In a parametric study of reactor size DT targets driven by beams of heavy ions it was found that spark ignition and high energy gains can be achieved in four-layer single-shell targets irradiated by a nonshaped box pulse of 10 GeV 209Bi ions. With an input energy of Ein ≈ 6 MJ delivered in tin ⩽ 10 ns, one-dimensional energy gains of G ≳ 400 are possible in the optimum cases. It is shown that, to obtain spark ignition and high energy gain, two conditions must be necessarily met: (1) a high enough implosion velocity, U∞ ≳ 6.2 × 107 Ω-1/2 cm/s, must be reached, and (2) the fuel compression must be accomplished with a low enough pusher/fuel mass ratio, Mp/MDT ≲ 5-7 (Ω is a dimensionless parameter determined by the density distribution in the compressed target core). It was found also that when the ⟨ρΔr⟩ of the cold part of the compressed fuel is ≃ 2-5 g/cm2, the main portion of the fuel is ignited owing to the heating by 14 MeV neutrons emitted from the central hot region