Local Regimes of Turbulence in 3D Magnetic Reconnection

The process of magnetic reconnection when studied in nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by many fluctuations in the electromagnetic fields and plasma properties. We developed a diagnostics to study the spectrum of fluctuations in the various regions around a reconnection site. We define the regions in terms of the local value of the flux function that determines the distance from the reconnection site, with positive values in the outflow and negative values in the inflow. We find that fluctuations belong to two very different regimes depending on the local plasma beta (defined as the ratio of plasma and magnetic pressures). The first regime develops in the reconnection outflows where beta is high and it is characterized by a strong link between plasma and electromagnetic fluctuations, leading to momentum and energy exchanges via anomalous viscosity and resistivity. But there is a second, low-beta regime: it develops in the inflow and in the region around the separatrix surfaces, including the reconnection electron diffusion region itself. It is remarkable that this low-beta plasma, where the magnetic pressure dominates, remains laminar even though the electromagnetic fields are turbulent.


Introduction
Magnetic reconnection is a process believed to release large amounts of magnetic energy into kinetic energy (Zweibel & Yamada 2016) in systems ranging from tokamaks (e.g., during disruptions) (Wesson 1990) to astrophysical flows (Sironi & Spitkovsky 2014) to solar eruptions (Wyper et al. 2017) and geomagnetic storms (Birn et al. 2001) to experiments especially designed to study it (Yamada et al. 2010). Recently, the Magnetospheric Multiscale (MMS) mission brought an unprecedented level of resolution to the field thanks to high-cadence observations (Burch et al. 2016). A key finding of the new mission is the confirmation that reconnection is associated with the development of strong electromagnetic fluctuations (Ergun et al. 2016(Ergun et al. , 2017. Previous observations from earlier missions (Retinò et al. 2007;Eastwood et al. 2009) and laboratory experiments (Ji et al. 2004) had already pointed to a link between reconnection and turbulence. One of the longest-known instabilities connected with reconnection is the lower hybrid drift instability (LHDI), long suspected to play a role in promoting reconnection (Huba et al. 1977) and observed in space (Vaivads et al. 2004) and in the laboratory (Carter et al. 2001). The LHDI is driven by drifts caused by the presence of pressure (either density or temperature or both) gradients (Huba et al. 1977). As such the LHDI is potentially present in the vicinity of reconnection in regions where gradients are present, and it has indeed been observed in reconnecting current layers (Vaivads et al. 2004;Norgren et al. 2012).
If reconnection can be caused by turbulence, it is also known to produce turbulence (Karimabadi et al. 2013). In 2D simulations, turbulence can be generated in the reconnection site itself via the tearing instability (Galeev & Zelenyi 1976) and the plasmoid instability (Loureiro et al. 2007), and in the region around the separatrices where electron holes form and slide rapidly (Cattell et al. 2005;Divin et al. 2012;Fujimoto 2014;. When the third dimension is added, the possible instabilities increase (Scholer et al. 2003;Fujimoto et al. 2011).
In the reconnection outflows, the presence of gradients and currents allows the development of drift instabilities such as the LHDI (Yin et al. 2008;Divin et al. 2015aDivin et al. , 2015bLe et al. 2017;Price et al. 2017). In the outflow region the strong density gradients have an unfavorable magnetic field curvature, leading to ballooning and interchange instabilities (Lapenta & Bettarini 2011;Pritchett & Coroniti 2011;Nakamura et al. 2016) and flapping motions (Vapirev et al. 2013;Sitnov et al. 2014).
The separatrix regions develop strong currents that can produce filamentation (Che et al. 2011), drift tearing (Daughton et al. 2011), and instabilities triggered in the separatrix density cavities ) and velocity shears (Fermo et al. 2012). In the separatrices electron holes are driven by the streaming instabilities produced by strong electron beams (Cattell et al. 2005;Goldman et al. 2014). The electron holes can themselves become the source of whistler waves produced by Čerenkov emission (Goldman et al. 2014) that travel into the inflow region. Whistler waves can also be emitted by temperature anisotropy instabilities (Gary & Karimabadi 2006) in the outflow of reconnection (Fujimoto & Sydora 2008).
A practical consequence of these fluctuations is the creation of anomalous momentum exchanges via viscosity and resistivity within the generalized Ohm's law, as recently reported (Price et al. 2017).
