a distinct decrease through the SIR compression regions. This work demonstrates the success of the Alfvén wave turbulence theory for predicting interplanetary magnetic turbulence levels, while self-consistently reproducing solar wind speeds, densities, and overall temperatures, including at small heliocentric distances and through SIR compression regions.


Introduction
The Parker Solar Probe (PSP; Fox et al. 2016) successfully launched on 2018 August 12, to a high-eccentricity orbit with the perihelion at unprecedentedly low heliocentric distances.The science objectives are to study the structure and dynamics of the solar corona at both kinetic and fluid scales and to better understand the heating mechanism of the solar corona and solar wind and acceleration of energetic particles.PSP contains four instrument suites, two of which are central to our study: the Solar Wind Electrons Alphas and Protons (SWEAP; Kasper et al. 2016) investigation and the Fields Experiment (FIELDS; Bale et al. 2016), which together observe the plasma properties, magnetic field, and Alfvén wave turbulence in situ.SWEAP contains an array of electrostatic analyzers and a Faraday cup to measure the solar wind's density, temperature, and velocity in situ (Kasper et al. 2016).The FIELDS instrument suite has three magnetometers and several antennae to measure the magnetic field of the solar wind (Bale et al. 2016).These in situ observations provide high-cadence data at unprecedented heliocentric distances.The first perihelion of PSP occurred on 2018 November 6, at ≈36.5 R e , where R e equates to one solar radius (696,340 km).
The novelty of PSP's results has opened the door for many models of the heliosphere to provide context and explanation for the observations.Xiong et al. (2018) performed forward modeling of the corona and heliosphere during solar minimum conditions (Carrington rotation; CR 2060) using the 3D Conservation Element/Solution Element Magnetohydrodynamics (MHD) model (Feng et al. 2010).Riley et al. (2019) used the Magnetohydrodynamic Algorithm outside a Sphere to simulate the heliosphere for CR 2208 and 2209 from 1 R e to 1 au.These results were extended in Riley et al. (2021), where three MHD models with different levels of sophistication were compared, which concluded that a thermodynamic model, involving an empirically based treatment of the energy transport equation in the corona, most closely matched the PSP observations.Chhiber et al. (2019a) used 3D MHD modeling to characterize the sonic, Alfvén, and first plasma-β unity surfaces to determine how long PSP's trajectory would remain within those critical surfaces, which was found to depend on the solar activity, the tilt of the solar dipole, and the location of the heliocentric current sheet (HCS).Subsequently, Chhiber et al. (2019b) used the global MHD results to understand the turbulence that PSP would observe.Generally, they found that the turbulence would be "young" turbulence, which means that there would be increased fluctuations with smaller correlation length scales, as discussed in previous work (e.g., Bruno & Carbone 2013).Potential field source surface models, like Badman et al. (2020) and Szabo et al. (2020), found good agreement with the magnetic field observations and the HCS geometry during PSP's first perihelion.Wallace et al. (2022)  atmosphere Solar Model (AWSoM) to simulate the steady-state solar corona and heliosphere for the PSP perihelion, which were found to agree well with PSP observations.Unique to the van der Holst et al. (2019Holst et al. ( , 2022) ) simulations are predictions of parallel and perpendicular proton temperatures, as well as an isotropic electron temperature, which allowed for detailed physics of the thermodynamics and turbulence of the perihelion to be studied.
Here, we extend the work of van der Holst et al. (2022) by simulating the PSP's first approach with the stream-aligned MHD model (SA-MHD; Sokolov et al. 2022) and comparing to the in situ observations made at PSP and near 1 au with the Advanced Composition Explorer (ACE), Wind, and the Solar Terrestrial Relations Observatory-A (STEREO-A).Of particular interest to this study is the pair of stream interaction regions (SIRs) that formed during the deep solar minimum.SIRs form when a high-speed stream interacts with a slowspeed stream, creating a compression region in the solar wind (e.g., Belcher & Davis 1971;Richardson 2018).SIRs are most prominent at solar minimum when the tilt of the current sheet naturally leads to a pair of SIRs, as is the case in our study.The compression caused by the collision of the fast stream with the slow stream steepens as it propagates outward until it forms a shock, which often occurs well beyond 1 au (e.g., Jian et al. 2006Jian et al. , 2009;;Richardson 2018).The compression and shock regions are areas of interest because of the plasma heating, enhanced turbulence, and energization of the particles.
Before PSP, there were some in situ observations of SIRs within 1 au, from missions such as Helios 1 and 2, Pioneer, Venus Orbiter, and Venus Express (e.g., Richter & Luttrell 1986;Jian 2008).However, the majority of SIR observations are near 1 au from the Wind and ACE spacecraft.The SIRs observed during PSP's first perihelion are considered to be typical SIRs when considering the observed plasma properties and magnetic field; there is an increase in density ahead of the interface, a low-density region after the interface, a temperature increase, an entropy increase, a pressure peak at the interface, and an increase in the magnetic field magnitude (Allen et al. 2020).
In this study, we simulate CR 2210 with the SA-MHD model from Sokolov et al. (2022).We then compare these results to the PSP Encounter 1 observations and the PSP, Earth, and STEREO-A observations of the two SIRs.Our paper is organized as follows.We first provide a summary of the physics used in the AWSoM model and the results from van der Holst et al. (2022).Then, in Section 3, we summarize the stream-aligned MHD model and simulation setup.In Section 4, we show the results and discuss the two SIRs observed during this time period in comparison to the model results.Finally, in Section 5, we conclude and summarize our results.

