# PIC Simulations of Microinstabilities and Waves at Near-Sun Solar Wind Perpendicular Shocks: Predictions for Parker Solar Probe and Solar Orbiter

Zhongwei Yang, Ying Liu, Shuichi Matsukiyo, Quanming Lu, Fan Guo, Mingzhe Liu, Huasheng Xie, Xinliang Gao, Jun Guo

► To cite this version:

Zhongwei Yang, Ying Liu, Shuichi Matsukiyo, Quanming Lu, Fan Guo, et al., PIC Simulations of Microinstabilities and Waves at Near-Sun Solar Wind Perpendicular Shocks: Predictions for Parker Solar Probe and Solar Orbiter. The Astrophysical Journal Letters, 2020, 900 (2), pp.L24. 10.3847/2041-8213/abaf59. hal-03257910

HAL Id: hal-03257910

https://hal.science/hal-03257910v1

Submitted on 1 Aug 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# PIC Simulations of Microinstabilities and Waves at Near-Sun Solar Wind Perpendicular Shocks: Predictions for Parker Solar Probe and Solar Orbiter

Zhongwei Yang<sup>1,2,3</sup>①, Ying D. Liu<sup>1,4</sup>①, Shuichi Matsukiyo<sup>5</sup>①, Quanming Lu<sup>2</sup>①, Fan Guo<sup>6</sup>①, Mingzhe Liu<sup>7</sup>①, Huasheng Xie<sup>8,9</sup>, Xinliang Gao<sup>2</sup>, and Jun Guo<sup>10</sup>

## Abstract

Microinstabilities and waves excited at moderate-Mach-number perpendicular shocks in the near-Sun solar wind are investigated by full particle-in-cell simulations. By analyzing the dispersion relation of fluctuating field components directly issued from the shock simulation, we obtain key findings concerning wave excitations at the shock front: (1) at the leading edge of the foot, two types of electrostatic (ES) waves are observed. The relative drift of the reflected ions versus the electrons triggers an electron cyclotron drift instability (ECDI) that excites the first ES wave. Because the bulk velocity of gyro-reflected ions shifts to the direction of the shock front, the resulting ES wave propagates oblique to the shock normal. Immediately, a fraction of incident electrons are accelerated by this ES wave and a ring-like velocity distribution is generated. They can couple with the hot Maxwellian core and excite the second ES wave around the upper hybrid frequency. (2) From the middle of the foot all the way to the ramp, electrons can couple with both incident and reflected ions. ES waves excited by ECDI in different directions propagate across each other. Electromagnetic (EM) waves (X mode) emitted toward upstream are observed in both regions. They are probably induced by a small fraction of relativistic electrons. Results shed new insight on the mechanism for the occurrence of ES wave excitations and possible EM wave emissions at young coronal mass ejection-driven shocks in the near-Sun solar wind.

*Unified Astronomy Thesaurus concepts: Plasma astrophysics (1261); Space plasmas (1544); Plasma physics (2089); Interplanetary shocks (829)*

## 1. Introduction

Collisionless shocks are of fundamental interests in astrophysics and space physics. They have been proposed as primary mechanisms for energy dissipation (e.g., Richardson et al. 2008; Parks et al. 2012) and particle acceleration (e.g., Zank et al. 2006; Guo & Giacalone 2010). Observational studies suggest that large solar eruptions are often accompanied with shocks driven by corona mass ejections (CMEs). They are rich in various plasma waves (Wilson et al. 2007; Liu et al. 2018) and usually associated with type II radio bursts (Bale et al. 1999; Liu et al. 2009). Previous investigations reveal that there are two main mechanisms for high-frequency electromagnetic (EM) wave emissions (e.g., O or X modes) at collisionless shocks. One is synchrotron maser instability (SMI), which usually refers to an electromagnetic wave emission mechanism at relativistic magnetized shocks (Hoshino & Arons 1991; Plotnikov & Sironi 2019). This mechanism is in favor of a positive slope in an electron velocity distribution function (VDF) perpendicular to the ambient magnetic field, such as due to a loss cone or ring velocity distribution, which can become a free energy source for wave emissions. Essentially the same mechanism may operate as long as weakly relativistic anisotropic electrons exist

(even down to a few keV) in the case of auroral electrons (Wu & Lee 1979). So it may indeed be a potential candidate for radio emissions at nonrelativistic CME-driven shocks associated with enhanced electron intensities from <40 keV to about 200 keV (Liu et al. 2008). The other is the nonlinear three-wave interaction (Pulupa et al. 2010; Guo et al. 2017). First, suprathermal and nonthermal electrons are produced in the shock. Then, these energetic electrons stimulate the growth of high-frequency electrostatic (ES) waves, such as Langmuir waves. These ES waves interact with each other in the nonuniform background solar wind or rippling shock front to produce the observed EM emissions due to the nonlinear wave interactions (Umeda 2010; Ganse et al. 2012). However, it is still unclear which mechanism and what wave mode plays a major role at CME-driven shocks near the Sun.

