Interaction of Cold Streaming Protons with the Reconnection Process

We employ a 2.5D particle-in-cell simulation to study a scenario where the reconnection process captures cold streaming protons. As soon as the tailward streaming protons become involved, they contribute to the overall momentum balance, altering the initially symmetric dynamics. Adding tailward-directed momentum to the reconnection process results in a tailward propagation of the reconnection site. We investigate how the reconnection process reorganizes itself due to the changing momentum conditions on the kinetic scale and how the reconnection rate is affected. We find that adding tailward momentum does not result in a significantly different reconnection rate compared to the case without cold streaming protons, when scaled to the total Alfvén velocity. This implies that the effect of changing inflow conditions due to the motion of the reconnection site appears to be minimal. The dynamics of the particles are, however, significantly different depending on whether they enter on the tailward or Earthward side of the reconnection site. On the Earthward side they are reflected and thermalized, while on the tailward side they are picked up and accelerated. The cold proton density and E z on the Earthward side are turbulent, while the tailward side has laminar cold proton density striations and an embedded E z layer. Also, since the initial plasma sheet population is swept up on one side and flushed out on the other, asymmetries in the densities and strength of Hall fields emerge. Our results are important for understanding the development and dynamics of magnetospheric substorms and storms.


Introduction
Magnetic reconnection describes the process facilitating the release of stored electromagnetic energy into mechanical (kinetic and thermal) energy of the plasma, producing a global change of the magnetic configuration due to local decoupling of plasma from the magnetic field. In many plasma systems this intricate interaction between the fields and particles includes populations with different properties, such as heavy ions, cold ions, streaming populations, or a combination of these (Kistler & Mouikis, 2016). The presence of additional ion populations can, if magnetized, mass load the system, and the resulting reduction of the Alfvén velocity is believed to be a mechanism, which can slow down reconnection (Hesse & Birn, 2004;Shay & Swisdak, 2004). In addition to the mass-loading effect, other mechanisms such as the effect of heavy ions on the tearing growth rate (Karimabadi et al., 2011) and induced ambipolar (charge separation) electric fields (Liang et al., 2016(Liang et al., , 2017 have been suggested. Heavy ions, such as O + (and their accompanying electrons), have been found to affect the reconnection process by extracting energy from the system that would otherwise go to the protons, thereby significantly reducing the reconnection rate, but less than expected by mass loading (Kolstø et al., 2020;Tenfjord et al., 2018Tenfjord et al., , 2019. Magnetic reconnection in the presence of shear (oppositely directed) flow has previously been investigated in detail (Cassak, 2011;Cassak & Otto, 2011;Mitchell & Kan, 1978). Reconnection occurs for such configurations in, for instance, tokamaks, at the dayside magnetopause (especially during northward directed interplanetary magnetic field) (e.g., Gosling et al., 1986;La Belle-Hamer et al., 1995) and in the magnetosheath (Eriksson et al., 2018). Based on theoretical arguments and fluid simulations, it is believed that such flow will reduce the reconnection rate by effectively reducing part of the magnetic tension that drives the outflow (Cassak, 2011). It has also been observed that shear flow causes the outflow jet and current sheet to tilt (La Belle-Hamer et al., 1994) and causes a configuration that is susceptible to tearing mode and Kelvin-Helmholtz instabilities (Chen et al., 1997;Li & Ma, 2010;Roytershteyn & Daughton, 2008).
Varying conditions in the inflow regions, such as different plasma populations or plasma properties, can also have an impact on the reconnection process. On the dayside, the effect of plasmaspheric drainage plumes has been found to mass load the reconnection site, thereby reducing the effective solar wind magnetosphere coupling (Borovsky & Denton, 2006;Dargent et al., 2020). However, the effect of ions originating from the ring current and warm plasma cloak has been observed not to greatly affect the reconnection rate (Fuselier et al., 2016;Wang et al., 2015). Another source of heavy ions on the dayside is O + originating from the high-latitude ionosphere. During northward directed IMF B z dual-lobe reconnection can trap O + and mass load the dayside magnetopause boundary, which may affect the reconnection rate (Fuselier et al., 2019). On both the dayside and nightside, observations show that the involvement of additional cold, dense plasma or plasma beams can alter the dynamics of the reconnection process, affect the reconnection rate, and modify the Hall term in Ohms law (Li et al., 2017;Toledo-Redondo et al., 2018;Xu et al., 2019). Since the Larmor radius depends on the mass and velocity, these different ion populations will lead to a different kinetic behavior and additional scale lengths in the system (Alm et al., 2019;André et al., 2016;Dargent et al., 2019;Divin et al., 2016;Toledo-Redondo et al., 2015).
