On the Impact of a Streaming Oxygen Population on Collisionless Magnetic Reconnection

Using 2.5‐D Particle‐In‐Cell (PIC) simulations, we investigate how magnetotail reconnection is affected by a cold, streaming, oxygen plasma population, attributed to an ionospheric source, in the inflow region. As the tailward streaming oxygen reaches the current layer, a tailward motion of the reconnection site is induced. Due to the much longer cyclotron period of the oxygen ions, oxygen cannot couple as directly into the reconnection dynamics as protons. We find that the oxygen ions couple indirectly by means of impacting the electron dynamics. Therefore, a demagnetized species can, in fact, alter the dynamics of the reconnection site. We see further that the reconnection rate remains unchanged relative to a nonstreaming run. Our results may prove useful for understanding the development and dynamics of magnetospheric substorms and storms.


Introduction
Magnetic reconnection is one of the primary energy conversion and transport mechanisms in space plasmas. It converts stored electromagnetic energy to thermal and kinetic energy of the plasma particles and is the motor behind large-scale phenomena such as particle acceleration, momentum, and magnetic flux transport throughout the magnetosphere and beyond. In order for reconnection to take place, the frozen-in condition needs to be violated (Vasyliunas, 1975); that is, the bulk motion of the electrons should decouple from the transport of magnetic flux.
In the plasma sheet, abundant species such as protons and electrons may at certain times be accompanied by heavier species as, for example, O + (Baker et al., 1982;Chappell et al., 1987;Moore et al., 2001). The presence of oxygen ions whose origin is from the high-latitude ionosphere has been observed in the Earth's magnetotail (Frank et al., 2012;Grande et al., 2013;Mouikis et al., 2018;Moore et al., 2001;Wilken et al., 1995;Zong et al., 1998), and the ionospheric outflow rate is proportional to geomagnetic activity (Baker et al., 1982). Spacecraft observations by Cluster reveal that O + may be the dominating ion species during storm time conditions (Kistler et al., 2005;Wygant et al., 2005). The GEOTAIL spacecraft observed bursts of tailward streaming oxygen ions of ionospheric origin in the magnetotail with a peak of the velocity distribution function (VDF) at 1,700 km/s (Wilken et al., 1995).
In this paper we investigate how the reconnection process is affected by a streaming oxygen population. Previous studies have shown that tailward streaming protons lead to a tailward motion of the X-point . While the temperature of the inflow population does not seem to play a major role for the reconnection rate (Dargent et al., 2020;Divin et al., 2016;Tenfjord et al., 2019), its mass density does Tenfjord et al., 2019). The inclusion of additional ion species has been shown to result in distinct spatial and time scales for the reconnection process (Divin et al., 2016;Shay & Swisdak, 2004;Toledo-Redondo et al., 2015). Compared to protons, the oxygen ions have a much larger cyclotron period, and thus, their coupling to the magnetic flux is less evident. Throughout the times of investigation, the oxygen ions in this simulation remain demagnetized. We here report on the effect a demagnetized streaming oxygen species has on the reconnection process.
The outline of this paper is as follows: Section 2 gives an overview of the simulation setup employed for this investigation. Section 3 examines the motion of the X-point, the evolution of the reconnection process, and the associated distribution functions. Finally, in section 4, we investigate how the reconnection rate is affected.

