# Triggering the magnetopause reconnection by solar wind discontinuities

Alexander Lukin  Space Research Institute, RAS, Moscow, Russia  Faculty of
Physics, National Research University Higher School of Economics, Moscow,
Russia  Zhifang Guo  School of Geophysics and Information Technology, China
University of Geosciences, Beijing, China  Physics Department, Auburn
University, Auburn, AL, USA  Yu Lin  Physics Department, Auburn University,
Auburn, AL, USA  Evgeny Panov  Space Research Institute, Austrian Academy of
Sciences, Schmiedlstrasse 6, 8042 Graz, Austria  Anton Artemyev  Department of
Earth, Planetary, and Space Sciences and Institute of Geophysics and Planetary
Physics,
University of California, Los Angeles, CA, USA  Space Research Institute, RAS,
Moscow, Russia  Xiaojia Zhang  Department of Physics, University of Texas at
Dallas, Richardson, TX, USA  Department of Earth, Planetary, and Space
Sciences and Institute of Geophysics and Planetary Physics,
University of California, Los Angeles, CA, USA  Anatoli Petrukovich  Space
Research Institute, RAS, Moscow, Russia

###### Abstract

Magnetic reconnection is one of the most universal processes in space plasma
that is responsible for charged particle acceleration, mixing and heating of
plasma populations. In this paper we consider a triggering process of
reconnection that is driven by interaction of two discontinuities: solar wind
rotational discontinuity and tangential discontinuity at the Earth’s
magnetospheric boundary, magnetopause. Combining the multispacecraft
measurements and global hybrid simulations, we show that solar wind
discontinuities may drive the magnetopause reconnection and cause the mixing
of the solar wind and magnetosphere plasmas around the magnetopause, well
downstream of the solar wind flow. Since large-amplitude discontinuities are
frequently observed in the solar wind and predicted for various stellar winds,
our results of reconnection driven by the discontinuity-discontinuity
interaction may have a broad application beyond the magnetosphere.

solar wind – turbulence, magnetopause, reconnection, hybrid simulation

††journal: ApJ

##  1 Introduction

Magnetohydrodynamic (MHD) discontinuities are basic solutions for boundaries
of plasmas with different properties (Landau & Lifshitz, 1960; Hudson, 1970),
and are fundamental element of space plasma flows, e.g., solar wind (Tsurutani
& Ho, 1999) and stellar winds (Arons, 2012; Sironi & Spitkovsky, 2011). Such
discontinuities are considered as elementary blocks of MHD turbulence
(Servidio et al., 2011b; Matthaeus et al., 2015; Loureiro & Boldyrev, 2017)
and serve as a primary framework for magnetic field line reconnection, a major
process responsible for the transfer of magnetic field energy to plasma
heating and charged particle acceleration (Birn & Priest, 2007; Gonzalez &
Parker, 2016; Pontin & Priest, 2022). Besides the spontaneous magnetic
reconnection due to discontinuity instability (Syrovatskii, 1981; Loureiro et
al., 2007; Pucci & Velli, 2014), magnetic reconnection can be driven by an
interaction of two discontinuities. The most investigated type of such driven
reconnections is that due to interaction of a tangential discontinuity and a
shock wave (see examples of simulations for astrophysical and solar plasma
systems in, e.g., Phan et al., 2007; Sironi & Spitkovsky, 2012; Matsumoto et
al., 2015; Omidi et al., 2009; Guo et al., 2018, 2021a, 2021b). Numerical
simulations and theoretical models of discontinuity interactions associated
with magnetic reconnection are largely motivated by multiple spacecraft
observations in the near-Earth space environment and in the solar wind, the
natural laboratory of plasma dynamics.

Earth’s bow shock and magnetopause are formed by solar wind interaction with
the Earth’s dipole field and are separated by the magnetosheath, the region
filled by subsonic (shocked) plasma flow. The magnetosheath-magnetosphere
boundary, magnetopause, can be described as a tangential discontinuity (De
Keyser et al., 2005), an equilibrium current sheet where the geomagnetic field
lines are ’closed’. Solar wind flow transport kinetic-scale discontinuities
(see statistical properties of such discontinuities in Söding et al., 2001;
Vasquez et al., 2007; Artemyev et al., 2018; Vasko et al., 2021) sharing
properties of both rotational and tangential discontinuities (Neugebauer,
2006; Artemyev et al., 2019) and carrying strong current density (Podesta,
2017; Greco et al., 2016; Newman et al., 2020). Interaction of solar wind
discontinuities with the bow shock significantly modifies the discontinuity
structure (Yan & Lee, 1996; Lin et al., 1996a; Cable & Lin, 1998) and can also
produce various types of magnetosheath perturbations: plasma bubbles (Liu et
al., 2015; An et al., 2020; Vu et al., 2022), density cavities (Lin, 2003; Lin
& Wang, 2005; Sibeck et al., 2002, 2021; Omidi et al., 2013), hot flow
anomalies (Lin, 1997, 2002; Omidi & Sibeck, 2007; Omidi et al., 2016), and
plasma pressure pulses (Hubert & Harvey, 2000; Farrugia et al., 2018). Both
modification of the initial discontinuity configuration and generation of
magnetosheath perturbations involve ion kinetic processes, and thus are well
reproduced by hybrid simulations treating ions as particles and electrons as a
fluid (e.g., Lin et al., 1996a, b; Lin & Wang, 2005; Omidi et al., 2016, 2020;
Ng et al., 2021; Chen et al., 2021).

Schematic 1 shows main types of magnetic reconnections observed within the
day-side Earth’s magnetosphere environment: reconnection at solar wind
discontinuities (Farrugia et al., 2001; Gosling, 2012; Phan et al., 2006),
reconnection due to the discontinuity interaction with the bow shock (Pang et
al., 2010; Vörös et al., 2017; Wang et al., 2019; Gingell et al., 2019, 2020;
Guo et al., 2021b), and reconnection on the magnetopause (Paschmann et al.,
1979, 2013; Phan et al., 2014; Burch et al., 2016). The latter one is
generally driven by a change of the interplanetary magnetic field direction,
i.e. by solar wind discontinuity arriving to the magnetopause. In this study
we focus on this last type of reconnection associated with magnetopause
interaction with magnetosheath perturbations, in which the sheath
perturbations are generated by the solar wind discontinuity interaction with
the bow shock. We consider very coherent perturbations, and study the
magnetopause (that is tangential discontinuity, see Roth et al. (1996); De
Keyser et al. (2005)) interaction with the solar wind rotational discontinuity
modified by the passage through the bow shock (that is the shock-type
discontinuity).