In the present work, we consider the different regimes of fluctuation present in different regions around a reconnection site. To do this we developed an investigative method designed to provide statistical information on the fluctuation spectra in different regions. We identify two regimes of fluctuations. One in the outflow leads to a turbulent regime where the fluctuations involve both fields and particles. In contrast, the fluctuations in the inflow and separatrix region involve only the fields, without affecting the particles significantly.
The two regimes differ much in practical consequences. The outflow regime is capable of inducing a strong and turbulent energy exchange as well as strong anomalous momentum exchange dominated primarily by the electrostatic term in Ohm's law. The inflow regime, in contrast, does not lead to substantial fluctuations in the field-particle energy exchange nor significant anomalous viscosity or resistivity. Turbulence remains limited to the electromagnetic fields.
The work is organized as follows. Section 2 describes the simulation approach used and the diagnostics developed to analyze it; we focus in particular on a conditional analysis of statistical fluctuations that identifies the properties in different regions. Section 3 describes the main finding of the present work: the existence of two distinct regimes in the energy transfer due to the turbulent fluctuations. Section 4 discusses the origins and the causes of the two turbulent regimes observed. Section 5 analyses the consequences of the fluctuation regimes for momentum exchange via the generalized Ohm's law. The summary and conclusions are drawn in Section 6.

Methodology
Our investigation uses the 3D fully kinetic particle-in-cell (PIC) code iPic3D (Markidis et al. 2010). The present simulation is similar to the one reported in Lapenta et al. (2015), and uses a standard Harris equilibrium (Harris 1962 are imposed, where B 0 is the asymptotic in a plane field and n 0 is the peak Harris density. This choice of initial equilibrium corresponds to the plasma beta (ratio of plasma pressure to magnetic pressure) peaking in the center of the sheet: Using the parameters listed above, the plasma β ranges from 11 in the center to 0.09 at the edge, covering three orders of magnitude. These conditions are common in space plasmas, for example in the Earth's magnetotail where both density and temperature peak in the center of the current layer (Runov et al. 2006), but also in the solar wind (Eriksson et al. 2014).
The coordinates are chosen with the initial Harris magnetic field along x with size = L d 40 Unlike the simulation reported in Lapenta et al. (2015) and Pucci et al. (2017), where there was a relative drift between the particles in the Harris equilibrium and those in the background, we choose to set the simulation initially in the ion rest frame so that all the current is initially carried by the electrons: ) is the normalization coefficient of the Maxwellian distribution and = - is the drift speed of the electrons required to support the Harris current when the simulation frame corresponds to the ion frame. In this frame the background plasma and the Harris ions are not drifting and the overall system has no velocity shear (since the electron mass is much smaller and the center-of-mass speed is essentially the speed of the ions, which is initially zero). This choice avoids the presence of shear-driven modes that tend to kink the current sheet, an effect that would have complicated the interpretation of the fluctuations (Daughton 2002; Karimabadi et al. 2003;Lapenta et al. 2003). The four plasma species (ions and electrons in both the Harris field and background) are each described by 125 particles per cell, with non-uniform weight in the case of the Harris species. The grid has 512×192×128 cells, resolving the electron skin depth well, in the reconnecting background plasma , (the initial Harris plasma is quickly swept away by reconnection). The time step also resolves the electron cyclotron frequency well, even in the strongest field, w D » t 0.3 ce B , max (and even better in more average fields). Figure 1 shows an overview of the simulation. The divergence of the Poynting flux is shown in the y=L y /2 plane (panel (a)) to highlight the fluctuations in the outflow. The standard deviation (STD) of the same flux computed using the values along z, for each point in the x-y plane, shows , with the contour plot of the mean flux function several regions of fluctuations also at the separatrices and the inflow, although at lower intensity than the outflow (panel (b)). We can distinguish three regions: (1) the inflow region above and below the central reconnection region (blue in Figure 1(c)), (2) the central reconnection region and the band around the separatrices (white in Figure 1(c)), (3) the outflow region where the downstream pileup front forms (red in Figure 1(c)). In a previous study (Pucci et al. 2017) based on a similar 3D reconnection simulation (with different parameters), we investigated all these fluctuations collectively, determining the spectrum to have a power-law distribution compatible with a turbulent cascade and with the same index as observed in space (Eastwood et al. 2009). However, the fluctuations are far from homogeneous, and visual inspection clearly points to different types of fluctuations in different parts of the domain. To analyze the fluctuations in each region, we have developed a conditional fluctuation analysis (CFA). The idea is to use the same statistical tools used in demographics. A statistician might pose the question of what is the income distribution among the people living in different districts of a city. Similarly we study the spectrum of fluctuations in different regions around the reconnection region.