Simulation Setup
The analysis is performed by employing a 2.5-D Particle-In-Cell (PIC) simulation, that is, two spatial components and three field and velocity components, designed to model the magnetotail conditions during a burst of ionospheric oxygen outflow. The coordinate system is as follows: x is the reconnection outflow direction, y is the current direction, and z is the inflow direction. Initially, the magnetic field configuration is given by a generalized Harris-type equilibrium defined as B x = B 0 tanh(z∕ ), where = 2d p is the half width of the initial current sheet and d p = c∕ pi (= c √ m p ∕4 n 0 e 2 ) is the proton inertial length. Densities are normalized to the foreground density at the center of the initial current sheet n 0 .
A uniform proton distribution with a density of n b = 0.2 is added to the initial Harris sheet density configuration n p = n 0 ∕cosh 2 (z∕2d p ) resulting in a peak density of 1.2 in the current layer. The protons initially have no x-directed bulk velocity. Oxygen ions are distributed homogeneously above a specific field line, corresponding to a distance of |z| > 3d p from the current sheet. The O + has initially zero thermal velocity but where v A is the proton Alfvén velocity. The electrons associated with the oxygen ions have the same initial bulk velocity, that is, v e x = 0.5v A , whereas the electrons initially accompanying the protons are stationary. When referring to tailward streaming O + of ionospheric origin, this setup presumes that the oxygen ions has been preaccelerated to move in the x-direction.
The following mass ratios are employed: m p ∕m e = 25 for the protons/electrons and m O + ∕m p = 16 for the oxygen/protons. A total of ∼10 10 macroparticles is used. Boundary conditions are periodic at x = x min and x = x max . At z = z min and z = z max , specular reflection is enabled and the out-of-plane electric field E y is set to zero, preserving magnetic flux in the simulation domain.
Lengths are normalized to d p , whereas time is normalized to the inverse of the proton cyclotron frequency Ω −1 p = m p ∕eB. The size of our simulation domain is 410d p × 50d p with a grid size of 6,400 × 1,600. We employ a time step of pe t = 0.5. The velocity normalization is the proton Alfvén speed, based on the foreground current sheet density n 0 . The foreground temperatures fulfill T p + T e = 0.5, in units of (m p v 2 A ), derived from pressure balance n 0 (T p + T e ) = B 2 0 2 with n 0 = 1 and B 0 = 1, and the ratio of proton-electron temperature is chosen to be T p ∕T e = 5. The ratio between the electron plasma frequency and gyrofrequency is pe ∕Ω e = 2. Figure 1a shows the time evolution of the x-location of the X-point. Initially, the X-point is located at x = 205d p . At Ω p t = 50, the X-point shows an earthward displacement due to the formation of an island. It is not until the oxygen ions reach the reconnection site at Ω p t ≈ 120 that the X-point starts to move in the positive x-direction. When the oxygen density at the reconnection site is of significance, the X-point moves at the center-of-mass velocity, given by

Motion of the Reconnection Site
where the summation index i sums over all three species in the simulation domain and M i is the total mass of the respective species. The oxygen ions are the main contributor to v c due to their much higher momentum as compared to the other species.
The motion of the X-point is associated with a gradient of the y-component of the electric field by virtue of Faraday's law. As the oxygen ions are the drivers of the X-point motion, we investigate how E y is supported by O + , through Ohm's law, given by Figure 1b, we see a clear gradient of E y in the vicinity of the X-point. The finite gradient E y / x > 0 results in a local decrease of the magnetic field as B z / t < 0, leading to a tailward shift of the X-point. Furthermore, we see that E y is sustained by a variety of contributors of comparable size, such as the Lorentz term and the inertia and pressure terms. Hence, the oxygen ions are not ⃗ E× ⃗ B drifting and thus not frozen-in. In Figure 1c, to the right of the X-point, we see that the oxygen density enhancement moves close to the magnetic flux velocity, even though the O + does not exhibit a magnetized behavior. This apparent motion of the O + density enhancement is strongly influenced by the z-motion of the oxygen ions. Since the velocity of the X-point is essentially determined by O + , some mechanism must allow the oxygen ions to deliver their momentum to the magnetic flux tubes. As the electrons are well magnetized, we propose that there must be a coupling between O + and e − . We speculate that this alignment may result from electrostatic coupling between O + and e − , which enables an indirect coupling of the oxygen ions to the magnetic field. In the next section we explore how such a coupling occurs.