AWSoM Model
AWSoM is a 3D, global extended MHD model describing the solar environment from the upper chromosphere to the corona and heliosphere (van der Holst et al. 2010;Sokolov et al. 2013;van der Holst et al. 2014;Sokolov et al. 2021).The computational domain is split into two components, the solar corona (SC) and inner heliosphere (IH), which are coupled together within the Space Weather Modeling Framework (Tóth et al. 2005(Tóth et al. , 2012)).The model uses low-frequency, reflectiondriven Alfvén wave turbulence to address the coronal heating and solar wind acceleration.Photospheric synoptic/synchronic maps created by the Global Oscillation Network Group (GONG) or the Helioseismic Magnetic Imager magnetograms provide the inner boundary condition to the model (van der Holst et al. 2014).AWSoM extends the physics of the classical MHD model to include collisional and collisionless electron heat conduction, coronal radiative losses, proton temperature anisotropy, Alfvén wave turbulence with reflection leading to a nonlinear turbulent cascade, and wave dissipation through linear wave damping and nonlinear stochastic heating.The proton energy partitioning can lead to large temperature anisotropies, which can then leave the plasma susceptible to kinetic instabilities.Depending on the temperature ratio and the parallel plasma β term, either firehose, mirror, or ion-cyclotron instabilities are invoked to redistribute proton thermal energy (van der Holst et al. 2014;Meng et al. 2015).In van der Holst et al. ( 2022), the Chew-Goldberger-Low (CGL) firehose instability (Chew et al. 1956) was used.Multiple modules can be coupled with AWSoM to gain more insight into the underlying physics of the system.For example, spectroscopic images can be made with the SPECTRUM module (Szente et al. 2019;Shi et al. 2022) and the charge states' composition through the heliosphere can be modeled using the nonequilibrium ionization charge state calculations (Szente et al. 2022(Szente et al. , 2023)).
The SC component of AWSoM uses a highly refined, spherical grid ranging from 1 to 24 R e with extreme grid stretching to allow for the smallest radial grid spacing being ≈0.001R e .This allows the steep density gradient in the transition region to be resolved.The transition region is artificially broadened to reduce the computational time of the SC component.There is also block-based adaptive mesh refinement (AMR) in the SC component where all blocks contain 6 × 8 × 8 internal grid cells, but vary in size by 2 n .The IH component extends from −250 to 250 R e in the X, Y, and Z directions with an empty cavity within 20 R e , where the SC domain resides.The AMR in the IH component uses 8 × 8 × 8 blocks.There is enhanced refinement where the SC and IH components couple together and in the heliospheric current sheet (van der Holst et al. 2014(van der Holst et al. , 2022)).
AWSoM has been thoroughly validated in previous work by van (1960), describes the behavior of highly conducting plasmas with frozen-in magnetic fields, such that, in a certain frame of reference, the magnetic field vector is aligned with the velocity vector at each point.The primary purpose of this model is to resolve the issues of the disconnected, "V-shaped," field lines in the low solar corona caused by excessive reconnection, highly extended closed loops, and the general distortion of the magnetic field often seen in the equatorial plane, all of which would make it difficult to solve for magnetic connectivity, which has become more important in recent years in understanding the solar wind source regions (see Figure 2 for example).The full set of equations for the SA-MHD model can be found in Sokolov et al. (2022).
The inner boundary used an ADAPT-GONG synchronic magnetic map centered on 2018 November 6 at 4:00 UT (see Figure 1).ADAPT is a flux transport model used to predict the radial magnetic field of the Sun based on supergranulation transport in the photosphere, based on the observed synoptic magnetograms (Henney et al. 2012;Hickmann et al. 2015).This produces 12 realizations and the seventh realization was used in the model, as shown in Figure 1 (van der Holst et al. 2019Holst et al. , 2022)).
At the inner boundary, the model parameters were set so that the lower transition region had an isotropic electron and parallel and perpendicular proton temperatures set at 50,000 K.The proton number density is set to 2 × 10 17 m −3 to overestimate the density to prevent chromospheric evaporation (Lionello et al. 2009).The Poynting flux to field strength ratio was optimized to 7.5 × 10 5 W m −2 T −1 .
The reduced set of MHD equations in the SA-MHD model cannot be applied to the entire solar corona, due to the slowly expanding atmosphere at the top of the transition region and in closed field regions.Thus, we apply the SA-MHD only beyond 3.5 R e , where no closed field lines are assumed.Below 2.5 R e , the regular MHD equations are solved, as described in Section 2, while in the intermediate region (2.5-3.5 R e ) the said MHD equations are complemented with special field aligning source terms, which both allow for the helmet streamer tops and ensures field alignment at r → 3.5 R e .The SC and IH components were iterated until converged to the steady-state solution in the heliographic rotating coordinate system.The model results were interpolated along the satellite trajectories for this time period.