Electrostatic waves, such as (1) Langmuir waves and their higher harmonics (Bale et al. 1999; Thejappa & MacDo wall 2019) and (2) electron cyclotron harmonic waves (Bernstein waves; Wilson et al. 2010; Goodrich et al. 2018), have been widely observed at shocks by spacecraft (ISEE 1, WIND, STEREO, CLUSTER, MMS, etc.) around 1 au. They are commonly believed to accelerate electrons and provide possible free energy sources of EM emissions at shocks,

<footnote n="1">¹ State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China;
*zwyang1984@gmail.com*, liuxying@swl.ac.cn</footnote>

<footnote n="2">² CAS Key Laboratory of Geospace Environment, Chinese Academy of Sciences, University of Science and Technology of China, Hefei, 230026, People's Republic of China</footnote>

<footnote n="3">³ Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, People's Republic of China
⁴ University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China</footnote>

<footnote n="5">⁵ Faculty of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga, Fukuoka, 816-8580, Japan</footnote>

<footnote n="6">⁶ Los Alamos National Laboratory, Los Alamos, NM 87545, USA</footnote>

<footnote n="7">⁷ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, F-92195 Meudon, France</footnote>

<footnote n="8">⁸ Hebei Key Laboratory of Compact Fusion, Langfang, 065001, People's Republic of China</footnote>

<footnote n="9">⁹ ENN Science and Technology Development Co., Ltd., Langfang, 065001, People's Republic of China</footnote>

<footnote n="10">¹⁰ College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, People's Republic of China
*Received 2020 May 21; revised 2020 August 12; accepted 2020 August 14; published 2020 September 4*</footnote>
magnetopause, and solar flares (Graham et al. 2018; Horký et al. 2018; Henri et al. 2019). Despite this, there is a lack of in situ observations accurately determining shock microstructures and associated plasma waves excited in the near-Sun solar wind. Bale et al. (2016) extracted some solar wind parameters in the near-Sun conditions based on data from HELIOS and models, which give us some inspiration. The study of wave properties at shocks under the near-Sun solar wind condition could help understand ES wave excitations and EM wave emissions at young CME-driven shocks observed by Parker Solar Probe (PSP) or Solar Orbiter near the perihelion at later encounters. Near the Sun, we expect a strong magnetization and relatively low values of plasma $\beta$ (Bale et al. 2016) that may affect characteristics of waves excited at the shock front. This is our motivation to do the work.

Umeda et al. (2012a) directly extract the field components of the wave from a 2D shock simulation (ambient $B_0$ in-plane case) with a relatively small box along the shock front (~1c/$\omega_{pi}$, where c/$\omega_{pi}$ is the ion inertial length). They identify whistler waves excited by modified two-stream instability (Matsukiyo & Scholer 2003) by using a dispersion relation analysis of fluctuating electromagnetic field components $\delta B$ and $\delta E$. Based on this method, we directly extract high-resolution fluctuating electromagnetic field components from 2D large-scale shock simulations (ambient $B_0$ out-of-plane case, including the complete particle gyromotion perpendicular to the background $B_0$), and check the wave modes from the leading edge of the foot to the ramp. Furthermore, observed linear waves are confirmed by a linear theory tool (BO, a new version of PDRK; Xie 2019).

This Letter is organized as follows. We present a description of the simulation model and setup in Section 2. The shock front wave analysis is presented in Section 3, and we conclude with a summary in Section 4 and discuss the implications of our results for PSP and Solar Orbiter.