Electrostatic Coupling Between O + and e −
Even though the oxygen ions are not ⃗ E × ⃗ B drifting, they move close to the magnetic flux velocity as seen in the local density enhancement to the right of the X-point in Figure 1c. In Figure 2a, we see the frozen-in behavior of the electrons, as E ≈ v e x B z which implies that the magnetic flux is moving with the electrons as v e z B x ≈ 0. This is suggestive of some underlying mechanism, which enables the coupling between the oxygen ions and the electrons. We investigate this by evaluating the electron momentum equation, given by across the local density enhancement, indicated by the peak of n e and n O + occurring at x ≈ 218d p and Ω p t = 152.
By studying the x-component, we can investigate how the actual coupling takes place. Leading up to the density enhancement seen in Figure 2b at x ≈ 218d p , we see a sharp increase in the pressure gradient. The enhanced O + density binds the electrons, and this configuration is kept stable by the x-component of the electric field. The pressure gradient of the electrons is directed toward the density peak and attempts to diffuse this enhancement but are instead kept together by electric forces such that x P e xx ≈ −en e E x is fulfilled. This electrostatic coupling now forces the e − to move with the O + . In turn, this induced electron motion leads to the flux transport consistent with the X-point motion. Shown in Figure 2c, the protons also display frozen-in behavior as E + v p x B z ≈ 0. Hence, they are moving with the magnetic flux as well, at the cost of a small fraction of the oxygen ion's momentum.

Evaluation of Coupling With a Lower O + Density Run
In order to test if such a coupling still occurs with a substantially lower O + density, we perform a simulation with the same conditions as described in section 2, except with an oxygen number density of a tenth of the first shown run, that is, n O + = 0.02. In this case, we also observe an x-directed motion of the X-point moving at approximately the center-of-mass velocity, which now is v c = 0.25. The electrostatic coupling between O + and e − is less profound but remains adequate to result in a clear motion of the X-point. In Figures 3a  and 3b we see the clear motion of the X-point together with the matching motion of the oxygen ions and the magnetic flux seen to the right of the X-point. When the oxygen content in the reconnection region is of significance, and the X-point starts moving at approximately v c , we evaluate the electron momentum equation over the rightmost n O + enhancement at Ω p t = 184, indicated by the white line in Figure 3b. In Figure 3c, we see the frozen-in behavior of the electrons over the density enhancements as E ≈ v e x B z . Furthermore, Figure 3d reveals the same manifestation as the high oxygen density, seen in Figure 2b, run with the pressure gradient x P e xx balanced by the electric force −en e E x , thus permitting a coupling between O + and e − . From this, we conclude that such a coupling may still occur even with a substantial reduction of the oxygen abundance.

Density Striations
In this section we investigate the intricate density striations, seen in Figures 4a-4c, which, as we will see, can be attributed to the additional x-directed momentum of O + . In Figure 4a, we see the formation of an oxygen wave, due to the collective acceleration of O + by the Hall electric field E z , thus leaving behind a density cavity (Tenfjord et al., 2018). This is the same manifestation as for the nonstreaming case, but as the system evolves, new types of striations arise as a result of the oxygen's more complicated interactions with E z prior to reaching the reconnection site. This interaction results in more complex distribution functions specific to the streaming case, and an example is shown in Figures 4d-4f (1) and (2), shown in Figure 4. Their initial conditions are selected as the most probable phase-space coordinate for the respective population. As the system is symmetric in z, Population (3) exhibits the same features as Population (1), only with the opposite z-direction of the velocity. Figures 4g and 4h show the trajectories of the test particles from Populations (1) and (2) which have been traced ±20Ω −1 p in dynamically changing fields with a time step of 0.5Ω −1 p from Ω p t = 140 by the initial conditions obtained from the VDF shown in Figures 4d-4f. Dependent on the regions at which O + originates from, they interact differently with the Hall electric field E z . This can be seen in Figures 4i and 4j, which show the forces acting on the test particles from the respective populations.
The test particle from Population (1), seen in Figures 4g and 4h as the white trajectory, originates from further out in the lobe and experiences a much stronger acceleration as it encounters a different E z region. Seen in Figure 4i, its substantially higher v z enables it to overcome the electric potential and continue its motion out to the lobes before it is reflected by the Lorentz force due to −v z B x and subsequently v y B x . Particles that exhibit similar properties trace out the outermost striations evident in Figure 4c. The test particle from 10.1029/2020GL089462  Population (2), seen in Figures 4g and 4h as the black trajectory, travels along the clear density enhancement upon interacting with E z . The E z this particle encounters is not strong enough for it to be accelerated to a sufficiently high v z to overcome the electric potential on the opposite side of the current sheet; see Figure 4j. It is thus reflected in the z-direction by E z and proceeds with a bounce motion across the current sheet until it reaches the exhaust. Such particles trace out the innermost striation seen in Figure 4c.
Particles originating from Populations (1) and (3) both trace out the outer striations as they share similar acceleration histories, only from the southern and northern lobes, respectively. These particles are collectively accelerated by the Hall electric field, which forms an oxygen wave leaving behind a density cavity (Tenfjord et al., 2018). As the Hall electric field expands, oxygen ions further into the lobes are accelerated toward the diffusion region causing an expansion in the z-direction of the outermost striations. Figures 4a-4c and 1b create the impression of an outflow of oxygen ions toward the Earth-counter to the original tailward motion of the O + . This apparent motion in the negative x-direction is solely the result of an earthward shift of the intersection between the outer striations as they expand. There are therefore not indications of any transport of O + in the negative x-direction.
The striations discussed in this section may be observed by spacecraft, but it is, in principle, possible that they are unstable to various waves. In the simulation, the velocity of the O + is small compared to the thermal velocity of the protons and the electrons, and thus, it is less likely that the oxygen ions will drive any instabilities. However, other instabilities could, of course, cause fluctuations in the Hall electric field that accelerates O + and therefore impact the integrity of the structures.