Figure 1: Schematic view of main types of magnetic reconnection associated
with the solar wind discontinuities.

One of the important consequences of discontinuity interaction with the bow
shock is its compression with the significant increase of the current density
(Phan et al., 2007; Webster et al., 2021; Kropotina et al., 2021). Therefore,
such amplified discontinuities should be more unstable to magnetic
reconnection in the magnetosheath. Indeed, recent observations (Vörös et al.,
2017; Wang et al., 2019; Gingell et al., 2019, 2020) and kinetic simulations
(Guo et al., 2018) show reconnection signatures downstream of the Earth’s bow
shock, and such reconnection is associated with the tangential discontinuity
interaction with the bow shock. However, reconnection does not necessary
destroy the current layer, which can reach the magnetopause. Rotational
discontinuities are especially stable to magnetic reconnection (see Discussion
for more details). Interaction between the modified rotational discontinuity
and the magnetopause, that is a tangential discontinuity, may also drive the
magnetic field line reconnection and magnetosheath-magnetosphere plasma
exchange. This type of reconnection is in focus of our study.

Roles of various magnetosheath perturbations in the magnetopause dynamics is
well documented by in-situ spacecraft measurements (e.g., Sibeck et al., 2000;
Jacobsen et al., 2009; Archer et al., 2014; Hietala et al., 2018) and ground-
based magnetometers (e.g., Archer et al., 2015). Moreover, such dynamics
results in the generation of a broad range of ultra-low-frequency (MHD) waves
within the Earth’s magnetosphere, and these waves are usually detected by the
ground-based and spacecraft magnetic field and plasma measurements (e.g., Wang
et al., 2018a, 2020a; Shi et al., 2021). Such magnetosheath perturbations may
propagate from the day-side to midtail magnetosheath (Wang et al., 2018b) and
drive the flank magnetopause dynamics (Wang et al., 2020b). Therefore, we
shall consider possibility of both day-side and night-side (flank)
magnetopause reconnection driven by the solar wind discontinuity crossing the
bow shock.

In this study we combine the 3D global hybrid simulation (see model
description in Lin & Wang, 2005) of the interaction between the magnetopause
and the solar wind discontinuities with THEMIS (Angelopoulos, 2008), MMS
(Burch et al., 2016), and ARTEMIS (Angelopoulos, 2011) observations to
investigate the subsequent discontinuity interaction with the magnetopause and
driven magnetopause reconnection. Our main event describes the day-side
reconnection, and for this event we use the simulation results to confirm our
interpretation of ARTEMIS and THEMIS measurements. The second event describes
ARTEMIS and MMS observations of night-side magnetopause reconnection driven by
a solar wind discontinuity. We use this event to demonstrate that
discontinuity-magnetopause interaction may drive magnetic reconnection in
different plasma flow configurations. We also analyze three supplementary
events with magnetopause crossings before and after the solar wind
discontinuity impact, which confirm that the solar wind discontinuity impact
may trigger magnetic reconnection at the initially non-reconnected
magnetopause.

##  2 Spacecraft observations

###  2.1 Data and methods

Below we show two events of interaction between solar wind rotational
discontinuities and the Earth’s magnetopause. We use the data obtained onboard
THEMIS/ARTEMIS (Angelopoulos, 2008, 2011) and MMS (Burch et al., 2016)
missions. THEMIS/ARTEMIS fluxgate magnetometers (Auster et al., 2008) and
electrostatic analyzers (ESA; McFadden et al. (2008)) provide us with the
magnetic field vector, moments of ion and electron distribution functions
(number density, temperatures and bulk velocities) and phase space density
measurements with a spin time resolution (3 and 4 second for THEMIS and
ARTEMIS respectively). MMS fluxgate magnetometer (Russell et al., 2016)
measurements are available with 1/16s resolution, while the plasma moments
measured by Fast Plasma Investigation (FPI) instrument (Pollock et al., 2016)
are provided with $4.5$ seconds resolution.

To restore the local (lmn) coordinate system of the discontinuity we use the
minimum variance analysis (MVA; Sonnerup & Scheible (2000)). To estimate the
spatial scale of the discontinuity we use almost the same single-spacecraft
technique as proposed by Haaland & Gjerloev (2013), but since the MVA often
does not distinguish between the intermediate and normal directions we use the
velocity component perpendicular to the main magnetic field ($l$) component,
$\bm{v_{mn}}=\bm{v}-(\bm{v}\cdot\bm{e_{l}})\bm{e_{l}}$ in our analysis, i.e.
we may overestimate the discontinuity thickness $L=\Delta t|\bm{v_{mn}}|$
($\Delta t$ is the time interval of discontinuity crossing by spacecraft).

For steady reconnection process under symmetrical boundary conditions and a
finite guide field, there exist two symmetrical rotational discontinuities
bounding the outflow region, and thus we expect that the variation of the
plasma flow velocity across the outflow region discontinuities should satisfy
the Walen relation $\Delta\bm{v}=\pm\Delta\bm{B}/(4\pi\rho)$ (Parker, 1957;
Petschek, 1964; Lin & Lee, 1993). The magnetopause reconnection however, are
usually characterized by asymmetrical boundary conditions (Phan et al., 2007,
2014) so the jump of plasma flow speed should be comparable to the asymmetric
Alfven speed $v_{Al,asym}$ (Cassak & Shay, 2007; Swisdak & Drake, 2007):

$v_{Al,asym}^{2}=\frac{B_{l1}B_{l2}(B_{l1}+B_{l2})}{4\pi(\rho_{1}B_{l2}+\rho_{2}B_{l1})},$
(1)

where $B_{l1,2}$, $\rho_{1,2}$ are the values of anti-parallel reconnecting
magnetic field component and plasma density on both sides of the outflow
region boundaries. In our selected events, spacecraft do not cross the
reconnecting magnetopause, but observe the discontinuities likely connecting
to the magnetopause reconnection side. Therefore, we may not estimate the
magnetic field configuration of the reconnecting magnetopause, and we use
component-wise estimates of the asymmetrical Alfven speed
$v_{Aj,asym}^{2}=(B_{j1}B_{j2}(B_{j1}+B_{j2}))/(4\pi(\rho_{1}B_{j2}+\rho_{2}B_{j1}))$,
where $j=x,y,z$ (we use GSM coordinate system through the paper), and
$B_{j1}$, $\rho_{1}$ and $B_{j2}$, $\rho_{2}$ are measured in the
magnetosheath near the discontinuity and in the magnetosphere.