## 2. Simulation Model

We carry out shock simulations using an open-source electromagnetic particle-in-cell (PIC) code named EPOCH (Arber et al. 2015) with a normalization that is the same as that used in our previous works (Yang et al. 2016, 2018; Lembege et al. 2020) to simulate the waves excited at moderate-Mach-number, perpendicular shocks. In this Letter, collisionless shocks were generated by the so-called injection method (Matsukiyo & Scholer 2012; Yang et al. 2015), in which particles are injected from one side of the simulation boundary (at $X=0$) at super-Alfvénic speed $V_{\text{inj}} = 6V_A$ in the $+X$ direction and specularly reflected at the other side of the simulation boundary ($X = L_x$). The shock propagates in the $-X$ direction in the present downstream rest frame. The periodic boundary condition is applied in the $Y$ direction. The number of grid cells is $n_x \times n_y = 25,600 \times 2000$. The spatial resolution $\Delta X = \Delta y = 0.0025c/\omega_{pi}$. The box size along the shock surface is $5c/\omega_{pi}$. The ion-to-electron mass ratio $m_i/m_e$ is 100, and the particle number per cell is 50. In the 2D simulation, the ambient magnetic field $B_0$ is along Z and strictly perpendicular to the $X-Y$ simulation plane (i.e., the shock normal angle $\theta_{Bn}$) is nearly 90°. This $B_0$ configuration is similar to that in previous simulations (Amano & Hoshino 2009; Matsumoto et al. 2013). Based on fitting methods similar to Bale et al. (2016), plasma parameters in the near-Sun solar wind (at about $10R_s$) can be estimated by using PSP data

observed around its perihelion in the first three encounters at about $36R_s$. The magnetic field $B \sim 591$ nT, the proton density $N_p \sim 1932$ cm$^{-3}$, the proton temperature $T_p \sim 45.3$ eV, and the Alfvénic velocity $V_A \sim 290$ km s$^{-1}$. $T_e/T_i = 3$ is adopted based on previous observations from HELIOS (Liu et al. 2005) and PSP (Maksimovic et al. 2020). The speed of fast CME-driven shocks at $10R_s$ can often exceed $1500 \sim 2200$ km s$^{-1}$ (Zhao et al. 2019), and a fraction of them have extremely high speeds (~3300 km s$^{-1}$; Liu et al. 2013, 2019). Their corresponding average $\bar{M}_A$ is 5 ~ 9 and the extreme ones can reach 10 ~ 15. Such Mach numbers are much larger than those observed at interplanetary (IP) shocks at 1 au (Wilson et al. 2007; Liu et al. 2018). In this simulation, the Alfvénic Mach number of the shock is about 7 ~ 9. Plasma beta values $\beta_e = 0.3$ and $\beta_i = 0.1$ are employed for the real solar wind condition. We adopted the upstream magnetization $\omega_{pe}/\Omega_{ce} \sim 7.8$, on the order of 10 for the near-Sun solar wind conditions. In addition, we examined wave properties at 2D shocks with similar setups for different Mach numbers: $M_A = 5 \sim 6$ and $>10$ for slower and faster shocks, respectively. A 3D shock simulation is also carried out for comparing the ES wave property in higher dimensions. In this Letter, we focus on the moderate-Mach-number 2D shock with universal significance. The other cases will be discussed in Section 4.

## 3. Simulation Results: Wave Analysis in 2D Shock Simulations

Figure 1(a) shows an overview of the time-evolving shock magnetic field $\bar{B}_z$ averaged along $Y$ in the simulation. The shock becomes mature and has reached a fully evolved state after $t > 2.5\Omega_{ci}^{-1}$ in this case. In order to study wave properties at the shock front with a relatively high resolution in $\kappa - \omega$ space, the electromagnetic field components are sampled in a long period: $t = 3.5 \sim 4.5\Omega_{ci}^{-1}$, and a large box including the whole shock front. Figures 1(b)–(d) represent the snapshots of the fluctuations of $\delta E_x$, $\delta E_y$, and $\delta B_z$ at a typical time $t = 3.5\Omega_{ci}^{-1}$ within the sampling period. The zoomed $\bar{B}_z$ profile consisting of typical shock structures (upstream, foot, ramp, overshoot, and downstream) is shown in Figure 1(d) for reference. The shock ramp is located at about $X = 56.4 c/\omega_{pi}$ and marked by a vertical black line. From left to right, fluctuation profiles reveal different wave properties. Two regions are selected for wave analysis (marked by red and blue horizontal lines: A and B). In region A, ES waves are dominant and propagate in nearly the same direction. In region B, ES waves have different propagation directions and pass through each other. Long-wavelength EM waves appear and gradually increase from the middle of the foot to the ramp. Let us take the fluctuation $\delta E_x(x, y, t)$ as an example to show how the data are sampled for the wave analysis. Figures 1(e)–(f) illustrate a slice of the sampled shock profile $\delta E_x$ at $Y = L_y/2$ in regions A and B, respectively. In order to investigate the dispersion relation of waves, the 3D fluctuation data in the $X-Y-t$ space are converted to the shock ramp rest frame. A 3D fast Fourier transform (FFT) is applied after Hanning windowing to compensate for the nonperiodicity of the data, in both the $X$ and $t$ directions (Figures 1(g)–(h)). Similar processes are also carried out for the other fluctuation components, $\delta E_y$ and $\delta B_z$.