In this manuscript we study how a streaming population is captured by the reconnection process and what the effects are. This scenario is studied using a 2.5D particle-in-cell (PIC) simulation where a cold streaming population is inserted in the two lobes and eventually is captured by the reconnection process. Scenarios where streaming populations interact with magnetic reconnection can be attributed to ionospheric ion outflow (characteristically observed as cold ions with a parallel velocity), streaming mantle interaction, or high-latitude magnetopause reconnection where streaming magnetosheath interacts with the magnetopause. Ion outflow from the high-latitude ionosphere is believed to be a significant source of plasma for the terrestrial magnetosphere (Chappell et al., 1980;Haaland, Svenes, et al., 2012). These ions (mostly O + and H + ) flow parallel to the magnetic field and fill the lobes with streaming low-energy ions. The outward velocity is typically observed to be up to ≈50 km/s Haaland, Li, et al., 2012). The Earth's plasma mantle is one of the major suppliers of particles for the plasma sheet. The plasma mantle was first reported by Rosenbauer et al. (1975), as a persistent layer of tailward-flowing magnetosheath-like plasma inside of and adjacent to the magnetopause. The tailward-directed parallel flow speed was found to usually lie between 100-200 km/s and always less than the adjacent magnetosheath flow velocity. Observations from ARTEMIS reported an average temperature of about ≈0.05-0.2 keV and density ≈0.1-1 cm −3 (Wang et al., 2014). Magnetotail observations have revealed that the distant plasma mantle can occur even near the equatorial plane (Schillings et al., 2019;Siscoe et al., 1994;Taguchi et al., 2001). In our simulation we have chosen the streaming velocity of v = 0.5V A , which should be considered as an extreme (based on a lobe magnetic field of B 0 = 20 nT and a current sheet density of n 0 = 0.2 cm −3 , the Alfvén velocity is 1,000 km/s, which would correspond to a streaming velocity of 500 km/s).
The manuscript is organized as follows: In Section 2 we describe the simulation setup. Section 3 describes the motion of the X line as the streaming cold plasma interacts with the reconnection process. In Section 4 we show specific velocity distributions, representative ion particle trajectories, and describe which forces these particles experience during their evolution. In Section 5 we discuss the asymmetries in the Hall electric field and the additional scale length introduced by the cold plasma population. In Section 6 we compare the reconnection rate of our simulation to a separate simulation without cold streaming ions and discuss how the streaming plasma population affects the rate. A discussion and a summary are given in Section 7.

Simulation Setup
The simulation is designed to study how a streaming population is captured by the reconnection process. The streaming protons and electrons are chosen to have zero temperature and a streaming velocity of v x = 0.5V A on both sides of the neutral sheet. We employ a 2.5D (two spatial dimensions [x and z] and three velocity dimensions [x, y, and z]) PIC, which has previously been applied to a variety of reconnection problems (e.g., Hesse et al., 2001Hesse et al., , 2018Tenfjord et al., 2018Tenfjord et al., , 2019. The initial magnetic field configuration is a two-dimensional generalized Harris-type equilibrium (see Hesse & Bern, 2004, for details) with zero guide field (B y = 0). It is defined as B x = B 0 tanh(z∕ ), where = 2d p is the half-width of the current sheet layer. Lengths are normalized to the proton inertial length: d p = c∕ pi . Time is normalized to the inverse of the proton cyclotron frequency: Ω −1 p . All calculations use a proton/electron mass ratio of m p ∕m e = 25. A total of ∼1·10 10 macroparticles are employed, divided equally between the four species (warm protons, warm electrons, streaming cold protons, and streaming cold electrons). Boundary conditions are periodic at x = 0 and x = x max . At the upper and lower boundaries, we employ specular reflection for particles, and the out-of-plane electric field is set to 0, implying flux conservation in the simulation domain. Our simulation domain size is 400 × 50d p , divided into a grid of 6, 400 × 1, 600 cells. The grid is extended in the x-direction to account for the X-line propagation. A time step of pe t = 0.5 is employed. The density is normalized to the foreground current sheet density n 0 (unity), which supports the initial Harris sheet equilibrium. The velocity is normalized to the proton Alfvén speed, based on n 0 , and the electric field is normalized by V A B 0 . The foreground temperatures fulfill T p + T e = 0.5m p V 2 A , and proton-to-electron temperature ratio is T p ∕T e = 5. The ratio between the