###  2.2 Day-side event

Figure 2 shows an overview of the event with the day-side magnetopause
reconnection driven by the solar wind discontinuity. THEMIS C (ARTEMIS P2) is
in the solar wind, upstream of the bow shock (see panels ($l$), ($m$)), and
observes a series of the solar wind discontinuities (shaded in red in Fig.
2(a),(b)) at $\sim$12:41, $\sim$12:44, $\sim$12:55 and $\sim$13:10 with the
magnetic field rotation mostly seen in GSM $B_{x}$, $B_{z}$ for the first and
second events, and in GSM $B_{y}$, $B_{z}$ for in the third and fourth events.
The magnetic field rotation is accompanied by jumps of solar wind flow $\Delta
v_{x,y,z}\approx B_{x,y,z}/\sqrt{4\pi\rho}$ (not shown) with the almost
constant field magnitude $|B|$. These are typical properties of rotational
discontinuity (Tsurutani & Ho, 1999; Neugebauer, 2006). Although single
spacecraft measurements do not allow to check the normal magnetic field
component with necessary accuracy (see Knetter et al., 2004), we use the time
delay of discontinuity measurements by two ARTEMIS spacecraft to improve
accuracy of MVA (see details of this method in Artemyev et al., 2019) and
estimate a normal magnetic field component: $B_{n}/\Delta
B_{l}\approx(0.2,0.1,0.1,0.05)$ for four discontinuities shown in Fig. 2. For
three first discontinuities $B_{n}$ is quite comparable to the $B_{l}$ change
across the discontinuity (the discontinuity amplitude), and thus we can
confirm that these are rotational discontinuities. Their spatial scales
(thicknesses) in the solar wind, based on THEMIS C observations, are
$L_{1}\sim 7500$km, $L_{2}\sim 6200$km, $L_{3}\sim 3050$km and $L_{4}\sim
2200$km.

These rotational discontinuities cross the bow shock and are observed
downstream (in the magnetosheath) by THEMIS D and E. The interaction with the
bow shock compresses the discontinuity and increases the magnetic field
amplitude from $\sim 5$nT in the solar wind to $\sim 20-30$nT in the
magnetosheath. The spatial scales of these discontinuities in the
magnetosheath, based on THEMIS D and E observations, are $L_{1d}\sim 2000$km,
$L_{2d}\sim 5300$km, $L_{3d}\sim 1500$km, $L_{4d}\sim 550$km and $L_{1e}\sim
2500$km, $L_{2e}\sim 7600$km, $L_{3e}\sim 2000$km, $L_{4e}\sim 800$km. Such
intensification of discontinuities downstraeam of the bow shock has been
reproduced in simulations (e.g., Yan & Lee, 1996; Lin et al., 1996a; Guo et
al., 2018, 2021b, 2021a; Kropotina et al., 2021) and reported in spacecraft
observations (e.g., Webster et al., 2021; Kropotina et al., 2021). The
interesting aspect of the discontinuity observation in the magnetosheath is
the population of energetic ions (mostly seen around the last discontinuity).
Energy spectrum clearly shows this population at $>5$keV range, significantly
higher than the shocked solar wind energies. The pitch-angle distribution of
this population indicates that energetic ions are moving along magnetic field
lines (not shown), i.e. along $-y$ direction from the magnetopause. Therefore,
this may be a leakage of the magnetopsheric population (for which $5-15$keV
energy range is expected). Such observations in the magnetosheath suggest that
discontinuity are connected to the magnetopause reconnection region. The
scenario for such observations includes the discontinuity impact on the
magnetopause, local reconnection between the magnetosheath and magnetospheric
field lines, and ion leakage along the reconnected magnetic field lines (along
the discontinuity surface) to the magnetosheath, where this magnetospheric ion
population is observed in association with the discontinuities. An
alternative, or rather supplementary mechanism can be the magnetospheric
plasma leakage into the magnetosheath due to magnetosphere compression by the
pressure pulse formed by the discontinuity interaction with the bow shock (see
Lin et al., 1996b; Archer et al., 2012). Such a compression may release
magnetospheric plasma into magnetosheath and may drive the magnetopause
reconnection (e.g., Hietala et al., 2018).

Before the discontinuity arrives to the magnetopause, THEMIS A was inside the
magnetosphere (the magnetopause crossing from the magnetosheath to the
magnetosphere occurs at $\sim$12:05) and observed almost stationary magnetic
field, stagnant plasma, low plasma density, and hot ions (before 13:17). Then
THEMIS A detected several injections of the cold dense magnetosheath plasma
into the magnetosphere: increase of density, low-energy population in ion and
electron spectra, magnetic field perturbations. These injections of cold
plasma are accompanied by observations of plasma jets seen as bipolar flows
around $\sim$12:57, $\sim$13:18 and $\sim$13:22. The component-wise estimates
of asymmetric Alfven speed calculated for all marked discontinuties are
$v_{Ax,asym}\sim 50-70$km/s, $v_{Ay,asym}\sim 20-30$km/s, $v_{Az,asym}\sim
90-120$km/s and comparable to the observed jet speeds. Therefore, we may
suggest that discontinuity’s impact on the magnetopause triggers magnetic
reconnection that is responsible for the magnetosheath plasma penetration into
the magnetosphere and the magnetospheric plasma penetration into the
magnetosheath. This impact (and magnetic reconnection) also drives MHD waves
propagating away from the magnetopause and observed by THEMIS A as quasi-
periodic $v_{x}$ variations modulating the cold ion and electron populations
after 13:22:00 (see discussion of such waves in Hartinger et al., 2013; Zhang
et al., 2020; Wright & Elsden, 2020).