Simulation Results and Discussion
Figure 2 demonstrates the SA-MHD solution in the IH component.As shown, all field lines follow the Parker spiral without any deviation into "V-shaped" field lines or disconnected flux, as is expected for SA-MHD.The coloring of the Z = 0 plane is the radial magnetic field, clearly showing the regions of positive and negative magnetic polarity of the plasma source regions and the location of the HCS. Figure 3 shows the connectivity of the field lines integrated from the spacecraft trajectory to the solar surface for PSP, Earth, and STEREO-A.Here, the 3D field lines are produced at a 1 hr cadence and shown colored with the solar    Figure 4 shows further plasma parameters on the HCS, which were extracted from the simulation results where the magnetic field vector went to zero and the full satellite trajectories for this time period.In the SIR compression regions, there is an increase in the number density and both the   In Figure 5, we compare the in situ observations of the total magnetic field, proton density, radial velocity, and magnetic field turbulence of PSP for the full CR, highlighting SIR 1.The magnetic field turbulence is defined as the total sum of the wave energy densities, 2 .The total magnetic field is the total of the magnetic field magnitude and the magnetic field turbulence, . The in situ data show a clear compression with elevated proton density and slow wind speed (300 km s −1 ), which progresses in time to fast (600 km s −1 ) and low proton density with a small rise in the magnitude of the magnetic field, as discussed in Allen et al. (2020).Figure 6 compares the isotropic proton temperature, parallel and perpendicular proton temperature, the proton temperature anisotropy, and β ||,p as observed by PSP, highlighting SIR 1.The in situ data show a clear spike in the isotropic proton temperature, along with the parallel and perpendicular proton temperatures during the SIR.The β ||,p term shows a distinct decrease when the spacecraft enters the high-speed stream.
In the simulation, the SIR occurs approximately three days after the observation.This is due to the SIR occurring near the end of the CR, where the magnetogram is older and, thus, less accurate.The simulation results near 2018 November 17 show a reverse compression with a forward propagating shock with a similar structure as the observation, a slight increase in the magnetic field strength and turbulence, a decrease in the proton density, an increase in the radial speed, and a sharp decrease in β ||,p .However, all the proton temperatures miss the sharp peak in the temperature observed in the compression region.
In addition, during this CR, PSP made a perihelion.The SA-MHD simulation reproduces the perihelion on 2018 November 6 well in all plasma parameters, with the exception of the total magnetic field, which is underestimated.However, the magnetic field fluctuations are well-resolved, indicating that the magnetic turbulence driving the model is well-resolved.Throughout this time period, the proton temperatures at PSP are lower than observed.This is ongoing work to better understand this discrepancy.
Figure 7 shows the magnitude of the magnetic field, proton density, radial velocity, and magnetic field turbulence comparing the in situ and SA-MHD results at Earth, highlighting each SIR.The in situ data clearly show the two SIR compression regions, which the SA-MHD simulation resolves.The density peaks occur ahead of the increase in the radial velocity, magnetic field strength, and magnetic field turbulence, showcasing the higher density region in the slow solar wind ahead of the high-speed stream.Again, the total magnetic field is underestimated, while the turbulence is better resolved but still underpredicted.