The main question is how do we identify the regions? The flux function is a natural choice, considering that the simulation is initially invariant in z, and throughout the evolution this invariance remains valid on average, except for the fluctuations. We define in each plane at constant z a flux function Φ(x, y) as the scalar function whose contours are everywhere parallel to the magnetic field on that plane (i.e., the function is defined by the generating equation ). Note that this function is not the out-of-plane component of the vector potential: this property will be true only in a 2D domain. In our 3D case, the flux function defined above is just a useful function to define the intersection of the magnetic field surfaces with a plane at given z.
The flux function is defined minus a constant on each plane: we define it to be zero in each plane at the intersection where the separatrix surfaces meet identifies the so-called x-point in each plane, defined as the saddle point of F x y , ( )). Figure 1(c) reports an example of such a flux function for the central plane ( = z L 2 z / ). It obviously resembles the out-of-plane component of the vector potential in 2D domains despite the warning above. Similar plots are obtained in each plane along z.
To define the CFA, we subdivide the range of Φ into 100 3D regions between two surfaces at two consecutive values of Φ. The regions are 3D because Φ is defined in every z plane. The region around Φ=0, by construction, is centered on the reconnection site. We then measure in each of these regions how the fluctuations for a given quantity are statistically distributed and report the histogram of the fluctuations with respect to the mean in each region using a color scale.

Two Regimes of Turbulence near a Reconnection Site
The result of the analysis described above is shown in Figure 2. What can be observed is the fluctuation range, defined with a sign because fluctuations can be positive or negative relative to the mean. In each panel we can observe the fluctuation spectrum in the region where the separatrices meet (around Φ = 0), in the inflow (Φ < 0), and in the outflow (Φ > 0). The precise location corresponding to a given value of Φ can be obtained from Figure 1(c).
From the top, we report first the electromagnetic energy exchange between Poynting flux and magnetic energy (the electric field energy is negligible in our simulation, where the speeds remain much below the speed of light). Next we report the electron energy exchange with the electromagnetic field and the electron particle energy flux (inclusive of all energy fluxes: bulk, enthalpy, and heat flux). Finally the ions are shown.
The most striking feature is that in the inflow (Φ < 0) and reconnection region proper (Φ ≈ 0) almost only the electromagnetic energy channels fluctuate. In essence the fluctuations only transfer energy between magnetic and Poynting fluxes, without affecting ions and electrons. In the downstream region (Φ > 0), in contrast, all energy exchanges fluctuate together. The rate of energy exchange with the electric field, J E s · , and the particle energy fluxes fluctuate only in the outflow.
The CFA clearly identifies two different regimes for the fluctuations. The first is in the region of inflow (F < 0) where only the electromagnetic fields fluctuate, and the particle energy exchange with the fields (J E s · ) does not respond to the fluctuations. The second region is that of the outflow (Φ > 0) where the species start to respond to the fluctuations.
The fluctuations can be characterized by their mean and STD, reported in Figure 3. The region of the inflow is characterized by a strong mean and STD for the magnetic energy and divergence of the Poynting flux but almost no response at all from the particles, either as a mean or as an STD. Just at the region Φ=0, corresponding to the separatrices, the divergence of the ion energy flux has a significant spike. This effect is caused by the Hall electric field present at the separatrices, which accelerates the ions (Aunai et al. 2011). Conversely, the outflow region involves a large mean and STD for all quantities; in fact, the ion energy exchange term becomes dominant.
These two regimes of fluctuation are linked with two different physical conditions. Figure 4 shows the mean plasma beta for electrons and ions in the different regions defined above via Φ. The inflow region has a low beta, lower than one. The outflow region has a plasma local beta exceeding, even greatly exceeding, unity. Beta for a species is defined as or the ratio of the species pressure defined as the trace of the pressure tensor and the magnetic field pressure. In the inflow region the magnetic field pressure largely dominates and the turbulence remains mostly limited to the electromagnetic field.