Figure 2: The overview of THEMIS observations on 2020-01-22. (a),(b): solar
wind discontinuity (magnetic field and ion spectrum on THEMIS C), (c)-(f): the
same discontinuity observed downstream of the bow shock (magnetic fields and
ion spectra on THEMIS D&E), (g)-(k) magnetospheric observations (magnetic
fields, plasma flow velocities, electron density and temperature, ion and
electron spectra on THEMIS A). Panels (l) and (m) show spacecraft location in
$XY$ and $XZ$ GSM planes relative to the model bow shock (Wu et al., 2000) and
magnetopause (Shue et al., 1997).

To investigate details of the discontinuity interaction with the magnetopause,
we zoom in THEMIS A observations and add information about ion kinetics in
Fig. 3. Pitch-angle distributions of thermal ($<2$keV) and hot ($\in[4,20]$
keV) ions show that the bipolar $v_{z}$ signature around 13:17-13:19 consists
of cold (magnetosheath) ions flowing parallel and hot (magnetosheric) ions
flowing anti-parallel to the background magnetic field. This result resembles
well the bipolar (reversal) plasma flows from the asymmetric magnetoause
reconnection (see review by Paschmann et al., 2013, and references therein),
i.e. THEMIS A may have crossed the outflow region of reconnection. Comparison
of velocity distributions collected before 12:55 (subinterval #1), during
observations of $v_{z}>0$ (subintervals #2 and #3), and well after the bipolar
$v_{z}$ (subinterval #6) shows that magnetospeheric plasma (subinterval #1,6)
are predominantly field-aligned anisotropic, whereas injected magnetosheath
plasma (subintervals #2, #3 and #5) is transversely anisotropic (both these
types of anisotropy are quite typical for the magnetopshere and magnetosheath,
see Gary et al. (1995); Samsonov et al. (2007) showing that magnetosheath
plasma generally has $T_{\perp}/T_{\parallel}>1$, and Wang et al. (2013)
showing the magnetospheric thermal plasma often has
$T_{\parallel}>T_{\perp}$). Therefore, Fig. 3 further confirms that THEMIS A
observed signatures of magnetic reconnection at the magnetopause: bipolar
$v_{z}$ pulses and injection of cold magnetotheath plasma into the
magnetosphere. This reconnection triggers the MHD (ultra-low-frequency) waves
that quasi-periodically brings the magnetosheath population (likely entered
into magnetosphere through the reconnected magnetopause) to THEMIS A location
via ${\bf E}\times{\bf B}$ drift, as shown in the cold transversely
anisotropic population in the distribution functions measured during
subinterval #2-5.

Figure 3: The overview of the solar wind discontinuity interaction with the
magnetopause observed by THEMIS A: magnetic field components (a), ion flow
components (b), ion energy spectrum (c), ion pitch-angle distributions for
different energy ranges ($[100-2000]$ eV for (d), and $[4-20]$ keV for (e)),
2D cuts of ion distributions in ($m_{p}v_{\parallel}^{2}/2$,
$m_{p}v_{\perp}^{2}/2$) plane for several intervals indicated by numbers.

###  2.3 Night-side event

To investigate a possibility for a solar wind discontinuity to trigger the
night-side (flank) magnetopause reconnection, we consider MMS and THEMIS
observations during 2021-03-01 event shown in Fig. 4. MMS upstream of the bow
shock observes several solar wind discontinuities: large scale magnetic field
rotation between 04:35 and 04:50 (marked as 1 in panel (a) of Fig. 4), smaller
scale rotation between 04:52 and 04:56 (marked as 2) and a series of $B_{z}$
reversals between 06:00 and 06:20 (marked as 3). The spatial scale of the
first discontinuity estimated from MMS1 data is about $10^{5}$ km. In fact
this structure consists of several embedded discontinuities with spatial
scales of 11700, 23500 and 9800 km. The second discontinuity have a spatial
scale of about 7400 km and consists of two adjacent discontinuities with
estimated scales of 2000 and 1900 km. The last marked interval includes
several $B_{z}$ reversals, the first one, observed at 06:03, have a spatial
scale of about 31000 km and consists of two smaller scale discontinuities with
scales of 6200 and 1800 km. The one, observed at 06:15, has spatial scale of
5800 km and doesn’t appear in the magnetosheath and nigh-side observations.

Each discontinuity is accompanied by solar wind velocity jump (not shown). The
same series of discontinuities is observed by THEMIS D downstream of the bow
shock in the dayside magnetosheath. Discontinuities are compressed at the bow
shock: the magnetic field increases from $10$nT in the solar wind to $\sim
40$nT in the dayside magnetosheath (THEMIS D). Spatial scale decreases to
35000 km ($2500+4000+6800$ km) for the first group of discontinuities, 1200 km
for the second discontinuity, and 18000 km ($4200+4800$ km) for the third
group of discontinuities. Note the downstream of the day side bow shock is
further compressed by plasma flow breaking at the magnetoapuse, and this
results in large discontinuity magnitude increase (see discussion in Kropotina
et al., 2021). Thus, it would be interesting to check the discontinuity effect
on the night side magnetosheath (see examples confirming such propagation of
solar wind discontinuities to the night-side magnetopause in, e.g., Wang et
al., 2018c, 2020c), where magnetopause surface is almost parallel to the
plasma flow Hasegawa (2012); Lukin et al. (2019).

THEMIS B and C (ARTEMIS P1 and P2) show several discontinuities in the night
side magnetosheath (downstream from the bow shock, $\sim 50$ Earth radii away
from the day side THEMIS D observations). These discontinuities are only
weakly compressed by the bow shock: magnetic field magnitude increases from
$10$nT to $15$nT and discontinuity spatial scales stay almost the same or even
increase: $10^{5}$ km ($11000+17000+12400$ km) for the first group of
discontinuities, 9000 km for the second discontinuity, and 64000 km
($22000+15000$ km) for the third group of discontinuities. Note a typical ion
thermal gyroradius in the shocked solar wind (in the magnetosheath) is $\sim
100$km for cold ions and $\sim 1000$km for hot (magnetospheric) ions. Thus
small-scale discontinuities are ion kinetic structures for hot ions, but is
quite thick for cold magnetosheath ions.