Figures 2(a)–(d) show corresponding phase-space plots ($X - V_{x,y}$) of particles at $t = 3.5\Omega_{ci}^{-1}$. The solar wind is coming from the left-hand side, and the shock ramp is marked by a
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) An overview of the time-evolving Y-averaged shock magnetic field $\bar{B}_z$. The sampling period for the wave analysis is denoted by white lines. (b)–(d) Snapshots of electromagnetic fluctuations $\delta E_x$, $\delta E_y$, and $\delta B_z$ at $t = 3.5\Omega_{ci}^{-1}$ within the sampling period. The ramp location $X = 56.4c/\omega_{pi}$ is marked by black vertical lines. The Y-averaged $B_z/2$ profile is shown in panel (d) for reference (black curve). Sampling regions A and B are marked out by red and blue horizontal lines at the top of panel (b). (e)–(f) Cross sections of 3D sampled-data $\delta E_x(x, y, t)$ at $Y = L_y/2$ from regions A and B, respectively. They are plotted in the shock rest frame where $X_{ramp} = 0$. (g)–(h) Hanning windows are used to compensate for the nonperiodicity of the data, in both the X and t directions. The same post-processing is performed on other fluctuation components before doing the 3D FFT.</figcaption></figure>

black vertical line as in Figures 1(b)–(d). In region A (Figures 2(a)–(b)), some electrons are trapped and accelerated by the excited ES waves (Figures 1(b)–(c)) at the leading edge of the foot (Amano & Hoshino 2009; Umeda et al. 2009; Yang et al. 2018). They immediately form a ring-like velocity distribution relative to the hot drifting Maxwellian core. Figures 2(c)–(d) show that a fraction of incident ions are reflected at the ramp, and the others are directly transmitted to the downstream. At the same time, the electron bulk velocity shifts in both the X and Y directions to keep the quasi-neutrality. The ion bulk velocity component $V_{iy}$ can be larger

than $V_{ix}$ in region A due to their gyromotion and the shock acceleration along the shock surface. This overall picture is consistent with previous simulations (Scholer et al. 2003; Yang et al. 2009). Figure 2(e) shows Y-averaged number density profiles of electrons (green), incident ions (blue), and reflected ions (red). Here, we only focus on the wave analysis region and quickly separate the reflected ions before the ramp as in Otsuka et al. (2019). From the foot to the ramp, the percentage of reflected ions increases. Figures 2(f)–(h) represent the 2D density profiles of electrons, reflected ions, and incident ions. Combined with corresponding field fluctuations (Figures 1(b)–
<figure><img src="image_4.png" /><figcaption>**Figure 3.** (a)–(c) A 3D view of the dispersion relation diagram of fluctuating fields $\delta E_x$, $\delta E_y$, and $\delta B_z$ in region A of the shock front. The color indicates the amplitude of Fourier-transformed fields in the $\kappa_x – \kappa_y – \omega$ space. The excited ES and EM waves are marked. (d)–(f) Similar plots as in (a)–(c), but for fluctuating fields in region B. On the upper edge of each panel, the black arrow indicates the shock normal direction $n$.</figcaption></figure>

Matsumoto et al. 2017). The accelerated electrons immediately form a ring-like velocity distribution. This VDF has a weak positive slope in the velocity space perpendicular to the magnetic field. Free energy is quickly released through the coupling between the ring and the hot Maxwellian core. The growth rate of “ES-2” peaks at about $\kappa = \pm 0.23 \lambda_{\text{De}}^{-1}$ in the linear theory around the Doppler-shifted upper hybrid frequency (Figure 4). It is consistent with the simulation results (purple regions in Figures 3(a)–(b)). (3) The third wave is an electromagnetic mode (marked by “EM-1” in Figure 3(c)). This high-frequency EM wave is emitted facing the upstream and is visible in both the $\delta E_{\perp}$ and $\delta B_z$ diagrams. In this case, the $\delta E_z$ only has a background noise (not shown here). Hence, the EM mode is an extraordinary electromagnetic mode (X mode). This

X-mode emission cannot be described in Figure 4 because kinetic relativistic effects are not included in the present version of our linear solver yet. One possible scenario is the synchrotron maser radiation excited by relativistic electrons with a ring-type velocity distribution at strongly magnetized plasmas (Hoshino & Arons 1991; Plotnikov & Sironi 2019) under a Doppler-shifted condition. In summary, this EM wave is locally emitted at the shock front and propagates toward the upstream.

