Numerical study of fast ignition of ablatively imploded DT fusion capsules by ultra-intense proton beams

Compression and ignition of deuterium–tritium fuel under conditions relevant to the scheme of fast ignition by laser generated proton beams [Roth et al., Phys. Rev. Lett. 86, 436 (2001)] are studied by numerical simulation. Compression of a fuel containing spherical capsule driven by a pulse of thermal radiation is studied by a one-dimensional radiation hydrodynamics code. Irradiation of the compressed fuel by an intense proton beam, generated by a target at distance d from the capsule center, and subsequent ignition and burn are simulated by a two-dimensional code. A robust capsule, absorbing 635 kJ of 210 eV (peak) thermal x rays, with fusion yield of almost 500 MJ, has been designed, which could allow for target gain of 200. On the other hand, for a reasonable proton spectrum the required proton beam energy Eig, exceeds 25 kJ (for d = 4 mm), even neglecting beam losses in the hohlraum and assuming that the beam can be focused on a spot with radius of 10 μm. The effects of proton range lengthening due to the increasing plasma temperature and of beam temporal spread caused by velocity dispersion are discussed. Ways to reduce Eig to about 10 kJ are discussed and analyzed by simulations.