THEMIS C and B cross the magnetopause at 03:50 and 04:05 (a clear change in
ion spectra is seen in Fig. 4(g,j)), and after the magnetopause crossing both
THEMIS B and C stably measure magnetosheath plasma. However, there are several
bursts of hot magnetospeheric ion population on the magnetosheath side around
discontinuities, between 05:12 and 05:20, 06:20 and 07:00. In Fig. 5 we
describe details of these hot plasma bursts associated with discontinuities.
For reference we use ion velocity distributions measured within the
magnetosphere (interval #1 in Fig. 5(f)) and in the quiet magnetosheath
(intervals #2,3,5 in Fig. 5(g,h,j)): the magnetospheric population is
characterized by a finite $\sim 10$ keV fluxes isotropically distributed in
$(\parallel,\perp)$ energy space, whereas the magnetosheath population is
characterized by large amplitude fluxes of field-aligned flow
($E_{\parallel}\sim 1$keV). During interval #4 (the first group of
discontinuities) ion distribution function shows a combination of
magnetosheath (flowing) and magnetospheric (hot isotropic) plasmas. Pitch-
angle distributions in Fig. 5(d,e) confirms that discontinuities are
associated with appearance of hot isotropic ion population. A similar picture
is observed for the third group of discontinuities (interval #6): pitch-angle
distributions and velocity distribution show an appearance of a population of
hot ($\sim 10$ keV) isotropic magnetosphereic plasma (see Fig. 5(d,e, k)).
Observation of magnetosphereic plasma far from the magnetopause (deep inside
the magnetosheath) in association with discontinuities suggest that THEMIS C&B
cross field lines connecting to the reconnected magnetopause, i.e. there is a
magnetic reconnection in regions where these discontinuities impact to the
magnetopause.

Figure 4: The overview of MMS&THEMIS&ARTEMIS observations on 2021-03-01. From
top to bottom: (a) solar wind discontinuity (magnetic field on MMS#1), the
same discontinuity observed downstream of the bow shock (magnetic fields (b)
and ion spectra (c) on THEMIS D), magnetic fields observed downstream of the
flank bow shock ((d) for THEMIS B & (i) for THEMIS C), plasma flow velocities
on THEMIS B (e), electron density and temperature on THEMIS B (f), ion and
electron spectra on ((g,j) for THEMIS B & (h,k) for THEMIS C). Bottom panel
shows spacecraft location relative to the model bow shock and magnetopause.
Figure 5: The overview of the solar wind discontinuity interaction with the
magnetopause (THEMIS B): magnetic field components (a), ion flow components
(b), ion energy spectrum (c), ion pitch-angle distributions for different
energy ranges ($[100-2000]$ eV for (d) and $[4-20]$ keV for (e)), 2D cuts of
ion distributions in ($m_{p}v_{\parallel}^{2}/2$, $m_{p}v_{\perp}^{2}/2$)
plane for several intervals indicated by numbers.

###  2.4 Supporting events

Events in Figs. 2, 4 demonstrate the magnetopause reconnection after the solar
wind discontinuity impact, but for these events we do not have observations of
the non-reconnected magnetopause before the arrival of the discontinuity.
Thus, the reconnection might have already started even before the
discontinuity arrives, and would be only modified by this impact. To verify
the key role of the discontinuity impact in triggering the reconnection, we
analyze three supporting events when the spacecraft crossed the magnetopause
before and after the discontinuity arrives. In all three events the
magnetopause does not show reconnection signatures before the discontinuity
impact, but becomes reconnected only afterwards.

Figure 6: Overview of THEMIS&ARTEMIS observations on 2019-09-20. From top to
bottom: (a) solar wind discontinuity shown by two red dashed lines (magnetic
field at ARTEMIS#2); magnetic field of the magnetopause crossings by THEMIS A
and D before (b1) and after (b2-b4) the solar wind discontinuity impact;
plasma flow velocities (c), plasma density and ion temperature (d), ion
spectra (e) for the magnetopause crossings before (1) and after (2-4) the
solar wind discontinuity impact; the corresponding ion velocity distributions
around the magnetopause (f1-f4).

Figure 6 shows an overview of the 2019-09-20 event. THEMIS C is at
$r_{GSM}\sim(-24,-57,12)R_{E}$ and observes a series of discontinuities at
$\sim$00:48-00:55 UT. During 00:20-01:20 UT, THEMIS A crosses the magnetopause
several times, and two such crossings are shown in panels (b1-e1) and (b2-e2).
As shown in the figure, during the first crossing before the discontinuity
arrives at the magnetopause, there are no ion jets or other signatures of the
reconnection, i.e., THEMIS A crosses non-reconnected magnetopause.

In the second crossing right after the discontinuity arrives at the
magnetopause, THEMIS A is at $r_{GSM}\sim(9,9,2)R_{E}$ and observes the
bifurcated current sheet with several ion jets, the primary signatures of the
magnetic reconnection. In the local coordinate system, the observed ion bulk
velocity change across the magnetopause at two times, as marked by the black
dashed lines in panels (b2-e2), are $\Delta v_{1obs}\sim(-56,-34,-79)$ km/s
and $\Delta v_{2obs}\sim(5,25,-65)$ km/s. Magnitudes of these velocities,
however, are much smaller than magnitudes of velocity changes estimated from
the model of the reconnected magnetopause Phan et al. (2013); Hudson (1970);
Paschmann et al. (1986):

$\Delta\bm{v_{pred}}=\bm{v_{2}}-\bm{v_{1}}=\pm\sqrt{\frac{1-\alpha_{1}}{4\pi\rho_{i}}}\left(\bm{B_{2}}(1-\alpha_{2})/(1-\alpha_{1})-\bm{B_{1}}\right)$

where $\alpha=\frac{4\pi(p_{\parallel}-p_{\perp})}{B^{2}}$ is the anisotropy
factor, $p_{\parallel},\;p_{\perp}$ are the plasma pressures parallel and
perpendicular to $\bm{B}$. Subscripts 1 and 2 denote the magnetosheath inflow
region (marked by red dashed lines in Fig. 6(b-e)) and the jet region,
respectively. For this crossing, $\Delta v_{1pred}\sim(-250,81,-16)$ km/s and
$\Delta v_{2pred}\sim(230,-107,3)$ km/s. Moreover, the observed velocity
changes are also smaller than the estimate of the asymmetric Alfven velocity,
$V_{Al,asym}\sim 133.05$ km/s. Therefore, despite that quasi-parallel ion
flows are observed in the ion velocity distribution (see panels (f1-f2)), the
observed and predicted values of ion velocity changes are much different, and
THEMIS A may not observe the reconnected magnetopause.

