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tokens: the stepwise trajectories of incident CH ions within Titan’s upper atmosphere, all starting at an energy of 50 keV under normal incidence. Three different cases are indicated in the upper panel. For each incident ion, the portion of its trajectory between two consecutive collisions is displayed as the projection to the local plane formed by the vertical direction and the direction of ion velocity, with the x -axis aligned with the projected ion trajectory on the horizontal plane. Our model calculations indicate that some of the incident ions are backscattered and escape at the top of the atmosphere. For the condition of incidence shown in Fig. 2 , the backscattered CH ions typically undergo 20 collisions before they leave the top of the simulation box. Throughout our calculations, the effect of the background magnetic field, typically at the level of several nT (e.g., Backes et al. 2005 ; Bertucci et al. 2008 , 2009 ), is ignored for simplicity since the gyroradii of the incident ions could be estimated to exceed substantially their mean free paths due to elastic scattering by ambient neutrals. Taking incident CH as an example, the mean free path ranges from 110 to 6500 km over the full incidence energy range of 10 to 100 keV, where we use for illustrative purposes a background N 2 density of 1.7 × 10 7 cm −3 at 1500 km ( Strobel 2012 ). For comparison, the CH gyroradius is typically a factor of 5 larger, suggesting that the effect of ion gyromotion is of minor importance here. In addition, we note that the effect of the background magnetic field has not been included in previous modelings of Titan’s atmospheric sputtering (e.g., Shematovich et al. 2001 , 2003 ; Michael et al. 2005 ), and a similar approximation adopted here facilitates a comparison of the derived sputtering yields between different studies in terms of the differentchoices of collision parameterization and of background atmosphere (see Sect. 5 for details). 3 Sputtering yields We show in Fig. 3 the N 2 and CH 4 sputtering yields as a function of the incidence energy of the three categories of incident ions, all assuming normal incidence. The two different collision models, ZBL and ZBL+Firsov, are compared. Several interesting features are immediately seen in the figure. First, both the N 2 and CH 4 sputtering yields increase steadily with the increasing energy of incident ions, which is a natural result of the fact that more energetic ions tend to produce more atmospheric recoils along their energy degradation processes. Second, the sputtering yields increase with the ion mass, maximized for N and minimized for H + , and this is explained by more efficient momentum transfer to atmospheric recoils for heavier incident ions. Third, the sputtering yields for ZBL are enhanced over ZBL+Firsov due to the extra energy spent in electronic excitation, but such an enhancement is suppressed for low energy incident ions because they are not able to excite atmospheric neutrals