Ion acceleration at dipolarization fronts associated with 1 interchange instability in the magnetotail 2

Abstract. It has been confirmed that dipolarization fronts (DFs) can be a result from the existence of interchange instability in the magnetotail. In this paper, we used a Hall MHD model to simulate the evolution of the interchange instability, which produces DFs on the leading edge. A test particle simulation was performed to study the physical phenomenon of ion acceleration on DF. Numerical simulation indicates that almost all particles move towards the earthward and dawnward and then drift to the tail. The DF-reflected ion population on the duskside appears earlier as a consequence of the asymmetric Hall electric field. Ions, with dawn-dusk asymmetric semicircle behind the DF, may tend to be accelerated to a higher energy (> 13.5 keV). These high-energy particles are eventually concentrated in the dawnside. Ions experience effective acceleration by the dawnward electric field Ey while they drift through the dawn flank of the front towards the tail.



Introduction
Earthward moving high-speed plasma flows, which are called bursty bulk flows (BBFs), play a vital important role in carrying significant amounts of mass, energy, and magnetic flux from the reconnection region to the near-Earth magnetotail (Angelopoulos et al., 1994).BBFs are often accompanied with a strong (∼10nT), abrupt (several seconds), transient enhancement of the magnetic field component Bz in the leading part, known as a dipolarization front (DF) (Nakamura et al., 2009;Sergeev et al.,2009;Fu et al., 2012a).Ahead of the DF, a minor Bz dip usually be observed by THEMIS and MMS (Runov et al., 2009;Schmid et al., 2016), which may be typically interpreted as strong diamagnetic currents caused by a plasma pressure drop over the front or magnetic flux passing over the SC or transient reconnection (Kiehas et al., 2009;Ge et al., 2011;Schmid et al., 2011).Simulations have suggested that the magnetic energy would be transferred to plasma on the DF layer in the Bz dip region ahead of trailing fronts (Lu et al., 2017).Many of studies show that the passage of a magnetic island (Ohtani et al., 2004), jet braking (Birn et al., 2011), transient reconnection (Sitnov et al., 2009;Fu et al., 2013), and/or the interchange/ballooning instability (Guzdar et al., 2010;Pritchett and Coroniti, 2013) may account for DF generation.Both Cluster and MMS observed that DFs propagate not only earthward but also tailward, since the fast-moving DFs are compressed and reflected, three quarters of the DFs propagate earthward and about one quarter tailward (Zhou et al., 2011;Nakamura et al., 2013;Huang et al., 2015;Schmid et al., 2016).
Spacecraft observations showed that the sudden energy increase in charged particle fluxes at DFs from tens to hundreds of keV in the magnetotail (Runov et al., 2011;Zhou et al., 2010;Fu et al., 2011;Li et al., 2011;Artemyev et al., 2012).A series of studies have been conducted to understand the signatures of DFs and particles, as well as the particle acceleration mechanisms on the DFs.Li et al., (2011) studied the force balance between the Maxwell tension and the total pressure gradient surrounding the DF and found that the imbalance between the curvature force density and the pressure gradient force density would lead to the flux tube acceleration.Ions, essentially nonadiabatic in the magnetotail, can be directly accelerated along the electric field produced by earthward convection of the front, such as due to surfing acceleration or shock drift acceleration (Birn et al., 2012(Birn et al., , 2013;;Ukhorskiy et al., 2013;Artemyev et al., 2014).Electrons, comparatively adiabatic over most of their orbits, can be accelerated through betatron and Fermi process (Birn et al., 2004(Birn et al., , 2012)).It is noticed that the magnetic field amplitude behind DF is much greater than that ahead of it, Zhou et al. (2011Zhou et al. ( , 2014) ) obtained that the earthward moving front can reflect and accelerate ions.Ukhorskiy et al. (2013Ukhorskiy et al. ( , 2017) ) took the magnetic field component Bz for different areas Nevertheless, the physical processes that generate suprathermal particles are not yet fully understood.
On the simulation ground, previous two-dimensional simulations just unveil large scale physical process concerning DFs, in their models, the electric field (most of them are derived from −V×B) is assumed to be solely in the y direction behind DFs (Ukhorskiy et al., 2012;Greco et al., 2014;Zhou et al., 2014).It has been found that the spatial scale of DFs in the dawn-dusk direction is about 1-3 R E and its thickness is on the order of the ion inertial length (Runov et al., 2011;Schmid et al., 2011), which would be between 500 and 1000 km.In the sub-proton scale, there is an electric field directed normal to the DF.The frozen-in condition is broken at the DF and the electric field is mainly attributed by the Hall and electron pressure gradient terms, with the Hall term dominants (Fu et al., 2012b;Lu et al., 2013;Lu et al., 2015).Therefore, the Hall MHD model is necessary to obtain the Hall electric field, which may determine the electric system on DFs.Lu et al. (2013) have successfully simulated the DF associated with interchange instability in the magnetotail and the trend of simulated physical variables are in good agreement with observations.In this paper, we improves the simulation model in order to study how the Hall electric field on DFs acts on the particle trajectories and ion energizations.Since the DF is produced by temporal evolution of interchange instability self-consistently, it would be meaningful to understand the ion acceleration mechanism associated with the interchange instability in the magnetotail.