After the discontinuity arrives at the magnetopause, both THEMIS D and THEMIS
E (not shown) observe almost the same signatures of magnetic reconnection,
though much more evident at THEMIS D. Both spacecraft are in the magnetosphere
near the magnetopause at $r_{dGSM}\sim(9,7,1)R_{E}$ and
$r_{eGSM}\sim(5,12,1)R_{E}$, and due to the magnetosphere compression by the
discontinuity both spacecraft appear in the magnetosheath after the
discontinuity (panels (b3-e3)). The estimated magnetopause thickness for the
two crossing shown in panels (b3-e3) and (b4-e4) are $L_{d1}\sim 924$ km
($\sim 2.38\rho_{iMSH}$, where $\rho_{iMSH}=\frac{m_{i}cv_{T}}{eB}$ is the
averaged value of the ion thermal gyroradius in the magnetosheath) and
$L_{d1}\sim 821$ km ($\sim 2.26\rho_{iMSH}$) (see detailed description of the
method in Haaland et al., 2014). Therefore, THEMIS D indeed crosses a ion-
scale magnetopause current sheet. In the local coordinate system, the observed
and predicted ion velocity changes across the magnetopause (at the two times
marked by the black dashed lines in panels (b3-e3) and (b4-e4)) are $\Delta
v_{1obs}\sim(-175,200,-9)$ km/s, $\Delta v_{1pred}\sim(-173,-1,6)$ km/s and
$\Delta v_{2obs}\sim(115,-21,-59)$ km/s, $\Delta v_{2pred}\sim(167,7,-12)$
km/s. The estimated asymmetric Alfven velocity is $V_{Al,asym}\sim 124.88$
km/s. Moreover, quasi-parallel flows are seen in the ion velocity distribution
(panel (f3)) during the first THEMIS D crossing. During the second THEMIS D
crossing, the strong ion jet is tangential to the magnetopause, but at the
moment of the jet observation the main magnetic field component is around
zero, i.e., there is a large uncertainty in projecting to the local magnetic
field direction. During both crossings, the nonzero normal velocity components
are observed together with the low energy population (panels (e3-e4)).
Therefore, THEMIS D observations clearly demonstrate the magnetopause
reconnection after the discontinuity impact, whereas THEMIS A observations
confirm that the magnetopause was not reconnected before this impact.

Figure 7: Overview of THEMIS&ARTEMIS observations on 2016-07-28. From top to
bottom: (a) solar wind discontinuity as marked by the two red dashed lines
(magnetic field at ARTEMIS#2); magnetic field of the magnetopause crossings by
THEMIS E before (b) and after (f) the solar wind discontinuity impact; plasma
flow velocities (c and g), plasma density and ion temperature (d and h), ion
spectra (e and i) for the magnetopause crossings from (b and f); ion velocity
distributions around the magnetopause crossing after the solar wind
discontinuity impact (j,k).

Figure 7 shows another example of the solar wind discontinuity interaction
with the magnetopause on 2016-07-28. During this event, THEMIS C is in the
solar wind at $r_{GSM}\sim(20,-52,16)R_{E}$ and observes a series of
discontinuities at $\sim$ 08:43-08:54 UT. The same series of discontinuities
are observed by THEMIS D in the magnetosheath around 09:00-09:05 UT (not
shown). Within 08:06-09:30UT, THEMIS A crosses the magnetopause twice. The
first crossing is shown in panels (b-e), and for this crossing the observed
and predicted flow changes are $\Delta v_{obs}\sim(163,-58,91)$ km/s and
$\Delta v_{pred}\sim(100,1047,-14)$ km/s, whereas the estimated asymmetric
Alfven velocity is $V_{Al,asym}\sim 16$ km/s. The large difference in the
observed and predicted ion velocity change indicates that THEMIS A crosses the
non-reconnected magnetopause.

Panels (f-i) show the second crossing, after the discontinuity arrives to the
magnetopause. Starting from 09:00UT (when the discontinuity is detected in the
magnetosheath by THEMIS D), THEMIS A observes variations in the magnetopsheric
magnetic field, whereas during the magnetopause crossing THEMIS A detects the
bifurcated current sheet and several ion jets (the primary signatures of the
magnetic reconnection). The observed and estimated ion velocity changes for
the two times marked by black dashed lines in panels (f-i) are $\Delta
v_{1obs}\sim(-206,-63,22)$ km/s, $\Delta v_{1pred}\sim(-332,-31,-11)$ km/s and
$\Delta v_{2obs}\sim(-251,-53,10)$ km/s, $\Delta v_{2pred}\sim(-211,1,2)$
km/s. The estimated asymmetric Alfven velocity is $V_{Al,asym}\sim 236.73$
km/s. Therefore, the similar velocity change between observations and the
model prediction suggests that THEMIS A indeed crosses the reconnected
magnetopause. Moreover, panels (j-k) show the corresponding 2D slices of the
ion distribution functions with clear quasi-parallel ion jets. Thus, these
observations show that the interaction between the solar wind discontinuity
and the magnetopause can trigger magnetic reconnection of the initially non-
reconnected magnetopause.

The third supplementary event is shown in Figure 8. During this event, THEMIS
C is in the solar wind at $r_{GSM}\sim(28,-51,15)R_{E}$ and observes a series
of discontinuities during $\sim$11:33-11:43 UT. The same series of
discontinuities are observed by THEMIS A in the magnetosheath around
$\sim$11:30 UT (not shown). Within 11:10-12:20 UT, THEMIS E crosses the
magnetopause several times. The first and the second crossings are shown in
panels (b-e). During these crossings, no ion jets or other reconnection
signatures are detected. Panels (f-i) show the third crossing, after the
discontinuity arrives at the magnetopause. During the magnetopause crossing,
THEMIS E is at $r_{GSM}\sim(11,-4,5)R_{E}$ and observes variations in the
magnetic field accompanied by ion jets. The observed and estimated ion
velocity changes for the two times marked by black dashed lines in panels
(f-i) are $\Delta v_{1obs}\sim(204,-82,-41)$ km/s, $\Delta
v_{1pred}\sim(225,61,-20)$ km/s and $\Delta v_{2obs}\sim(238,-29,-2)$ km/s,
$\Delta v_{2pred}\sim(251,16,-25)$ km/s. The estimated asymmetric Alfven
velocity is $V_{Al,asym}\sim 173$ km/s. Panels (j-k) show the corresponding 2D
slices of the ion distribution functions with quasi-parallel ion jets. As in
events from Figs. 6, 7, the observed ion velocity changes are comparable to
the predicted changes and to the value of the asymmetric Alfven velocity,
whereas ion velocity distributions show clear field-aligned ion jets.
Therefore, Fig. 8 confirms results from Figs. 6, 7 that the solar wind
discontinuity impact may trigger the reconnection of the initially non-
reconnected magnetopause.

