The coalescence process of fullerenes in the hollow core of single walled carbon nanotubes is systematically explored by the kinetic Monte Carlo method. Two elongation (or growth) modes via the coalescence (i) between an inner tube and fullerenes and (ii) between neighboring inner tubes are identified. It is found that the coalescence of two inner tubes mostly creates a very stable intra-tube junction which is composed of multiple pentagon-heptagon pairs. As a consequence, the study predicts that the inner tube of peapod derived double walled carbon nanotubes (DWNTs) must contain many intra-tube junctions. Careful high resolution transmission electron microscopy observation on peapod-grown DWNT sample provides experimental evidence of the presence of the junctions.