Figure 8 shows the isotropic proton temperature, the parallel and perpendicular proton temperatures, the temperature anisotropy, and the parallel plasma β term to compare the simulated results with the Wind in situ observations.The increases in the proton temperature and the individual proton temperature components are well-resolved in the simulation.The temperature anisotropy is underpredicted throughout the CR but shows an increase when the SIRs occur, indicating preferential heating in the perpendicular direction.Interestingly enough, the in situ observations of the proton temperature and temperature anisotropy show that the temperature peak associated with SIRs occurs after the characteristic velocity increase, while in the simulation, they occur concurrently.This indicates that the protons are being energized in a different part of the simulated compression region as compared to the observation.
Figure 9 compares the in situ observations from STEREO-A of the total magnetic field, proton density, radial magnetic field, magnetic turbulence, and proton temperature to the SA-MHD predictions for the full CR, highlighting the two SIRs.Overall, both structures appear to be well-resolved.In comparison to the observations, the simulation shows SIR 1 occurring <1 day late, whereas SIR 2 occurs <1 day early and underestimates both the magnetic field magnitude and, less so, the turbulence.
Figure 10 shows the relaxation time of the firehose and ioncyclotron instabilities in the SA-MHD model for each satellite trajectory for the full CR, with SIR 1 and SIR 2 highlighted at the times they occur in the simulation.In the model, the mirror (Tajiri 1967), ion-cyclotron (Kennel & Petschek 1966), and CGL firehose (Chew et al. 1956) instabilities are calculated.The relaxation time is the reciprocal of the growth rate of the instabilities (van der Holst et al. 2022).Therefore, if the relaxation time increases, the growth rate would decrease, until it is below a certain threshold where the plasma would be stable.
The mirror mode instability does not take effect during this CR, due to the plasma's large temperature anisotropy.As shown in van der Holst et al. (2022), the simulated trajectory remains within the stable plasma regime, occasionally dipping below the parallel and oblique firehose instability curves from Verscharen et al. (2016).In this work, we continue to see the firehose instability during times of spikes in the parallel proton plasma beta, at all simulated satellite trajectories, and the ion-cyclotron instability seems to be the dominant mode throughout the CR.
During the PSP's perihelion, there is a slow decrease in the relaxation time of the ion-cyclotron instability as PSP makes its perihelion and a slow increase as PSP moves radially outward.This may be due to the increased turbulence we expect to see at lower heliocentric distances (Chen et al. 2020).
During SIR 1 and SIR 2, at Earth an STEREO-A, there is a distinct decrease in the ion-cyclotron relaxation time and no evidence of the firehose instability.Thus, the heating is preferential heating to the perpendicular protons.At PSP, this decrease is less distinct but still occurring.The gradient is not   as severe because PSP is at lower heliocentric distances where there is a larger temperature anisotropy.