electron plasma frequency and gyrofrequency is pe ∕Ω ce = 2. The presented data are displayed in normalized units. A uniformly distributed proton (H + ) background with n p = 0.2 is added to the Harris sheet density distribution, which leads to a peak density of n = 1.2. In addition to the uniform H + population, the cold streaming population with number density n c = 0.8 is added to the inflow regions ("lobes"), above and below a specific field line, approximately at |z| > 3d i where the initial magnetic field perturbation is centered. We use the term "cold protons" (and the accompanying cold electrons) for the initially cold species inserted in the beginning of the simulation, even though they thermalize throughout the simulation and get heated. The cold protons do not contribute to the total pressure, so the plasma = 0.2 remains unchanged at 0.2 in the inflow. In our simulation we reserved the first 40 time steps for the system to equilibrate. During this period the cold electrons are somewhat heated numerically. For comparisons we also use output from a previous simulation used in Tenfjord et al. (2018).

Motion of X line
Reconnection initiates with warm nonstreaming populations only, and the reconnection site does not move. When the momentum-laden streaming cold ions are captured by the reconnection process, the momentum balance of the system is altered, causing a motion of the reconnection site in the direction of the streaming plasma. Figure 1 shows the cold streaming proton density, warm proton density, and the Hall electric field E z at four different times (a video of the evolution is provided as supporting information). In Figure 1, t = 0 represents the initial configuration, showing how the cold protons are distributed at the beginning of the simulation. At t = 72 the cold protons become involved in the reconnection process, and in the following time steps a tailward (toward the right) motion of the X line is apparent. This shows that once a sufficient amount of tailward-directed plasma has been captured by the reconnection process, the system reorganizes itself to incorporate the additional x-directed momentum by facilitating a tailward-directed motion of the X line. The Earthward (toward left) outflow region is stretched by the motion of the X line. On the opposite side, the outflow region is compressed, and the Hall field is broader in the z-direction. The x-directed velocity of the X line is determined by the total mass velocity: where the sum is taken over all plasma populations (warm protons, streaming protons, and the electrons) over the entire simulation domain. As seen in Figure 1, the streaming population gets involved around t = 72. After a short transition period (∼5 Ω −1 p ) the X line moves at a constant velocity determined by the total mass velocity. Such a convection velocity is expected based on fluid arguments; see Doss et al. (2015) for expected convection velocities and densities in the case of asymmetric magnetic reconnection.
In Figure 2 we show the in-plane velocity vectors and the x-directed velocity as background color. The top row shows the velocities in the simulation frame for the warm protons, cold streaming protons, and the total mass flow. The bottom row shows the same quantities transformed into the frame moving with the reconnection site (equal to total mass velocity). From these panels it is apparent that the reconnection process has facilitated the tailward propagation of the reconnection site so that in its frame of reference the inflow and outflow remain symmetric. In the next section we look in greater detail at the dynamics of the particles and how they lead to the tailward motion of the X line.

Particle Interactions
In Figure 3 we show velocity distributions of the cold protons taken at z = 0 and seven different x locations. At this time, t = 100, the X line is located at approximately x ∼ 215. On the right side of the X line the distributions consist of two cold counterstreaming populations. At this location and further tailward, the cold population undergoes meandering motions as they are streaming tailward. Thus, if a particle enters the exhaust to the right of the X line, it gets picked up and accelerated in the positive x-direction, while performing meandering motions. This behavior is seen in Figure 4 for the rightmost particle, where the particle enters the diffusion region from the southern lobe and is ejected to the tailward exhaust. This motion results in cold proton density striations (see Figure 4), visible above and below the current sheet. The striations extend in the tailward direction with a velocity that corresponds to the flux velocity (frozen in). Downstream, the density striations become progressively weaker and eventually disappear due to particle scattering in the curved magnetic field.