In the outflow, the plasma pressure becomes comparable to or even exceeds the magnetic pressure, and turbulence engulfs both particles and electromagnetic fields.

Origin of the Fluctuations
The system is initially laminar and reconnection is initiated in the same way in all planes z. In itself, reconnection would progress in a laminar way without any variation of the quantities along z. But as noted above, the conditions generated by reconnection produce secondary instabilities that lead to fluctuations, and eventually in the nonlinear phase of these instabilities to a turbulent spectrum. The nonlinearity of this process complicates the precise determination of the linear instabilities that develop first. We have in fact a system where the state is constantly altered by the reconnection process, and the onset of secondary instabilities cannot be identified and compared with a precise linear theory analysis. Nevertheless the fluctuation spectrum retains a memory of its cause that can be identified by measuring the local temporal evolution of the fields. We distribute probes uniformly within the simulation, arranged in an array of three probes per dimension in each processor of the simulation, for a total of 48×36×24 virtual probes. On these probes we save the electromagnetic fields and the species moments at all time steps. This information is complementary to the grid data. The grid data give the information at all points but can be saved only infrequently (once every 1000 time steps) as a result of practical limitations on disk space, whereas the probe data are limited in spatial resolution but have full temporal resolution.
The virtual probes represent a simulation analogy to a multispacecraft mission, except that we can afford a virtual mission of 41,472 spacecraft.
To analyze the origin of the fluctuations in the inflow and outflow we consider one array of 24 virtual probes along z at a given (x, y) location. Figure 5 shows two of these arrays, one in the inflow and one in the outflow. For each array of probes the average value of the local ion and electron plasma frequency, of the lower hybrid frequency, and of the electron cyclotron frequency are reported as vertical lines.
The fluctuations of the electric and magnetic fields are computed relative to the direction of the average magnetic field measured by each probe, i.e., the fluctuations are projected with respect to the local time-averaged magnetic field and then averaged over the 24 probes. The spectra in the inflow and the outflow show remarkable differences.
In the inflow, we observe a clear peak in the electron cyclotron frequency, ω ce . This peak is present primarily in the perturbations of the perpendicular electric field and in the parallel magnetic field, a direct indication that this wave is electromagnetic and propagates perpendicular to the direction of the average magnetic field. The two perpendicular components of the perturbations of B and E are nearly identical to each other, an indication of gyrotropy. Gyrotropy is broken only at very high frequencies where the electron gyromotion is not fast enough to re-equilibrate the two perpendicular components.
A similar peak in the cyclotron frequency was reported in previous studies . The frequencies reported are not precisely defined because the data provided are from 24 different probes and there is spatial and temporal variation. The value reported in Figure 5 is an average. Nevertheless the correspondence of the peak with the cyclotron frequency is remarkable. Several higher harmonics are also evident. The size  Perpendicular waves at the electron cyclotron frequency can be of different nature (Swanson 2003). The extraordinary mode is electromagnetic but is centered at the electron plasma frequency and at the upper hybrid frequency, which is above what we observe here. Bernstein modes are concentrated at the scale observed but their nature is primarily electrostatic. We observe larger magnetic than electric perturbations in our units where the speed of light is unitary; this means the waves are electromagnetic, and unlikely then to be Bernstein modes. However, recent MMS observations have reported peaks in the electron cyclotron range similar to those reported in Figure 5 and the authors suggest a Bernstein nature for these modes (Goodrich et al. 2018;Li 2018).
A different mechanism to generate multiple discrete peaks in the range from electron cyclotron to upper hybrid frequency has recently been suggested . Based on MMS observations of waves in the upper hybrid ) and in the cyclotron range (Goodrich et al. 2018;Li 2018), a model can be constructed based on the presence of a thermal plasma and a higher energy beam population spread over a range in pitch angles. The beamplasma interaction leads to the generation of both types of waves observed by MMS: upper hybrid and electron cyclotron. Multiple electron cyclotron peaks, similar to those observed in our study, are predicted by this theory when the beam is sufficiently dense compared with the thermal plasma . To resolve the issue a k-ω spectrum would be needed, but we do not have the resources to store all the time steps at all locations: we only save the data at the virtual probe locations, precluding the calculation of the k-ω spectrum.