Theoretical and Numerical Model
Numerical simulations have proved that the existence of interchange instability triggered by the tailward gradient of thermal pressure and the earthward magnetic curvature force is a possible generation mechanism of the DFs in the magnetotail (Guzdar et al., 2010).Based on the Hall MHD model associated with interchange instability (Lu et al., 2013), we conducted test particle simulations to track ions trajectories backward in time.
Our simulation was performed by two steps, the first is to establish a more realistic DF to get particle motion background.The other is to place test particles and track their trajectories.The simulation coordinate system is defined with the x-axis pointing away from the Earth, the y-axis pointing from dusk to dawn, and the z-axis pointing northward (Guzdar et al., 2010, Figure 1).The breaking of the earthward flow together with the curvature of the vertical field leads The dimensionless model with an effective gravity is as follows: ( ) Where P = p +  + 2 ., U and B are velocity vector and magnetic field vector, respectively, ρ 1 =  + 2 +  ( − 1) +  + 2 ., β is plasma beta,  ; is the effective gravitational force in x direction.In equation ( 1), the second and third terms on the right-hand side represent the Hall effect and the electron pressure gradient, respectively.In our present numerical cases, we postulate that plasma is under isothermal conditions with an isothermal equation of state p =  2 and take the adiabatic exponent γ = 5 3 .The ion inertial length  A = ( A  . +  +  +  A ) F + , given the reference length L = 1 R E , the dimensionless ion inertial length is taken as  A ≈ 0.1.Electron pressure  J is taken as  6, because the proton temperature is 5 times that of electron temperature (Baumjohann et al., 1989;Artemyev et al., 2011).
As for initial conditions, the quasi-stationary equilibrium built by the plasma pressure and effective gravity g (see equation ( 2)) (Guzdar et al. 2010and Lu et al. 2013, 2015) is theoretically reasonable.
It should be noticed that the dawn-dusk and earthward electric field components averagely, increase to ~5 mV/m along with the transient Bz increase and in some events, the electric field increase exceeded 10 mV/m (Runov et al., 2009(Runov et al., , 2011;;Schmid, D., et al. 2016).However, the electric fields calculated by the Hall MHD model in Lu et al. (2013) are smaller than the observations (see Lu et al., 2013, for a typical dipolarization event at x = -10 R E in the equatorial plane, we set B 0 = 15 nT, leading to Bz changed from 10.2 nT to 16.8 nT after DF propagation. The electric field components Ex and Ey are both less than 3 mV/m).So, it is reasonable that we improve the initial conditions to obtain a realistic electric field, which plays a vital important role in ion energization.
We take the initial conditions as follows: We solved equation ( 1) by adopting the second-order upwind total variation diminishing scheme.The simulation box is 2 R E and 1.5 R E in the direction of x and y, respectively.The x boundary is assumed to be zero for all perturbed quantities and the y boundary is to be periodic.
As the second simulation step, the control equations for ion motion should be given.Typically, the drift approximation breaks down in terms of ion motion in magnetotail.The dimensionless equations of motion are given by where  is the particle position,  is the particle velocity, the