Conclusion
We present an extension on the work of van der Holst et al. (2022), which demonstrated that the AWSoM model matches the in situ results of PSP's first perihelion on 2018 November 6.In this work, we simulated CR 2210 with the SA-MHD model of Sokolov et al. (2022), compared it to PSP's first encounter, and extended the results to the global context at 1 au with comparison to observations from the ACE, Wind, and STEREO-A spacecraft.Within the simulated Carrington rotation, there were two SIRs captured by the spacecraft and the simulation.
Overall, the SA-MHD model captures many aspects of PSP's perihelion in detail, including many aspects of the two SIRs.Interestingly enough, the magnetic field magnitude is underestimated, while the magnetic field fluctuations are captured properly.This indicates that the model correctly implements the magnetic field turbulence near the Sun, as compared to PSP.Additionally, the proton density, solar wind speed, and β ||,p are well-resolved.The temperature anisotropy is underestimated at the perihelion, indicating preferential heating to the parallel protons.
At all spacecraft, the SIRs were captured near the time of the observation and with the correct enhancements in the velocity, magnetic field, density, and temperatures.At PSP, the SIR is less well-resolved because it occurs at the end of the CR and, thus, the end of the magnetogram where the observations are less accurate.Through these compression regions, there is an increase in the magnetic field turbulence, as shown by the simulation results.The increases in the turbulence are related to the amount of compression in these regions, as STEREO-A has a larger change in the density and a larger magnitude and sharper peak in the simulated turbulence.In general, at 1 au, the amount of turbulence observed through the compression regions remains relatively constant.That being said, the overall change in the magnitude of the magnetic field is well-predicted by the model through the SIRs.
Generally, the compression regions through the SIRs have higher proton temperature anisotropy and lower β ||,p at PSP in comparison to Earth.Throughout the simulation, the mirror instability does not get triggered; thus, the temperature anisotropy is not affected by it, as also shown in van der Holst et al. (2022).During PSP's perihelion, there is a slow decrease in the relaxation time of the ion-cyclotron instability, being at minimum at perihelion, then slowly increasing again as it moves out of perihelion.In the simulation, at Earth and STEREO-A, there is a distinct decrease in the ion-cyclotron relaxation time.This is less evident at PSP, due to it occurring at the end of the CR and in a region of higher turbulence.This paper further illustrates the success of the Alfvén wave turbulence theory for predicting interplanetary turbulence levels, while also self-consistently reproducing solar wind speeds, densities, and overall temperatures.The specific details of energy partitioning remain a work in progress involving a host of kinetic processes.
used the Wang-Sheeley-Arge model driven by the Air Force Data Assimilation Photospheric Flux Transport (ADAPT) maps to identify the source locations of the solar wind during the first two perihelions and understand how the solar wind speed changes based on the coronal model changes.van der Holst et al. (2019, 2022) used the Alfvén-Wave Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
der Holst et al. (2014), Meng et al. (2015), Sachdeva et al. (2019), and Sachdeva et al. (2021).van der Holst et al. (2014) validated the CR 2107 simulation using EUV images to check coronal temperatures and electron densities.The simulated multiwavelength EUV images can reproduce many of the morphological features in the observed images better than previous models (van der Holst et al. 2014).Meng et al. (2015) showed that the global results matched well with in situ observations at 1 au.Sachdeva et al. (2019) compared remote sensing and in situ observations during solar minimum of CR 2208 and CR 2209 to the simulation results, while Sachdeva et al. (2021) compared results at solar maximum, using CR 2123 and CR 2152.Overall, there were good levels of agreement between observations and the simulation during solar minimum (Sachdeva et al. 2019) and solar maximum (Sachdeva et al. 2021).van der Holst et al. (2019) modeled the steady-state solar wind background during the first PSP perihelion using AWSoM and van der Holst et al. (2022) improved those predictions, by including an improved energy partitioning function to partition more energy to the electrons, slowing down the solar wind, and optimizing the results using the PSP in situ observations.3. Stream-aligned MHD SA-MHD (Sokolov et al. 2022), following the work by Grad