Just below the cyclotron peak, the perpendicular magnetic field perturbations become dominant over the parallel magnetic perturbation (conversely, for the electric field the parallel perturbation dominates over the perpendicular), indicating parallel propagation: this is a clear indication of whistler waves in the range below the electron cyclotron frequency, as noted in Pucci et al. (2018).
At even lower frequencies, a peak at the lower hybrid frequency is present in the fluctuations of B and in the perpendicular perturbations of E. The LHDI is characteristically present in the interface region between the center of the current sheet and the lobes, even in the absence of reconnection (Huba et al. 1980). The LHDI is a very common signature observed in current layers in space (Vaivads et al. 2004;Norgren et al. 2012) and in the laboratory (Carter et al. 2001;Ji et al. 2004) and it covers a wide range of frequencies both linearly (Daughton 2003) and nonlinearly (Innocenti et al. 2016).
In the outflow, the electron cyclotron peak and its higher harmonics are completely absent. Now the spectrum is virtually identical for all three components of each field and no significant peak is present. Rather, the spectrum presents the typical power-law decay of turbulence. Note also the scale: the spectrum is much stronger in the outflow; the level of fluctuation is much higher and turbulence develops more fully than in the inflow. Previous studies Vapirev et al. 2015) have shown that the turbulence in the outflow is generated by an instability in the lower hybrid range. A detailed comparison with linear theory shows that most of the growth rate observed can be explained by the lower hybrid instability, which is caused by the density gradients in the outflow, but additional effects due to field line curvature and velocity shear play a role as well (Divin et al. 2015b). This instability has then been confirmed by satellite observations (Divin et al. 2015a). Regardless of the origin, turbulence has developed fully by the time reported, losing any memory of the scales that have generated it (Innocenti et al. 2016).
The nature of the waves in the inflow and outflow is further clarified by analyzing the angle between the two perpendicular fluctuations of the magnetic and electric fields. We define the average mean magnetic field as the temporal average of the signal over all the 24 probes along z located at the same x-y location. We then consider the Fourier transform of the two If the signal is rotating in the same sense as the electrons (i.e., with right-handed polarization) then 1 signal precedes thê n 2 signal by 90°in phase angle. In Fourier space this can be measured as the angle between the complex values of the two Fourier transforms. This value is obtained taking the ratio of the two transforms and measuring the angle of the complex number in circular coordinates:^^ B B 1 2 ( )   .
As can be observed in the inflow the magnetic perturbation has a well defined +90°angle of polarization in the broad frequency range around the cyclotron region. Only at very high frequency, where likely the particle noise plays an important role, is the polarization lost.
A polarization angle of 90°in the magnetic field perturbation is not a coincidence, it is an indication of magnetic structures that are frozen into the electrons and rotate in the electron sense. An example of such a process is the whistler wave that has right-handed circular polarization. However, the electric field fluctuations have no clear polarization in this same frequency range, complicating a simple interpretation of the observed processes as whistler waves. The electric field includes both electromagnetic and electrostatic processes, resulting in the absence of a clear polarization. We cannot distinguish the contributions to the electric field from the electromagnetic and electrostatic fields, while in the magnetic field of course perturbations can only be electromagnetic.
In the outflow the 90°polarization is a fading memory and the angle betweenB 1  andB 2  is much wider. Another indication is that in the outflow turbulence is becoming fully developed and isotropic. At the highest frequency a new polarization of ±180°appears but with a broad spread: the two perpendicular directions of the magnetic field become out of phase, consistent with a linear polarization. At these very high frequencies, however, the results are polluted by particle noise typical of PIC simulations.

Contributions of Turbulence to Momentum Exchange
A key consequence of the two distinctly different regimes of fluctuation in the inflow and outflow is the impact that turbulence has on the momentum exchange as measured by the generalized Ohm's law. The electromagnetic-dominated regime does not produce sizable anomalous terms because it is not connected with fluctuations in the plasma species. Conversely, the fluctuation regime in the outflow leads to strong anomalous effects.