Simulation Results
From 0s to 144.5s, the simulation experienced a pre-onset phase, during which the DF formed as a consequence of effective gravity g interaction with plasma density gradient.In order to be more realistic, we set up the time interval from 144.5s to 187s as the acceleration period of the particles.the leading edge of the front, resulting in earthward motion and dawnward drift.Another is due to the electric field Ey at the dawn flank of the DF, leading to tailward drift.These results are consistent with observations and simulations (Nakamura et al., 2002;Greco et al., 2014;Zhou et al., 2011Zhou et al., , 2014)).Therefore, the electric field on the DF (Figure 1a), mainly produced by Hall term and always normal to the front (Fu et al., 2012b;Lu et al., 2013), makes the particles move in the way described above.Statistical analysis of the ions energy in Figure 2 indicates that the maximum energy is about 27 keV.In order to better distinguish particles from different energy, we assumed that the ions with the final energy greater than 13.5 keV are high-energy particles.Figure 3 gives the probability density function (PDF) of particle energy at different x positions.In order to better distinguish the curves of different x distances among the multiple fold lines, we show the results in two figures according to different region in x direction.It can be seen from Figure 3b that the high-energy particles are assembled in the region of x > -0.5 R E whereas Figure 3a shows that the small energy (~ 2keV) ions are concentrated in the region of x < -0.5 R E .At x = 0 R E , ion energy is evenly distributed between 2 keV and 16 keV practically.In combination  That is to say, only particles which diverted to the dawnside region closer to the front can be effectively accelerated.
In a previous paper, Zhou et al. (2014) inferred that the more energized DF-reflected ions originating from the duskside of the DF would be able to reach farther into the ambient.In their model the ions would have been accelerated more significantly in the DF duskside than in its dawnside which is due to the y displacements behind the convex DF (Zhou et al., 2014 Figure 3).However, observations and numerical simulations indicate that the convective electric field behind the front is smaller than the Hall term on the DF on the spatial scale of ion inertial length (Fu et al., 2012b).Therefore, the explanation based on the convective electric field Ey was inappropriate in oue model.Figure 4 has already illustrated that the ion acceleration process is on the dawnside.In addition, statistical   where the DF at t = 144.5 s is set as baseline and marked with black solid line.Kinetic energy at finial moment is indicated with color.
It is obviously seen in Figure 5 that the duskside ions tend to move to dawn at the front (Figure 5d, 90 °< θ < 180 °), while the dawnside ones divert toward tailward (Figure 5c, 0 °< θ < 90 °).This finding is similar to the fluxes of 78-300 keV protons in Birn et al. (2015).At about t = 146s ~153s, the particles with higher initial energy ahead of the front have large radius of gyration and those particles are minor affected by the smaller initial electric field, therefore they are almost simultaneously observed (Figure 5b and 5d).While at t > 153s ions with the initial position at duskside would be able to reach farther into the ambient, which is consistent with the results of Zhou et al. (2014) and Birn et al. (2015).On the other hand, the earlier observed ions are not the most energized ions compared with high-energy counterparts in our model, which is opposite to Zhou's conclusion.It can be easily understood by considering the Hall electric field.The small electric field near the duskside of the front allows particles to drift toward earthward and dawnward for a long time, whereas the high one close to dawnside forces ions to drift tailward quickly during the period that particles obtain most energy (Figure 4).
In order to study how the Hall field Ey on the dawnside of DF accelerate The label of t1 to t5 correspond to 163.2s, 164.9s, 166.6s, 168s and 170s 332 respectively.333

