Carbon nanotubes (CNTs) are nowadays routinely grown in a thermal CVD setup. State-of-the-art plasma-enhanced CVD (PECVD) growth, however, offers advantages over thermal CVD. A lower growth temperature and the growth of aligned freestanding single-walled CNTs (SWNTs) makes the technique very attractive. The atomic scale growth mechanisms of PECVD CNT growth, however, remain currently entirely unexplored. In this contribution, we employed molecular dynamics simulations to focus on the effect of applying an electric field on the SWNT growth process, as one of the effects coming into play in PECVD. Using sufficiently strong fields results in (a) alignment of the growing SWNTs, (b) a better ordering of the carbon network, and (c) a higher growth rate relative to thermal growth rate. We suggest that these effects are due to the small charge transfer occurring in the Ni/C system. These simulations constitute the first study of PECVD growth of SWNTs on the atomic level.