Figure 8: Overview of THEMIS&ARTEMIS observations on 2019-12-21. From top to
bottom: (a) solar wind discontinuity shown by two red dashed lines (magnetic
field at ARTEMIS#2); magnetic field of the magnetopause crossings by THEMIS E
before (b) and after (f) the solar wind discontinuity impact; plasma flow
velocities (c and g), plasma density and ion temperature (d and h), ion
spectra (e and i) for the magnetopause crossings from (b and f); ion velocity
distributions around the magnetopause crossing after the solar wind
discontinuity impact (j,k).

##  3 Global hybrid simulation

In this section, a 3-D global hybrid code of Lin & Wang (2005); Tan et al.
(2011); Guo et al. (2018, 2020) is applied to investigate the evolution of the
solar wind discontinuity and understand the dayside magnetopause reconnection
driven by the impact of the discontinuity. In this hybrid model, ions are
considered as fully kinetic particles, while electrons are taken to be a
massless fluid. A spherical coordinate system $(r,\theta,\phi)$ is employed.
The simulation domain covers the dayside region ($x\geq 0$) with
$r\in[3.5R_{E},25R_{E}]$, where $R_{E}$ is the Earth radius. A perfectly
conducting boundary condition is applied for the inner boundary at
$r=3.5R_{E}$. The inflow boundary is located at $r=20R_{E}$, where the solar
wind flows toward the Earth together with the interplanetary magnetic field
(IMF). The initial IMF is assumed to be $(-1.25,-3.96,-3.86)$nT, the solar
wind ion number density is set as $N_{0}=12.0{\rm cm}^{-3}$, and the ion
temperature is chosen as $6.7$eV, based on the conditions observed by THEMIS C
before the rotational discontinuity arrives (the first, day-side event). The
IMF on the sunward side of the discontinuity is chosen as $(-0.24,-5.45,1.52)$
nT. The solar wind velocity changes across the rotational discontinuity from
$(-356.4,-27.2,-3.87)$ km/s to $(-350.0,17.7,-30.37)$ km/s. More detailed
descriptions of how to impose discontinuity in the hybrid model can be found
elsewhere (Guo et al., 2018, 2021a). The number of grid cells is $n_{r}\times
n_{\theta}\times n_{\phi}=320\times 220\times 180$, and a total of $\sim
5\times 10^{9}$ particles are used. To reduce computing expenses, the grid
cells in the radial direction are set to be non-uniform. A smaller grid size
of $\Delta r\simeq 0.025\to 0.05R_{E}$ is used around the magnetopause and in
the magnetosheath, while a larger grid size is set in the solar wind. We also
set the solar wind ion inertial length equal to $0.1$Re, i.e., a scaling
factor is about $\sim 9.57$ is needed to scale the time and velocities to the
realistic values.

Figure 9 shows the discontinuity in the numerical simulation at three time
intervals. The initial solar wind discontinuity (left panels) repeats the
configuration and magnetic field components of the ARTEMIS observations from
Fig. 2, a rotational discontinuity with a constant plasma density and jumps of
plasma velocity across the discontinuity. The discontinuity downstream of the
bow shock (center panels) is characterized by a magnetic field increase from
the initial $\sim 5$nT to $\sim 20$nT. This magnetic field compression
resembles the THEMIS A observations in the magnetosheath (see Fig. 2). In the
magnetosheath, the ion number density $N_{i}$ (Fig. 9c2) and ion temperature
$T_{i}$ (Fig. 9d2) increase, and the ion flow brakes with the ion bulk
velocity $V_{i}$ (Fig. 9b2) slows down. When the discontinuity arrives at the
magnetopause (right panels), the simulation shows typical signatures of
magnetic reconnection: plasma jet in $V_{z}$ (Fig. 9b3) and an increase of ion
temperature (Fig. 9d3) due to magnetospheric plasma leakage (compare with
THEMIS A observations shown in Fig. 3).

To further confirm that the discontinuity interaction with the magnetopause
triggers magnetic reconnection, we visualize the solar wind discontinuity
motion. The contour plots of Figure 10 show the magnetic field strength for
three moments of time: before arriving the solar wind discontinuity (top
panels), when solar wind discontinuity interacts with the magnetopause (middle
panels), and when solar wind discontinuity passes through the magnetopause
(bottom panels). In the figure, the orange lines mark the magnetic field lines
outside the magnetopause, and the black lines denote the field lines at the
magnetopause. At $t=20$, before the solar wind discontinuity arrives at the
magnetopause, magnetopause flux ropes has formed by reconnection between the
initial IMF $(-1.25,-3.96,-3.86)$ nT and the dipole field, which are denoted
by the black field lines. It is found that the magnetopause reconnection
occurs in the high-latitude regions of the dayside magnetopause on the
dawnside and duskside, which is marked by the blue boxes (note this region
were not observed by spacecraft). When the solar wind discontinuity interacts
with the magnetopause, at $t=30$, magnetic reconnection is seen at low- and
middle latitudes of the dayside magnetopause, which is denoted as the red box.
Finally, when the solar wind discontinuity passes through the magnetopause, no
reconnection is found at the dayside magnetopause due to the magnetic field
turns from $(-1.25,-3.96,-3.86)$ nT to $(-0.14,-5.45,1.52)$ nT.