These clear density striations in the tailward exhaust are a signature that the cold streaming protons are confined and that the vertical distance corresponds to their meandering width (which in turn is related to their thermal energy). This layer and the asymmetries between the two exhaust regions will be discussed in Section 5.
On the Earthward (left) side of the X line the velocity distributions are different. Figure 3 for x = 195 shows cold protons with both positive and negative v x . By following a test particle from this region, we see that the particles that have a negative v x represent incoming particles that have been reflected (Figure 4), while the population with positive x-velocity is inbound, not yet reflected. Compared to the tailward side, the distribution here becomes largely thermalized, which produces a more turbulent region with fluctuations in both density and E z (discussed in Section 5).
To understand which forces cause a particle to reverse its x-velocity we show, in Figure 5, the forces acting on the particle, which passes through x = 213 at t = 100. At t = 100 (indicated by the black vertical line), the particle has the velocity: (v x , v y , v z ) = (0.3, −0.1, 0.5). From this time the particle is traced forward and backward in time based on interpolations of the dynamically changing fields, which are updated every 0.2 Figure 2. In-plane velocities of the warm, cold, and combined ion populations in the simulation frame (top row) and the frame moving with the X line at t = 100. The quivers show the in-plane velocity as wind vectors (the amplitude v = 0.5 is indicated in the top left panel), while the color map shows v x . In the frame moving with the reconnection site, the total mass velocity of the inflow and outflow remains symmetric. Ω −1 p . Once the particle enters the diffusion region (t > 100), it gets a significant y-directed velocity by the reconnection electric field. Meanwhile, in the x-direction, a combination of E x and, to a lesser degree, v y B z reverses v x from positive to negative (seen in Figure 5 at t > 100).
Ions that reverse their x-directed velocity all experience a significant E x field, as for the particle analyzed in Figure 5. Figure 6 shows the smoothed magnitude of E x and ∫ E x dx along x for z = 0. At this time, the X line is at x = 219. A significant negative E x exists in the range x = 195 − 215, which coincides with the location where the cold protons are turned around, at this time. To the right of the X-line location, at x = 225−240, a positive but weaker E x exists. The asymmetry of E x between the tailward and Earthward side is a consequence of the streaming motion of the cold plasma. In contrast to the ions, the electrons that enter the exhaust left of the X line will get magnetized and will be "picked up" by flux tubes moving Earthward. A relatively strong E x will then be induced in order to turn around the tailward streaming protons and to  Figure 5. Forces acting on particle that passes through x = 213 and z = −0.5 at t = 100 (marked by the vertical line). The particle starts in the southern lobe with an x-directed velocity of approximately 0.5; after performing a couple of bounces its positive x-directed motion is turned into a negative v x , primarily by a negative E x . In the time it spent inside the diffusion region it also gained a positive y-directed motion, and the force from v y B z also has a net contribution in the negative direction in the later stage of the evolution. accelerate the cold protons that have been turned around so that quasineutrality is maintained. The particles that enter to the right of the X line are to a much lesser degree affected by the above effect, since they already carry a tailward direction motion. Only a relatively small E x is therefore needed to sustain the outflow.

Asymmetries in E z
As seen in Figure 1 (also seen in Figure 4), the tailward side has a smaller E z region embedded in the larger Hall structure, whose width is comparable to the Earthward-side Hall field. This embedded E z region is not unique to this simulation and was produced on both sides prior to the involvement of the cold streaming protons. These electron-scale structures have been seen in numerous simulations (Chen et al., 2011;Liang et al., 2017;Shay et al., 1998;Zhou et al., 2012) and are attributed to electron meandering motions (Drake et al., 2008;Shuster et al., 2015). However, when the cold streaming protons get involved, an asymmetry between the two sides of the exhaust emerges. The density and E z electric field on the Earthward side are turbulent, while the tailward side has laminar cold proton density striations and an embedded E z layer.
