The penetration length of energetic neutral-atom beams injected into a tokamak plasma can be effectively increased by a large factor if the beams are injected vertically from the bottom and the toroidal magnetic field has significant ripple below the midplane. The energetic ions resulting from ionization of the fast neutrals are ripple-trapped and drift upward to the midplane region. The ripple must decrease substantially in the region above the midplane, so that the ions can be captured and retained in the central plasma region during their entire slowing-down period. Orbit calculations with a Monte-Carlo guiding-centre code demonstrate the feasibility of this trapping process. 110- to 150-keV deuterons can be deposited near the centre of plasmas with <ne> a Zeff ∼ 1017 cm−2, when the ripple near the magnetic axis and in the region below is of the order 1%.