The study of momentum exchange is based on the generalized Ohm's law that is in essence a rewriting of the electron momentum equation in a two-fluid approach (Braginskii 1965). For each term, we separate the contributions from the average and fluctuatings part of the fields and the moments. For example, the electric field is decomposed as d = á ñ + E E E. Substituting the decompositions for each quantity into the generalized Ohm law and averaging it over z, one obtains (Braginskii 1965) á ñá ñ = á ñ á ñ +  á ñ -á ñ´á ñ + X where the three fluctuation-supported terms are the electrostatic (or anomalous resistivity), inertia, and electromagnetic (or anomalous viscosity, Price et al. 2017) terms. The fluctuations of the pressure tensor in this formalism do not produce anomalous effects. Figures 8 and 9 show the different terms in the generalized Ohm's law for the z-component (similar conclusions apply for the other two components, not reported because the main driver of reconnection in the present case is E z ). At this relatively late stage of reconnection, the reconnection electric field has moved with the outgoing fronts and is no longer peaked in the center (Wan & Lapenta 2008;Sitnov et al. 2009). As predicted above, in the electromagnetic-dominated region, the fluctuations are not providing any momentum exchange; the mean and fluctuation terms remain negligible. In the outflow, in contrast, strong anomalous effect become relevant.
In Figure 8, the top panel shows the mean reconnection electric field á ñ E z . The other two panels report the cut along the x axis (at = y L 2 y ) of the terms of the generalized Ohm's law. Figure 9 reports the corresponding cuts along the y axis (at = x L 2 x ). The cuts along the x axis pass through the outflow region at Φ>0 and highlight the contributions from the fluctuations in the high-beta turbulence region where the particles contribute strongly to the turbulence processes. The majority of the outof-plane electric field is caused by the Hall and advection terms á ñ´á ñ B J e , with the pressure term being small in comparison. The anomalous terms, in contrast, provide a substantial minority contribution, especially the electrostatic fluctuation term, δnδE, but also the electromagnetic term, d d B J e . The inertia term is negligible by virtue of the mass ratio of the electrons being very small in the present simulation, a realistic effect because in reality it is even smaller (1836 instead of 256 for hydrogen plasma).
The cuts along the y axis pass through the inflow region at Φ<0 and highlight the contributions from the fluctuations in the low-beta turbulence region where the fluctuations remain primarily concentrated only in the electromagnetic field. Here the out-of-plane electric field is essentially given only by the á ñ´á ñ B J e term: in this region Ohm's law essentially reduces to the statement of the electron frozen-in condition: The contribution from the fluctuations is measurable in the simulation but nearly three orders of magnitude smaller than the mean electron frozen-in term, a small fraction of even the mean inertia and pressure tensor terms. Momentum in this regime remains laminar.

Summary and Conclusions
In summary, the reported work analyses the fluctuations around a reconnection site using full 3D PIC simulations with electrons and ions both treated as superparticles. The resolution includes the electron effects down to a fraction of the electron skin depth and electron cyclotron frequency, well beyond the scale of interest of the fluctuations studied. The results can then be considered well converged, as proven by simulations with lower resolution but substantially equivalent results not reported here. The main conclusion is that fluctuations in the outflow present the classic scenario of turbulent reconnection with plasma species and electromagnetic fields fluctuating in sync. The inflow and separatrix region, in contrast, present a different type of fluctuation: the fields fluctuate but the plasma species remain essentially laminar.
In the inflow, the plasma species pass quickly; waves are generated by their passage but the cause that created them is quickly removed. The electron population is rapidly and locally drifting, causing instabilities due to the relative ion-electron drift (Buneman instability, Goldman et al. 2008;Divin et al. 2012) and between different electron populations (Goldman et al. 2014). Currents associated with the strong drift also cause tearing and Kelvin-Helmholtz instabilities (Daughton et al. 2011;Divin et al. 2012;Fermo et al. 2012;). The waves generated at the separatrix layer travel in the inflow region, as is the case, for example, of Cerenkov emission of whistler waves from electron holes (Goldman et al. 2014) or kinetic Alfvén waves produced by the fast kinetic reconnection process and traveling at super-Alfvén speeds For an RHCP wave the^1 component is ahead by 90°i n phase angle. In the inflow region the magnetic field is predominantly in the x direction, and the two perpendicular directions correspond to the two coordinate axes as shown. (Shay et al. 2011). The particles travel through the separatrices at high speed but the fluctuating electromagnetic fields in the region linger, contributing to the electromagnetic fluctuations observed.
In the outflow, in contrast, the species slow down and interact with the ambient plasma, forming a pileup region. The conditions arise for the excitation of the lower hybrid drift instability due to the strong density gradients (Divin et al. 2015b;