Figure 2 .
Figure 2. Stream-aligned MHD solution in the IH component.A view of the solar equatorial plane is seen from the +Z direction colored to show the radial magnetic field component.Magnetic lines passing through the plane are shaded gray.

Figure 3 .
Figure 3. Spacecraft magnetic connectivity for (from left to right) PSP, Earth, and STEREO-A.Field lines produced at a 1 hr cadence are colored to show the radial velocity of the solar wind speed.The PSP orbital loop in the corotating frame produces a fold in the field line connectivity plane.

Figure 4 .
Figure4.HCS colored with: on the top row (from left to right), the perpendicular ion temperature, and parallel ion temperature; on the bottom row (from left to right), the proton density and ratio perpendicular to parallel pressure.The black line is the PSP trajectory, the blue line is the Earth's trajectory, and the purple line is the STEREO-A trajectory in the frame corotating with the Sun.The two SIRs are labeled in each plot for reference.

Figure 5 .
Figure 5.Comparison of the magnitude of the magnetic field, proton density, radial velocity, and magnetic field turbulence of the AWSoM model (red lines) with the PSP data (black lines).The total simulated magnetic field is the dashed line and the simulated magnetic field magnitude is the solid line.The blue box is the observed time of SIR 1 at PSP.

Figure 6 .
Figure 6.Comparison of isotropic proton temperature, parallel proton temperature, perpendicular proton temperature, proton temperature anisotropy, and the parallel plasma β for the AWSoM model (red lines) with the hourly PSP data (black lines) on log-scale.The blue box is the observed time of SIR 1 at PSP.
parallel and perpendicular proton temperatures.When comparing the energy partitioning of the proton temperature anisotropy through the SIR compression regions, the temperature anisotropy is enhanced (P ⊥ /P || > 1.1) with preferential heating of the perpendicular protons.One of the SIRs showcases a much more significant change in the plasma parameters through the compression region than the other.Allen et al. (2021) provide a catalog of the SIRs observed by PSP, on Earth, and by STEREO-A.The first SIR (hereafter SIR 1) was observed by PSP on 2018 November 15, by ACE and Wind at Earth on 2018 November 5, and by STEREO-A on 2018 October 27.For the other observed SIR (hereafter SIR 2), only Earth and STEREO-A observed the compression region during the simulated Carrington rotation.ACE and Wind observed SIR 2 on 2018 November 10 and STEREO-A on 2018 November 2. PSP observed SIR 2 outside of the simulated CR.

Figure 7 .
Figure 7.Comparison of the magnitude of the magnetic field, proton density, radial velocity, and the magnetic field turbulence (listed from top to bottom) of the AWSoM model (red lines) with the ACE data (black lines).The total simulated magnetic field is the dashed line and the simulated magnetic field magnitude is the solid line.The left set of plots contains the blue box indicating SIR 1 and the orange box indicating SIR 2. The right set of plots are zoom-ins on the features for each SIR.

Figure 8 .
Figure 8.Comparison of isotropic proton temperature, the perpendicular proton and parallel proton temperatures, the proton temperature anisotropy, and the parallel plasma β of the AWSoM model (red lines) with the Wind data (black lines).The left set of plots contains the blue box indicating SIR 1 and the orange box indicating SIR 2. The right set of plots are zoom-ins on the features for each SIR.

Figure 9 .
Figure 9.Comparison of the magnitude of the magnetic field, proton density, radial velocity, magnetic turbulence, and isotropic proton temperature between the AWSoM model (red line) and STEREO-A (black lines).The total simulated magnetic field is the dashed line and the simulated magnetic field magnitude is the solid line.The left set of plots is for the full CR with the blue box indicating SIR 1 and the orange box indicating SIR 2. The right set of plots are zoom-ins on each SIR.

Figure 10 .
Figure 10.Relaxation time of the firehose (red line) and ion-cyclotron (blue line) instabilities for PSP, Earth, and STEREO-A in the SA-MHD simulation for the full CR.The blue box indicates SIR 1, and the orange box indicates SIR 2.