tokens: density). From the 2D plot, it is seen that the distribution of the dust averaged velocity also has the filamentary structure with several minima of the V d,av, z -component. Positions of these velocity minima correspond to positions of maxima of the number density (it is clear from Fig. 7 B), i.e. dust accumulates in the regions of its deceleration. This is consistent with the continuity equation. Thus, dust number density is not uniform in the astrosphere due to periodical deceleration and acceleration of the dust grains. This non-monotonic behaviour of the dust velocity is caused by gyrorotation around magnetic field lines. For example, for the trajectory started at point P 0 gyrorotation takes place in the ( Z , Y )-plane, and during each rotation at the point with maximal y , velocity vector of gyromotion is opposite to the plasma velocity and, hence, the total individual dust velocity has a minimum; oppositely, at the point with minimal y , total velocity has a maximum (see the schematic illustration of this effect in Fig. 8 ). Figure 7. A. 2D distribution of the averaged dust z -velocity component (absolute value) in the ( ZX )-plane obtained for the perpendicular case. B. Dust number density and averaged velocity (absolute value of the z -component) along the Z -axis ( x = 0, y = 0). All results are presented for the dust grains with a d = 1.8. Distances are normalized to R 0 . Figure 8. Schematic picture of dust grain motion in the uniform perpendicular magnetic field. Green dots correspond to maxima of the local dust velocity, blue dots correspond to the local minima (see the text for details). The distance between the density maxima and their number depend on the period of gyrorotation of dust grains (see Fig. 8 ). Namely, in the case of the uniform electromagnetic field, the distance between two adjacent maxima of y ( z ) along the trajectory is equal to D gyr v p , z T gyr , where the dimensionless period of gyrorotation is T gyr 2/( Ba d ). In our case, when v p , z and B change along the trajectory, the distance between the density maxima depends on the averaged D gyr at each part of the trajectory (values of D gyr averaged over the whole trajectory are given in Table 2 ). Fig. 9 A shows y ( z ) along the trajectories (started at P 0 ) for different a d . It is seen that the grains are involved in the gyrorotation with corresponding gyroradius (given in Table 2 ). Distance between adjacent maxima of y ( z ) along the trajectory correspond to the distance between maxima of the dust number density in Figs 5 and 6 . Fig. 9 B shows D gyr as a function of z for the trajectories started at P 0 and the all considered values of a d . Note that D gyr decreases with approaching to the AP because the magnetic field B increases (see Fig. 3 B). This is why the dust density filaments become more frequent close to the AP (see Fig. 5 ). Figure 9. A. The trajectory ( y ( z )) started at P 0 is shown for dust grains with four different a d .
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O