Summary and Discussion 334
In this paper, we used a test particle simulation to investigate ion 335 acceleration at dipolarization fronts (DFs) produced by interchange instability in the magnetotail, by performing a Hall MHD simulation.The Hall MHD model was improved by applying the realistic initial conditions to obtain the fields which are better consistent with observation.
Test particles were settled in both the pre-DF and post-DF region, most of them exhibited earthward and dawnward drift and then diverted tailward.
It is found that ions with the initial position at duskside would be able to reach farther into the ambient plasma, which has been also proofed by Zhou et al. (2014) and Birn et al. (2015).Statistical analysis shows that the high-energy particles are mainly assembled in the dawnside of x > -0.5 R E region, which suggests the dawnside region of the DF is the main area for particle acceleration.
Numerical simulation results indicate that the ions initially settled behind the front may obtain higher energization.In order to explain how the Hall electric field influence ions, we tracked the trajectory of particular ions in the ion-scale electric field.As expected, the Ey component at the dawn flank of DF plays an important role in the acceleration of ion.Although the Ex component in the pre-DF region constitutes a potential drop of ~ 1 keV across the DF as reported by Fu et al., (2012b), the energy enhancement would be offset on their way out toward the magnetotail due to the Ey component.The spatial and temporal properties of Ey component are critical factors for particle acceleration (Greco et al., 2014; Nonlin.Processes Geophys.Discuss., https://doi.org/10.5194/npg-2018-43Manuscript under review for journal Nonlin.Processes Geophys.Discussion started: 9 October 2018 c Author(s) 2018.CC BY 4.0 License.Birn et al., 2013Birn et al., , 2015;;Artemyev et al., 2015;Ukhorskiy et al., 2017).In  (Fu et al.,2011;Artemyev et al., 2012), which is not discussed in this paper.Still, there is no doubt that our study suggests that the dawn flank dusk-dawn electric field plays an essential role in ions energization.
Nonlin.Processes Geophys.Discuss., https://doi.org/10.5194/npg-2018-43Manuscript under review for journal Nonlin.Processes Geophys.Discussion started: 9 October 2018 c Author(s) 2018.CC BY 4.0 License.and situations into account, revealing a new robust acceleration mechanism enabled by stable trapping of ions.In most cases, ions are energized by combined actions from different acceleration mechanisms.
Nonlin.Processes Geophys.Discuss., https://doi.org/10.5194/npg-2018-43Manuscript under review for journal Nonlin.Processes Geophys.Discussion started: 9 October 2018 c Author(s) 2018.CC BY 4.0 License.to an effective gravity g away from the earth.Dimensional units are based on a magnetic field of 15 nT, the Alfven velocity of 750 km/s, and reference length of 1 R E leading to a time unit of ~8.5 s, an electric field of 11.25 mV/m, and a pressure unit of 0.179 nPa.

Figure 1 Figure 1 .
Figure1shows the evolution of the electric field in the z = 0 plane and

Figure 2 .
Figure 2. Test particle simulations of proton energization at the DF,

Figure 3 .
Figure 3. PDFs of particle energy computed at the region of (a) x < 0 R E and (b) x > 0 R E .The red dotted line mark the high energy demarcation line 13.5 keV.

Nonlin.
Processes Geophys.Discuss., https://doi.org/10.5194/npg-2018-43Manuscript under review for journal Nonlin.Processes Geophys.Discussion started: 9 October 2018 c Author(s) 2018.CC BY 4.0 License.with Figure 2, we can further obtain that almost all the high-energy particles gathered in the dawnside of x > -0.5 R E region.It implies that ion acceleration is more effective at the dawnside of DF.To have a statistical description of high-energy ions, we picked out high-energy particles from the total number.The simulation results are shown in Figure 4 with ions energy marked with different color.It appears that high energy particles, accounting for 6 percent, mainly gathering at the dawnside of the DF.

Figure 4 .
Figure 4. Snapshots of high-energy ions at specific moment of the

Nonlin.
Processes Geophys.Discuss., https://doi.org/10.5194/npg-2018-43Manuscript under review for journal Nonlin.Processes Geophys.Discussion started: 9 October 2018 c Author(s) 2018.CC BY 4.0 License.analysis of 4863 high-energy ions indicates that 1570 ions were traced to the duskside of the DF, about 32 % of the total high-energy particles.The source area of ions reaches closer to the Earth, as shown in Figure5.

Figure 5 .
Figure 5. Simulation results of ion differential energy fluxes in the 1-20

Figure
Figure 5c and 5d show the distribution of differential energy flux as the

Nonlin.Figure 6 .Figure 7 .
Figure 6.Orbits of a proton with the initial energy 1 keV and final energy 322 contrast to the results from other MHD model, it makes sense in our self-consistent Hall MHD simulation that the accelerating electric field is the Ey component of the Hall electric field on the dawnside of the front instead of the convection electric field Ey behind the front in their model.Our two-dimensional Hall MHD model can well reproduce the direct acceleration process generated by the Hall field.Nevertheless, it should be pointed out that the ion acceleration mechanisms such as Fermi acceleration and resonance acceleration can also provide powerful ion energization with tens of keV to hundreds of keV