We thank the Reviewer for careful reading and valuable comments.

1. Page 14, lines 11-19. The authors interpret the ion velocity shift in the x and y directions (shown in Figures 6j and 6o) as ‘gyration in the increasing northward Bz’. However, this interpretation is inconsistent with the magnetic field configuration in Figure 6a, in which the magnetic field is in the earthward direction (with nearly zero Bz) at the location of the light blue virtual probe.

I would propose an alternative interpretation. Any duskward-moving ion at the virtual probe has its instantaneous gyro-center to the south of the probe, which indicates the possibility of Speiser-type meandering orbits. On the other hand, the dawnward-moving ions with gyrocenters further northward can only stay in the northern hemisphere. Therefore, the higher fluxes in the duskward rather than dawnward direction could be naturally understood by the higher density at locations closer to the neutral sheet.

In my understanding, the simulated ion distributions could be better explained by the model of Zhou et al. (2016, JGR, ‘Understanding the ion distributions near the boundaries of reconnection outflow region’). As reconnection happens, the ions originally in the plasma sheet are picked up by the reconnection-associated Ey and Bz fields to move downstream away from the reconnection site. On top of this convective bulk motion, the pickup ions also keep meandering across the neutral sheet. These meandering ions must exhibit duskward and downstream directed velocities when they reach the off-equatorial boundary of the reconnection exhaust.

Reply

We agree with the Reviewer that the velocity distribution functions, observed in our simulations, may be interpreted in different ways. Particle tracing is necessary to find the unique correct answer. The normal magnetic field component is, as correctly noted by the Reviewer, small but non-zero. Thus, ions of nearly thermal energy sense the positive Bz earthward of the X-line and negative Bz tailward of the X-line and gyrate accordingly. This, to our mind, explains the mirror-symmetric hook-like distributions  in Fig. 6 h and j. The duskward shift of the phase space density seen in Fig. 6 m and o is caused by the reconnection electric field in the Y direction. We think that our explanation is not significantly different from that described by Zhou et al. [2016]: the ions are moving in the reconnection-associated Ey and Bz away from the X-line and duskward.  We found the paper by Zhou et al. [2016] very instructive and will add the citation.

2. Page 16, First paragraph. The authors state that ‘Fermi acceleration continues during the tailward convection of the plasma’. I don’t get this picture, since my understanding of the Fermi acceleration is that requires two magnetic mirrors moving towards each other. But do we have magnetic mirrors tailward of the reconnection site?

Reply

We thank the Reviewer for valuable comment. In fact, we used the term ``Fermi acceleration'' mainly as a synonym for ``parallel energization''. Our simulations indicate that the energy of field-aligned beams in ion velocity distribution functions increases during tailward progression of the reconnected flux tube. That implies a mechanism of parallel energization. Again, because we cannot trace an individual particle in the Vlasiator code, we can only speculate that this energization is caused by the flux tube shortening, i.e., the Fermi acceleration process (e.g., Baumjohann and Treumann, Basic Space Plasma Physics, Revised Edition, 2012, p.32). It is seen from the magnetic field configuration shown in Figure 2 that there are X-lines tailward of the major X-line at -13 RE. These X-lines play a role of ``magnetic mirrors''.

Technical corrections:

1. Page 10, line 15: ‘12.5 R_E’ should be ‘-12.5 R_E’.

Reply

Point taken, thank you!

2. Figure 5, left panel: I don’t quite understand the label of the horizontal axis, ‘V_v perp B’.

Reply

It means velocity in V_perp direction, i.e., the direction of the ion bulk velocity component perpendicular to the instantaneous magnetic field in the grid cell where the vertual detector is placed.   The left panel in Figure 5 shows the ion velocity distribution function cut in the plane perpendicular to the instantaneous magnetic field. The x-axis is along V-perp and the y-axis is along VxB. We will edit the Figure and add the necessary explanation to the text.

We thank the Reviewer for careful reading and valuable comments.

Speiser orbits are particular orbits in magnetotail like fields with finite Bz that consist of quasi-adiabatic gyro motions outside the neutral sheet, turning into a meandering motion when the particle enters the central current sheet (together with an approximate half-gyration around the finite Bz), and become gyromotions again when the particle exits toward higher latitude on the same or the opposite side. It is not clear whether the author refer to such motion or just to the meandering part, which is an indication of non-adiabaticity. While distributions, such as in Fig. 6, are an indication of non-gyrotropy, it is not clear how they would indicate specifically Speiser type orbits.

Reply

We thank the Reviewer for a great question. In our study, we placed virtual detectors close to the equatorial plane (Bx=0). Therefore, we observe the meandering part of the Speiser trajectory. Particles there experience an acceleration in the dawn-to-dusk electric field that leads to an asymmetry in the phase space density (vy>0), that are visible in Figure 6 m, n, and o. Similar distributions were observed in simulations and observations and were attributed to the Speiser-type meandering motion (e.g., Nagai et al., 2015, doi:10.1002/2014JA020737; Hietala et al., 2015, doi:10.1002/2015GL065168). We interpreted the half-ring distributions in Fig. 6 m, n, and o as signatures of the meandering motion. We will add necessary explanations to the text.

Page 2, line 11: The original term used by Liu et al is “dipolarizing” flux bundle, as is used also later in the paper. One might, however, argue that “dipolarizing” implies “increasing Bz,” which probably was not intended by Liu and I would not object to leaving this as is.

Reply

Point taken. An increase in Bz is one of the criteria which were used by Liu et al (2013) to define ``dipolarazing flux bundles'' (DFB). Yet, one should distinguish DFBs, which are transient magnetic structures, and ``dipolarizations'', i.e., gradual, temporal increase in Bz. We will add the necessary clarification in the revised manuscript.

Page 3, line 24: The previous sentence refers to Fermi acceleration, causing the field-aligned beams. Simply change: “This” to “The” and a bit later eliminate “thus.” Also, the two effects are the same: adiabatic convection toward increasing B is, in the moving frame, the betatron effect.

Reply

We thank the Reviewer for the valuable suggestion.

Page 5, line 25: Shouldn’t this be a “cylinder” rather than a “sphere”?

Reply

Indeed, strictly speaking, the 2D geometry and the usage of a line dipole make it more exact to refer to the inner boundary as a perfectly conducting cylinder than a sphere. We will make the correction in the revised manuscript. Thank you!