Second, the waves in region B (i.e., in the middle of the foot) are investigated. Figure 2(e) shows that the values of $n_e$ and $B$ are $\ge 2$ times their upstream values $n_{e0}$ and $B_0$ in this region. The local ratios $\omega_{pe}/\omega_{pe0}$ and $\Omega_{ce}/\Omega_{ce0}$ are about 1.414 and 2, respectively. The frequency ratio $\omega_{pe}/\Omega_{ce}$ is about 5.5 and
<figure><img src="image_5.png" /><figcaption>**Figure 4.** A unified numerically solvable framework for complicated kinetic plasma dispersion relations (pdrk; Xie 2019) is used to identify the corresponding wave modes in Figure 3. Setups of the linear analysis are shown in Table 1. Real parts of main solutions are represented by black curves. Red line segments on these black curves indicate where the wave modes have positive growth rates. Corresponding zoomed imaginary parts are denoted by red dashed curves. Some high-frequency waves (e.g., O and X modes) are also plotted for reference in black. The labeled wave modes are described in the text.</figcaption></figure>

lower than its upstream value ($\omega_{pe0}/\Omega_{ce0} \approx 7.8$). This means that the magnetization of the plasma becomes greater. We keep using the upstream values $\omega_{pe0}$ and $\lambda_{De0}^{-1}$ as units of $\omega$ and $\kappa$ for region B in the bottom panels of Figure 3. Corresponding dispersion relations from the linear theory are shown in Figures 4(c)–(d). In region B, both reflected and incident ion beams couple with the electron cyclotron harmonic branches in all directions of the simulation plane. The main excited waves are as follows: (1) in Figure 3(d), “ES-3” wave modes are excited by ECDI on $\pm\kappa_x$ directions. The wave frequency in the $\pm\kappa_x$ directions are comparable to each other as predicted by the linear theory (Figure 4(c)). (2) In Figure 3(e), “ES-4” wave modes have more harmonic branches in the $+\kappa_y$ direction. This is because the old reflected ions are gyrating back toward the

ramp and they have a large bulk velocity ($>10V_A$) in the $+Y$ direction. In contrast, the bulk velocity of incident ions in the $-Y$ direction caused by the deflection ahead of the ramp is relatively low. In summary, the middle of the foot could be a zoom of ECDI, which is triggered in different directions. This is interesting and brand new relative to previous 1D simulations (Muschietti & Lembège 2006, 2013) that only discuss ECDI along the X-axis. Our work has taken a step forward on this basis, and finds that the ES waves can be excited along the shock surface as well as along the shock normal. In addition, we also find some low-frequency EM waves (marked by “EM-2” in Figure 3(f)) associated with the “ES-4” waves. Such a low-frequency EM wave has a modulating effect on the magnetic field and plasma density profiles (refer to Figures 1(d)
<table><caption>**Table 1**
Setups of Species Parameters for the Linear Analysis</caption><thead><tr><th>Run</th><th><i>B</i>/<i>B</i><sub>0</sub></th><th><i>N</i>/<i>N</i><sub>0</sub></th><th>Species</th><th><i>n</i>%</th><th><i>β</i><sub>+</sub></th><th><i>β</i><sub>⊥</sub></th><th><i>V</i><sub>dx</sub>/<i>V</i><sub>A</sub></th><th><i>V</i><sub>dy</sub>/<i>V</i><sub>A</sub></th><th><i>V</i><sub>dz</sub>/<i>V</i><sub>A</sub></th><th><i>V</i><sub>ring</sub>/<i>V</i><sub>A</sub></th><th><i>M</i></th></tr></thead><tbody><tr><td rowspan="4">1 (Region A)</td><td rowspan="4">1.0</td><td rowspan="4">1.0</td><td>Inc. H<sup>+</sup></td><td>83.5</td><td>0.1</td><td>0.25</td><td>9.00</td><td>-0.16</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Ref. H<sup>+</sup></td><td>16.5</td><td>0.1</td><td>0.75</td><td>-1.60</td><td>14.8</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Core e<sup>-</sup></td><td>90.0</td><td>0.3</td><td>0.75</td><td>7.25</td><td>2.30</td><td>0</td><td>0</td><td>1</td></tr><tr><td>Ring e<sup>-</sup></td><td>10.0</td><td>0.3</td><td>0.1</td><td>7.25</td><td>2.30</td><td>0</td><td>25.0</td><td>1</td></tr><tr><td rowspan="4">2 (Region B)</td><td rowspan="4">2.0</td><td rowspan="4">2.0</td><td>Inc. H<sup>+</sup></td><td>55.0</td><td>0.1</td><td>0.5</td><td>7.82</td><td>-0.83</td><td>0</td><td>0</td><td>0</td></tr><tr><td>New ref. H<sup>+</sup></td><td>25.4</td><td>0.1</td><td>0.5</td><td>-3.50</td><td>5.0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Old ref. H<sup>+</sup></td><td>19.6</td><td>0.1</td><td>0.5</td><td>3.63</td><td>12.5</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Core e<sup>-</sup></td><td>90.0</td><td>0.3</td><td>2.0</td><td>4.12</td><td>3.26</td><td>0</td><td>0</td><td>1</td></tr><tr><td></td><td></td><td></td><td>Ring e<sup>-</sup></td><td>10.0</td><td>0.3</td><td>0.1</td><td>4.12</td><td>3.26</td><td>0</td><td>28.0</td><td>1</td></tr></tbody></table>

