Two concepts have been applied to the classical problem of accelerators for the ignition of indirectly driven inertial fusion. The first is the use of non-Liouvillian stacking based on photoionisation of a singly charged ion beam. A special FEL appears the most suited device to generate the appropriate light beam intensity at the required wavelength. The second is based on the use of a large number of (>1000) beamlets–or “beam straws”–all focussed by an appropriate magnetic structure and concentrated on the same spot on the pellet. The use of a large number of beams–each with a relatively low-current density–elegantly circumvents the problems of space charge, making use of the non-Liouvillian nature of the stopping power of the material of the pellet. The present conceptual design is based on a low-current (〈i〉 ≈ 50 mA) heavy-ion beam accelerated with a standard LINAC structure and accumulated in a stack of rings with the help of photoionisation. Beams are then extracted simultaneously from all the rings and further subdivided with the help of a switchyard of alternate paths separating and synchronising the many bunches from each ring before they hit the pellet. Single beam straws carry a reasonable number of ions: Beams and technology are directly relatable to the ones presently employed, for instance, at the CERN-PS. Space-charge-dominated conditions arise only during the last few turns before extraction and in the beam transport channel to the reaction chamber. In a practical example, we aim at a peak power of 500 TW delivered to the pellet for a duration of 10–15 ns. High-energy (10 GeV) beam straws of Ba doubly ionised ions are concentrated on several (four) focal spots of a radius of about 1 mm. The power density deposited on these tiny cylindrical absorbers inside a hermetic “hohlraum” is about 2.5 × 1016 w/g. These conditions are believed to be optimal for X-ray conversion, i.e., with an estimated conversion efficiency of about 90%.