A dark-current-free plasma accelerator driven by a short (~ 150 fs) self-guided petawatt laser pulse is proposed. The accelerator uses two plasma layers, one of which, short and dense, acts as a thin nonlinear lens. It is followed by a long rarefied plasma (~ 10^{17} electrons cm^{−3}) in which background electrons are trapped and accelerated by a nonlinear laser wakefield. The pulse overfocused by the plasma lens diffracts in low-density plasma as in vacuum and drives in its wake a rapidly expanding electron density bubble. The expanding bubble effectively traps initially quiescent electrons. The trapped charge given by quasi-cylindrical three-dimensional particle-in-cell (PIC) simulations (using the CALDER-Circ code) is ~ 1.3 nC. When laser diffraction saturates and self-guiding begins, the bubble transforms into a bucket of a weakly nonlinear non-broken plasma wave. Self-injection thus never resumes, and the structure remains free of dark current. The CALDER-Circ modelling predicts a sub-10 mm mrad normalized transverse emittance of electron beam accelerated in the first wake bucket. Test-particle modelling of electron acceleration over 9 cm (using the quasistatic PIC codeWAKE) sets the upper limit of energy gain 2.6 GeV with ~ 2 percent relative spread.