The larger Hall region on the tailward side, extending up toward and along the separatrices, is generated by the warm protons and is a result of the tailward motion of the X line sweeping up warm plasma sheet protons that were originally part of the initial plasma sheet population. This is in contrast to the Earthward side where the warm plasma sheet population is flushed out and replaced with the cold proton population. This can be seen in Figure 1. On the Earthward side the cold protons now dominate the number density.
In Figure 4 we see the rightmost, tailward-directed particle entering the diffusion region from the southern lobe with a streaming velocity of v x = 0.5V A . In Figure 3 at X = 215 and x = 220, we see that the cold protons found within the embedded E z layer form two cold counterstreaming beams. The density striations seen in Figure 4 are therefore a result of the cold protons being confined and bouncing in this preexisting E z layer. The thermal energy of the cold protons confined in this embedded layer (−0.5 ≲ z ≲ 0.5) is comparable to the convection corrected potential ( they experience in the frame moving with the average velocities. Since the thermal energy of the cold protons confined in this layer is comparable to the convection corrected potential, it appears that the inner E z layer is shaped by a combination of electron and cold ion bounce motion (after being established by electrons alone).
On the Earthward side this influence is prominent. The electron-scale E z layer, which existed prior to the cold protons involvement, has disappeared and been replaced by a much broader, turbulent structure. Figure  3 shows that the cold proton population to the left of the X line (X < 215) is more thermalized. Their thermal energy is too high to confine them in the same way as on the tailward side, and the laminar embedded E z 10.1029/2019JA027619 Figure 7. Momentum balance for each species at two z cuts at t = 110. The inertia terms (calculated with time step 0.2 Ω −1 p ) are small and not shown but included in the sum. The figure shows significant asymmetries in the strength and width of the Hall E z electric field between the Earthward (top row) and tailward (bottom row) side. On the Earthward side (panels a-d) the warm plasma population has been flushed out and replaced by lobe densities (mostly cold streaming protons), resulting in a narrow and weaker Hall field. On the tailward side (panels e-h) the warm plasma sheet has been swept up by the motion of the X line, resulting in a thicker Hall region, with a smaller region embedded inside, whose width corresponds to the cold proton meandering width. layer that existed earlier has broken up and evolved into a turbulent region. This occurs in combination with the warm population having been flushed out by the motion of the X line, and the new "Hall" layer is primarily due to thermalized cold protons.
In Figure 7 we show the momentum balance for the warm and cold streaming protons − v e B x + n e z P e zz + inertia = 0) at x = 207 and x = 228. These two locations are about 10d i to each side from the active X line at t = 110. For the cold protons at the Earthward side (Figure 7c), the Hall electric field is balanced mainly by the thermal pressure. This shows that the cold protons get thermalized by the complicated motion, which includes reversing the x-directed motion (Figures 4 and 5). Since the majority of the warm plasma sheet protons, which initially preserved force balance, have been pushed out and replaced by cold protons, the vertical spatial extent of the Hall electric field has therefore decreased to a characteristic length dominated by the cold protons meandering width.
On the tailward side (Figure 7g), the cold streaming protons have not thermalized much, as seen in Figure 3 for X = 220. They continue with their tailward motion performing meandering motions as they are picked up by the outflow. At the same time, the warm plasma sheet protons are being swept up by the motion of the X line in the tailward direction. Therefore, contrary to the Earthward side, here the spatial extent of the Hall E z is still dominated by the warm protons' characteristic scale length (Figure 7f), with the embedded E z layer corresponding to the confined and bouncing cold protons. Figure 7g shows that for the cold protons E z is balanced by v × B forces in the broader diffusion region, while the thermal pressure becomes significant at |z| < 0.5, corresponding to the strong peak in E z seen at these locations. In Figure 7f, E z is balanced by the warm protons thermal pressure, which has a significantly larger scale length on the tailward side (∼3d i ) compared to the Earthward side (≤ 1d i ).

Figure 8.
Comparing the mass-loading-corrected reconnection rate to a baseline run without cold protons. The blue line shows the reconnection rate the simulation with streaming cold, scaled by √ (n p + n c )∕(n p ) = 2.23 (mass loading corrected). After correcting for the additional mass, there is no significant effect of the streaming cold proton population on the reconnection rate.