Reconnection Rate
The evolution of the reconnection rate is displayed in Figure 5. We compare the reconnection rate to a similar run with the same oxygen number density n O + but with no initial x-directed bulk velocity, hereafter referred to as the nonstreaming run. Compared to the nonstreaming run, the reconnection process reaches its fast phase at a later time due to a smaller initial perturbation. For illustrations purposes, we shift the nonstreaming run by Ω p t = 30 to have the fast phases aligned.
We do notice a slightly higher peak for the streaming run. This is a transient effect as a result of the low abundance of oxygen ions at the reconnection site. The difference between the distance of the initial location of the front of the oxygen ions to the current sheet is slightly larger for the streaming run. This allows, to a greater extent compared to the nonstreaming run, an unencumbered motion of the upstream magnetic flux tubes, which results in a faster reconnection rate. The reconnection process therefore proceeds faster until the density of the oxygen ions in the reconnection site becomes significant. From this we conclude that a streaming population does not impose any further reduction of the reconnection rate.

Discussion and Summary
Motivated by ionospheric outflow, the results provided in this paper provide insights into how a streaming demagnetized species alter the dynamics of the reconnection process. We have shown that the X-point moves with the center-of-mass velocity v c , which is predominantly provided by the oxygen ions. Tenfjord et al. (2020) performed a similar study with the protons as the streaming population and found that the X-point also moves with v c . The protons remain magnetized in the exhaust, and thus, their coupling to the magnetic field is evident. Having oxygen ions as the streaming population, however, is considerably different as they do not exhibit a magnetized behavior throughout the times of investigation. Our findings show that a demagnetized species alters the dynamics of the reconnection site long before the time of magnetization is realized. The coupling of O + to the magnetic flux occurs instead indirectly through the electrons by an electrostatic coupling. This shows that, regardless of whether the streaming population is magnetized or not, the system will reorganize itself in such a manner as to retain a net zero outflow momenta in the frame of reference of the X-point.
Compared to a nonstreaming run (e.g., Tenfjord et al., 2018), a streaming population gives rise to involved distribution functions due to the interaction with the Hall electric field E z . The O + populations shown in Figures 4d-4f trace out the distinct striations seen in Figure 4c. Regarding observations, the VDF shown here should be detectable by spacecraft, but may be modified by kinetic effects not included in our simulation. Furthermore, our results show that a streaming population does not impose any change to the reconnection rate.
The results obtained in this study may apply to magnetotail reconnection in case of ionospheric outflow which results in high momentum O + . With regard to space applications, we hope that the results laid out in this paper provide useful insight for future analysis of space mission data, in particular, the Magnetospheric Multiscale mission.

Data Availability Statement
Data set used in this analysis is available at Kolstø (2020).