Fast ignition with ponderomotively accelerated ions

Contrary to the central spark ignition concept, the fuel of the deuterium-tritium (DT) capsule in a fast ignition (FI) scheme will be compressed at lower implosion velocities to densities of several hundred g/cm, what reduces problems with high symmetry and hydrodynamic instabilities [1]. To ignite such a precompressed pellet, additional internal energy must be allocated in a local region of its dense core, the so-called hot spot, at the moment of stagnating implosion. As soon as fusion chain reactions will set in, a burn wave spreads over the whole volume of the target. For this secondary heating, intense beams of fast electrons or ions produced with help of an additional short and intense laser pulse were proposed. With the advent of ultra-intense laser pulses, a scheme of efficient ponderomotive ion acceleration from overdense plasma regions becomes conceivable, which may provide high particle numbers in the accelerated ion bunch [2]. This regime of hole boring should allow ion acceleration directly inside the fusion pellet without any secondary target (see Fig. 1 (a)), thus enabling fuel ignition and burn in high repetition rate operation [3]. To reduce the needed laser energy and power in a demonstration experiment, a cone-guided DT target could be applied [5], where the laser beam propagates through lowdensity carbon inside the cone and accelerates carbon ions with high efficiency and small beam divergence, as shown in Fig. 1 (b). The design of the ion beam parameters for such an experiment, based on analytical studies [4], was checked in hybrid numerical simulations. Ion beam propagation and energy deposition in the precompressed DT target were modeled with a two-dimensional kinetic transport code. The successive hydrodynamic evolution of the beam-heated target was calculated with the radiative hydrodynamic code CHIC. For a laser pulse with an intensity Ilas ≃ 5 × 10 W/cm and the focal radius rf ≃ 10μm, which propagates through the 200μm thick overcritical carbon layer of density ρC = 0.2 g/cm, the generated beam of 175MeV carbon ions will deposit 13.5 kJ of energy in the dense core of the pellet. The acceleration efficiency equals 16%. A transverse beam spread of 3◦ was supposed, which can be evaluated from two-dimensional particle-in-cell simulations. The ion temperature at this stage is shown in Fig. 2 (a). A CHIC simulation starting from these plasma parameter distributions confirmed pellet ignition after about 10 ps. The time delay can be explained by the density and temperature dependence of the DT fusion reaction rate, which describes the efficiency of ∗Work supported by the European support program Marie Curie IRSES project # 230777, by EURATOM in the framework of keep-intouch activities and by the HiPER European project. the α-particle release. The characteristic times for energy equilibration between α-particles and electrons and for the subsequent energy transfer to fuel ions are of the order of 1 ps in the parameter range at hand. The time dependence of the fusion power is depicted in Fig. 2 (b). The integral fusion energy amounts to 20MJ, the corresponding gain factor is 180. The ignitor laser energy is 100 kJ, its power equals 15 PW and the pulse duration is 7 ps.