Figure 9: The overview of global hybrid simulation of solar wind discontinuity
(left panels), the same discontinuity in the downstream of the bow shock
(center panels), and magnetopause reconnection (right panels): magnetic field
vector (a1-a3), ion velocity components (b1-b3), ion number density (c1-c3),
and ion temperature (d1-d3).  Figure 10: The overview of solar wind
discontinuity interaction with the magnetosphere: magnetic field strength in
3D and 2D planes. Three moments are shown: at $t\sim 20\Omega_{i}^{-1}$ the RD
was in the solar wind, at $t\sim 40\Omega_{i}^{-1}$ the RD interacts with the
magnetopause, at $t\sim 70\Omega_{i}^{-1}$ the RD passes through the
magnetopause.

Using advantage of the hybrid simulation which treats ions as particles, we
plot ion distribution functions right around the region of the magnetopause
impact by the solar wind discontinuity. Figure 11 shows that distributions on
the magnetosphere side contain two ion populations: the hot field-aligned
flowing population and cold population. The latter one penetrates from the
magnetosheath along reconnected magnetic field lines. These model
distributions resemble observational distributions #3,5 from Fig. 3, which are
measured when cold magnetosheath plasma injections are observed within the
magnetosphere. Therefore, simulation results shown in Fig. 9-11 confirm the
scenario of the magnetic reconenction driven by the magnetopause impact by
solar wind discontinuity.

Figure 11: (a) A zoom-in view of the ion number density in the y=0 plane; (b)
Ion velocity distributions in the ($V_{\perp,1}$,$v_{\parallel}$) and
($V_{\perp,1}$,$V_{\perp,2}$) planes on the magnetosphere side at the location
marked by the red box in Fig. 8a.

##  4 Discussion and Conclusions

We presented observational and simulation evidence that the solar wind
discontinuity impact may trigger the magnetic reconnection at the
magnetopause. More general, the rotational discontinuity is intensified by
crossing the shock wave (the Earth bow shock) and then impacts the tangential
discontinuity (magnetopause), triggering the magnetic reconnection and plasma
mixing (cross-penetration of magnetosheath and magnetospheric plasmas). We
note that the rotational discontinuity interaction with the bow shock
significantly modifies the discontinuity properties and add compressional
perturbations, and thus we shall rather discuss interaction of the tangential
discontinuity (magnetopause) with the discontinuity sharing properties of both
rotational and tangential discontinuities. Reconnection of such rotational
discontinuity downsteram of the bow shock is possible when the bow shock is
quasi-parallel (Guo et al., 2021a) or quasi-perpendicular, with large magnetic
field rotation angle (Guo et al., 2021b). In our cases, the bow shock
configuration does not support the discontinuity reconnection in the
magnetosheath, and thus discontinuity reaches the magnetopause and triggers
the magnetopause reconnection. Although this scenario has been considered for
the specific plasma system of the solar wind interaction with the Earth’s
magnetosphere, we may speculate about an application of the similar
discontinuity-discontinuity interaction in other systems.

Discontinuity interactions should be rather common phenomena for solar wind
(and more general, stellar wind) where such discontinuities may be formed by
Alfven wave turbulence (e.g., Buti et al., 1998; Vasquez & Hollweg, 1999,
2001) and nonlinear Alfven wave steepening (Hada et al., 1989; Kennel et al.,
1988; Malkov et al., 1991; Medvedev et al., 1997), and then are transported by
plasma flows having spatially and temporally varying flow speed and Alfven
speed. Such variations of plasma flow speed and Alfven speed would force
discontinuity-discontinuity interactions, with the possible triggering of the
magnetic reconnection and plasma mixing. This scenario is actively discussed
for the solar wind turbulence (see, e.g., in Greco et al., 2008, 2009;
Servidio et al., 2011a, b; Pecora et al., 2018; Vörös et al., 2021), and it
can be quite perspective for magnetized flows of pulsar wind carring multiple
discontinues (e.g., Coroniti, 1990; Bogovalov, 1999; Spitkovsky, 2006; Cerutti
& Giacinti, 2020). For pulsar wind the magnetic reconnection is considered as
an important mechanism of magnetic energy transformation to plasma energy with
the magnetic field reduction and formation of pulsar flares (Arons, 2012; Abdo
et al., 2011; Aharonian et al., 2012). However, only internal instabilities of
discontinuities and their interaction with the shock waves have been
considered as a trigger of the magnetic reconnection (e.g., Lyubarsky & Kirk,
2001; Uzdensky et al., 2011; Cerutti et al., 2012; Cerutti & Philippov, 2017).
A proposed here discontinuity-discontinuity interaction may be an alternative
mechanism for the magnetic reconnection triggering, that would work for
generally stable rotational discontinuities and would not require magnetic
reconnection localization around the shock wave.

To conclude, we have described the magnetic reconnection triggering due to the
interaction of two discontinuities: the solar wind rotational discontinuity
(modified and intensified via the bow shock crossing) and tangential
discontinuity of the Earth’s magnetopause. Spacecraft observations and global
hybrid simulations demonstrate that magnetic reconnection triggered by the
solar discontinuity impact on the magnetopause results in mixing of hot
rarefied magnetospheric plasma and cold dense solar wind (magnetosheath)
plasma. We also show that such discontinuity-driven reconnection can be
observed at both day-side magnetopause (where solar wind plasma flow
contributes significantly to the pressure balance across the magnetopause) and
the deep flank magnetopause (where solar wind plasma flow is almost tangential
to the magnetopause surface). These results underline an importance of
discontinuity-discontinuity interactions for plasma mixing via magnetic field
line reconnection.

## Acknowledgements

Alexander Lukin and Anatoli Petrukovich acknowledge support from Russian
Science Foundation through grant No. 19-12-00313 covering the covering general
spacecraft data analysis and data/model comparison parts of this work. Anton
Artemyev acknowledges support from NASA HSR 80NSSC20K1788 and HGI
80NSSC22K0752 covering analysis of discontinuity configuration aspect of this
work.

Anton Artemyev and Xiaojia Zhang also acknowledge NASA contract NAS5-02099 for
use of data from the THEMIS mission. We thank K. H. Glassmeier, U. Auster, and
W. Baumjohann for the use of FGM data provided under the lead of the Technical
University of Braunschweig and with financial support through the German
Ministry for Economy and Technology and the German Aerospace Center (DLR)
under contract 50 OC 0302. THEMIS data is available at
http://themis.ssl.berkeley.edu. Data access and processing was done using
SPEDAS V4.1 (Angelopoulos et al., 2019) available at https://spedas.org/.

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