**Note.** (1) The species can be treated as either magnetized ($M = 1$) or unmagnetized ($M = 0$). (2) $J = 8$ is used for the J-pole Padé expansion. (3) The electron VDF is contributed by a hot drifting Maxwellian core and a relatively cool Maxwellian ring. The ring velocity distribution and its drift across the field are modeled as that used by Umeda et al. (2012b) and Umeda & Nakamura (2018), respectively. The ion VDF is a superposition of two or three drifting Maxwellian subpopulations. As shown in Figure 2, “Inc.” and “Ref.” are abbreviations of “incident” and “reflected,” respectively. “New ref.” represents ions that are newly reflected at the ramp and moving toward upstream. “Old ref.” refers to the ions that are reflected at earlier time, and they are gyrating back toward the downstream at this time. (4) $V_{dx,y,z}$ and $V_{ring}$ indicate the drift velocity components and the radius of modeled ring distributions. (5) We consider the nearly perpendicular wave modes. Wave normal angles (WNAs) $\theta_{kB} = 89.9^{\circ}$ and $89^{\circ}$ are employed for regions A and B, respectively. (6) All parameters are issued from the simulation and averaged over the sampling period in the shock ramp rest frame.

and 2(f)–(h). The analysis of such EM wave amplification might require a theory considering nonuniform plasmas and gradient background magnetic fields. Hence, it will not be further discussed in this Letter. It is worth noting that the X mode can exist well in region B due to the local relativistic electrons, and it has a wavevector toward the upstream as in region A.

## 4. Conclusions and Discussions

This Letter presents PIC simulations of a perpendicular shock in the near-Sun solar wind condition, where the magnetization is relatively high, $\beta$ is relatively low, and the average shock Mach number is below 10, corresponding to a young, fast CME-driven shock propagating in the pristine solar wind. The simulated electromagnetic fluctuations show that the shock foot can be segmented into two parts by different wave features.

1. At the leading edge of the foot, ES waves are excited by ECDI in the $-X$ and $+Y$ directions. The instability is triggered by the coupling between the incident electrons and gyro-reflected ions. The wavevector of this ES wave is oblique to the shock normal, and is mainly along the shock surface. This is because the bulk velocity of reflected ions changes from the $-X$ direction to the $+Y$ direction during the gyro-reflection process.

2. In the same region, a fraction of incident electrons can be trapped and accelerated by the above exited ES waves. A secondary instability occurs around the Doppler-shifted upper hybrid frequency due to the coupling between these accelerated ring-like electrons and the hot Maxwellian core electrons. In addition, some weak relativistic electrons in the ring VDF could lead to a high-frequency EM emission probably induced by SMI. The emitted EM wave is an X mode and propagates upstream. Other potential candidates of X-mode emission mechanisms are also need to be considered for quasi-perpendicular shocks. For instance, a combination of wave growth due to electron cyclotron maser instability and nonlinear wave-coupling processes is suggested for plasmas with $\omega_{pe}/\Omega_{ce} \sim 10$ in the outer corona (Ni et al. 2020).

3. From the middle of the foot all the way to the ramp, the incident ions begin to couple with the electrons. In this region, the incident ion beam begins to deflect in the $-Y$ direction when approaching the ramp, and the old gyro-back-reflected ions have a large bulk velocity in the $+Y$ direction. Therefore, ES waves can be excited by ECDI in both the $\pm X$ and $\pm Y$ directions. These multidirectional ES waves propagate across each other and form fibrous-like pattern in electric field and particle number density profiles. This is brand new and different from early 1D simulations and theoretical models of shock front ES wave excitations.