Figures 7d and 7h also show the location where each species is no longer frozen in, denoted by the violation of the condition E ′ = E + v × B = 0. As expected, the warm population violates the frozen-in condition over a larger region, while the electrons and the cold protons both violate the frozen-in condition over smaller regions. The fact that the cold protons and electrons appear to have comparable scale lengths is related to the cold protons being confined in the electron-scale embedded E z . Additionally, it could also be influenced by our mass ratio and may be related to the heating of electrons during the period when the system equilibrates (see Section 2).

Reconnection Rate
In Figure 8 we show the mass-corrected reconnection rate and compare it to the reconnection rate of a simulation without cold plasma but otherwise identical. The reconnection rate is first calculated as d dt Φ rec = ∫ E d and thereafter scaled to v A (n = n c + n p )∕v A (n = n c ) = √ (n c + n p )∕n p = 2.23 (ratio between Alfvén velocities with and without including cold ions). The x-axis is the change of magnetic energy from the initial magnetic state. Presenting the reconnection rate as a function of spent magnetic energy allows us to compare the rates when the two different simulations are at the same evolutionary stage. The blue line is the reconnection rate for the simulation discussed in this manuscript. If we compare the rate of the streaming cold protons run to the baseline run there is a slight offset, but in general, the difference in the reconnection rate is well explained by simple mass loading. This is in agreement with previous numerical simulation of cold ions, which are not streaming (Dargent et al., 2017(Dargent et al., , 2020Divin et al., 2016). This study shows that there does not appear to be any additional effect of streaming proton-reconnection interaction on the reconnection rate.
Thus, even though the motion of the X line causes the reconnection site to propagate downstream, into a region of unperturbed inflow conditions, it appears that this does not lead to an additional decrease in the reconnection rate.

Discussion and Summary
In this study we have found that the addition of a tailward propagating cold species causes the reconnection site to move tailward with a velocity corresponding to the total mass velocity. This means that once a sufficient amount of tailward-directed plasma has been captured by the reconnection process, the system reorganizes itself to incorporate the additional x-directed momentum by facilitating a tailward-directed motion of the X line. In the frame of the moving X line, both the inflow and outflow are then organized symmetrically.
As the propagating cold species is captured by the reconnection process, they are either turned around if they enter some distance to the left of the X line or further accelerated if they enter some distance to the right of the X line. The velocity distributions (Figure 3) show that particles coming into the outflow region with a positive v x are mixed with particles that have previously entered and turned around. This results in circular v x -v z distributions (Figure 3).
The tailward motion causes asymmetries in the reconnection geometry, elongating the current sheet on one side and broadening it on the opposite side. Large asymmetries between the two outflow directions arise due to the presence of cold streaming proton population. The tailward propagation of the X line sweeps up the warm plasma on the tailward side, while it is flushed out on the opposite side. This results in a thicker Hall region on the side where warm protons are present. In addition to this extended Hall layer, an embedded E z layer with a significant smaller vertical extent is present. Cold protons are confined and meandering inside this structure, producing laminar density striations. On the Earthward side, the streaming cold protons are thermalized by the complicated motion, which includes reversing the x-directed motion. This leads to a smeared out, more turbulent region with fluctuations in both density and E z . An additional asymmetry in E x between the two outflow regions arises as a result of the tailward streaming cold protons getting reflected in the x-direction on the Earthward side, causing a larger charge imbalance compared to the tailward side, where they experience an acceleration in the same direction they were initially streaming in. By comparing our simulation to a simulation that did not include cold streaming protons, we found that the inclusion of an additional cold species reduces the reconnection rate as predicted by mass loading, regardless of the species tailward propagation. Although we simulate a cold streaming population, we expect that similar effects would occur for a warm streaming population. We would however expect the kinetic substructures to be more smeared out.
Our results are important for understanding the development and dynamics of magnetospheric substorms and storms. We have shown that streaming plasma can effectively move the reconnection site. In both the magnetotail and on the dayside streaming protons can move the reconnection site into regions where the magnetic field is weaker, which would result in effective reduction or even cessation of reconnection. In addition, especially for the magnetotail, the Earthward outflow velocity is reduced (by a factor corresponding the mass velocity) leading to a potential reduction of the ionospheric response.