A fundamentally new, to the best of our knowledge, class of linear (2D) dual-mirror aplanats tailored to tubular absorbers is developed for the types of solar concentrators used for thermal power. It is shown that prior investigation establishing this concept possesses unrecognized additional designs, as well as having missed high-performance configurations. It is shown that our line-focus solar concentrators can attain intercept factors exceeding 0.9 at concentration values as high as 55, with practical mirror contours and assemblies. Designed expressly for tubular absorbers, they represent improvements upon previous aplanatic concentrators that were tailored to flat one-sided absorbers but applied to tubular absorbers (as well as to conventional parabolic troughs).