4. The long-wavelength low-frequency EM waves associated with ES harmonics in the $+Y$ direction are strengthened as they approach the ramp. In addition, the high-frequency X mode is also observed in this region.

Furthermore, we carried out two additional shock simulations with lower and higher Mach numbers as mentioned in Section 2. Preliminary results indicate that the ECDI is robust and can be observed in all cases. Buneman instability appears only at extremely fast CME-driven shocks with a speed $>3000$ km s$^{-1}$ (i.e., $M_A > 10$; Liu et al. 2019). Normally this is not the case and the shock speed is as slow as that used in this Letter. At slower shocks ($M_A \le 6$), the reflected ion beam is modulated by the shock front self-reformation (Amano & Hoshino 2009) and results in a intermittent ES wave excitation.

A 3D shock simulation is also carried out for comparing ES wave excitations (not shown here). Briefly, ES waves sampled in the $B_0$ out-of-plane from the 3D simulation is similar to that observed in this Letter. However, ES waves sampled in the $B_0$ in-plane propagate almost along the shock normal. This is because the main ion bulk velocity components are not included in this cross section. More completely, a 4D FFT is required for the wave analysis in 3D shock cases. This is still infusible under most of the current storage conditions.

As we all know, the Sun is entering the solar maximum in the next 5 ~ 6 yr (solar cycle 25). More solar eruptions accompanied with fast CME-driven shocks are expected. The perihelion of PSP will be closer to the Sun (from 27.8 $R_s$ to less than 10 $R_s$; Bale et al. 2016; Fox et al. 2016; Kasper et al. 2016). PSP and Solar Orbiter are likely to observe high-frequency EM emissions (e.g., X modes) toward upstream
accompanied by local energetic electrons and electrostatic
waves induced by ECDI or BI along the shock normal or along
the shock surface at fast CME-driven shocks.

We thank the referee for helpful comments. We acknowl-
edge the NASA Parker Solar probe Mission, and FIELDS and
SWEAP instruments for use of data. The authors are grateful to
Dr. L. Muschietti from UC Berkeley for helpful discussions on
PDRK/BO benchmarks. The computations are performed by
Numerical Forecast Modeling R&D and VR System of State
Key Laboratory of Space Weather, and HPC of Chinese
Meridian Project. This work is supported by the NSFC
(41574140, 41674168, 41774179), the Specialized Research
Fund for State Key Laboratories of China, Youth Innovation
Promotion Association of the CAS (2017188), the Open
Research Program Key laboratory of Geospace Environment
CAS (GE2017-01), the Open Research Program Key labora-
tory of Polar Science, MNR (KP202005), Beijing NSF
(1192018), Beijing Municipal Science and Technology Com-
mission (Z191100004319001, Z191100004319003), Beijing
Outstanding Talent Training Foundation
(2017000097607G049), and the Strategic Priority Research
Program of CAS (XDA14040404). S.M. acknowledges partial
support by Grant-in-Aid for Scientific Research (C)
No.19K03953 and (B) No.17H02966 from JSPS. J.G. is
supported by the Shandong Provincial National Natural
Science Foundation (ZR2017MD012).

ORCID iDs

Zhongwei Yang https://orcid.org/0000-0002-1509-1529

Ying D. Liu https://orcid.org/0000-0002-3483-5909

Shuichi Matsukiyo https://orcid.org/0000-0002-4784-0301

Quanming Lu https://orcid.org/0000-0003-3041-2682

Fan Guo https://orcid.org/0000-0003-4315-3755

Mingzhe Liu https://orcid.org/0000-0003-2981-0544

References

Amano, T., & Hoshino, M. 2009, ApJ, 690, 244

Arber, T. D., Bennett, K., Brady, C. S., et al. 2015, PPCF, 57, 113001

Bale, S. D., Goetz, K., Harvey, P. R., et al. 2016, SSRv, 204, 49

Bale, S. D., Reiner, M. J., Bougeret, J.-L., et al. 1999, GeoRL, 26, 1573

Fox, N. J., Velli, M. C., Bale, S. D., et al. 2016, SSRv, 204, 7

Ganse, U., Kilian, P., Vainio, R., & Spanier, F. 2012, SoPh, 280, 551

Gao, X., Lu, Q., & Wang, S. 2017, GeoRL, 44, 5269

Goodrich, K. A., Ergun, R., Schwartz, S. J., et al. 2018, JGRA, 123, 9430

Graham, D. B., Vaivads, A., Khotyaintsev, Y. V., et al. 2018, JGRA, 123, 2630

Guo, F., & Giacalone, J. 2010, ApJ, 715, 406

Henri, P., Sgattoni, A., Briand, C., Amiranoff, F., & Riconda, C. 2019, JGRA, 124, 1475

Horký, M., Omura, Y., & Santolík, O. 2018, PhPl, 25, 042905

Hoshino, M., & Arons, J. 1991, PhFIB, 3, 818

Hoshino, M., & Shimada, N. 2002, ApJ, 572, 880

Kasper, J. C., Abiad, R., Austin, G., et al. 2016, SSRv, 204, 131

Lembege, B., Yang, Z., & Zank, G. P. 2020, ApJ, 890, 48

Liu, M., Liu, Y. D., Yang, Z., Wilson, L. B., III, & Hu, H. 2018, ApJL, 859, L4

Liu, Y., Luhmann, J. G., Bale, S. D., & Lin, R. P. 2009, ApJL, 691, L151

Liu, Y., Luhmann, J. G., Müller-Mellin, R., et al. 2008, ApJ, 689, 563

Liu, Y., Richardson, J. D., & Belcher, J. W. 2005, P&SS, 53, 3

Liu, Y. D., Luhmann, J. G., Lugaz, N., et al. 2013, ApJ, 769, 45

Liu, Y. D., Zhu, B., & Zhao, X. 2019, ApJ, 871, 8

Maksimovic, M., Bale, S. D., Berčič, L., et al. 2020, ApJS, 246, 62

Matsukiyo, S., & Scholer, M. 2003, JGRA, 108, 1459

Matsukiyo, S., & Scholer, M. 2012, JGRA, 117, 11105

Matsumoto, Y., Amano, T., & Hoshino, M. 2013, PhRvL, 111, 215003

Matsumoto, Y., Amano, T., Kato, T. N., & Hoshino, M. 2017, PhRvL, 119, 105101

Muschietti, L., & Lembège, B. 2006, AdSpR, 37, 483

Muschietti, L., & Lembège, B. 2013, JGRA, 118, 2267

Ni, S., Chen, Y., Li, C., et al. 2020, ApJL, 891, L25

Otsuka, F., Matsukiyo, S., & Hada, T. 2019, HEDP, 33, 100709

Parks, G. K., Lee, E., McCarthy, M., et al. 2012, PhRvL, 108, 061102

Plotnikov, I., & Sironi, L. 2019, MNRAS, 485, 3816

Pulupa, M. P., Bale, S. D., & Kasper, J. C. 2010, JGR, 115, A04106

Richardson, J. D., Kasper, J. C., Wang, C., Belcher, J. W., & Lazarus, A. J. 2008, Natur, 454, 63

Scholer, M., Shinohara, I., & Matsukiyo, S. 2003, JGRA, 108, 1014

Thejappa, G., & MacDowall, R. J. 2019, ApJ, 883, 199

Umeda, T. 2010, JGRA, 115, A01204

Umeda, T., Kidani, Y., Matsukiyo, S., & Yamazaki, R. 2012a, JGR, 117, A03206

Umeda, T., Matsukiyo, S., Amano, T., & Miyoshi, Y. 2012b, PhPl, 19, 072107

Umeda, T., & Nakamura, T. K. M. 2018, PhPl, 25, 102109

Umeda, T., Yamao, M., & Yamazaki, R. 2009, ApJ, 695, 574

Wilson, L. B. I., Cattell, C., Kellogg, P. J., et al. 2007, PhRvL, 99, 041101

Wilson, L. B. I., Cattell, C. A., Kellogg, P. J., et al. 2010, JGRA, 115, A12104

Wu, C. S., & Lee, L. C. 1979, ApJ, 230, 621

Xie, H. S. 2019, CoPhC, 244, 343

Yang, Z., Huang, C., Liu, Y. D., et al. 2016, ApJS, 225, 13

Yang, Z., Liu, Y. D., Richardson, J. D., et al. 2015, ApJ, 809, 28

Yang, Z., Lu, Q., Liu, Y. D., & Wang, R. 2018, ApJ, 857, 36

Yang, Z. W., Lu, Q. M., Lembège, B., & Wang, S. 2009, JGRA, 114, A03111

Zank, G. P., Li, G., Florinski, V., et al. 2006, JGRA, 111, A06108

Zank, G. P., Pauls, H. L., Cairns, I. H., & Webb, G. M. 1996, JGR, 101, 457

Zhao, X., Liu, Y. D., Hu, H., & Wang, R. 2019, ApJ, 882, 122