Abstract:
Fast ignition of inertial fusion targets driven by quasi-monoenergetic ion beams is investigated by means of numerical simulations. Light and intermediate ions such as lithium, carbon, aluminium and vanadium have been considered. Simulations show that the minimum ignition energies of an ideal configuration of compressed Deuterium-Tritium are almost independent on the ion atomic number. However, they are obtained for increasing ion energies, which scale, approximately, as Z^2, where Z is the ion atomic number. Assuming that the ion beam can be focused into 10 {\mu}m spots, a new irradiation scheme is proposed to reduce the ignition energies. The combination of intermediate Z ions, such as 5.5 GeV vanadium, and the new irradiation scheme allows a reduction of the number of ions required for ignition by, roughly, three orders of magnitude when compared with the standard proton fast ignition scheme.

Abstract:
Two-dimensional simulations of ion beam driven fast ignition are presented. Ignition energies of protons with Maxwellian spectrum and carbon ions with quasimonoenergetic and Maxwellian energy distributions are evaluated. The effect of the coronal plasma surrounding the compressed deuterium-tritium is studied for three different fuel density distributions. It is found that quasi- monoenergetic ions have better coupling with the compressed deuterium-tritium and substantially lower ignition energies. Comparison of quasimonoenergetic carbon ions and relativistic electrons as ignitor beams shows similar laser energy requirements, provided that a laser to quasimonoenergetic carbon ion conversion efficiency around 10% can be achieved.

Abstract:
We present hybrid PIC simulations of fast electron transport and energy deposition in pre-compressed fusion targets, taking full account of collective magnetic effects and the hydrodynamic response of the background plasma. Results on actual ignition of an imploded fast ignition configuration are shown accounting for the increased beam divergence found in recent experiments [J.S. Green et al., Phys. Rev. Lett. 100, 015003 (2008)] and the reduction of the electron kinetic energy due to profile steepening predicted by advanced PIC simulations [B. Chrisman et al. Phys. Plasmas 15, 056309 (2008)]. Target ignition is studied as a function of injected electron energy, distance of cone-tip to dense core, initial divergence and kinetic energy of the relativistic electron beam. We found that beam collimation reduces substantially the ignition energies of the cone-guided fuel configuration assumed here.

Abstract:
An integrated simulation approach fully based upon particle-in-cell (PIC) model is proposed, which involves both fast particle generation via laser solid-density plasma interaction and transport and energy deposition of the particles in extremely high density plasma. It is realized by introducing two independent systems in a simulation, where the fast particle generation is simulated by a full PIC system and the transport and energy deposition computed by a second PIC system with a reduced field solver. Data of the fast particles generated in the full PIC system are copied to the reduced PIC system in real time as the fast particle source. Unlike a two-region approach, which takes a single PIC system and two field solvers in two plasma density regions, respectively, the present one need not match the field-solvers since the reduced field solver and the full solver adopted respectively in the two systems are independent. A simulation case is presented, which demonstrates that this approach can be applied to integrated simulation of fast ignition with real target densities.

Abstract:
Two relatively simple analytic Models for investigation of fast ignition dynamics are developed, that are the subsonic and the supersonic models. On the basis of the subsonic model, which a pre-compressed fuel of density is heated by a subsonic thermal wave, the beam energy and the intensity required for ignition is closely related to proton range. Whereas, on the basis of supersonic model, for ranges shorter than 0.25 gr/cm2 , the mentioned energy remains constant and the intensity decreases. For ranges larger than this value, not only energy but also the beam intensity will increase with the proton range. Considering that proton pulse duration depend on proton range implicitly, these results allow for the determination of an optimum proton pulse duration value, that we have obtained this value equal to 2.14×103 po-1 ps.

Abstract:
The one-dimensional (1D) problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length $2H$ and density $\rho_0 \leqslant 100\rho_s$, where $\rho_s$ is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is $10^{19}$ W/cm$^2$ and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by alpha-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable $x$ and with a weak dependence of the thermodynamic functions of $x$ occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons $G\approx 200$ at $H\rho_0 \approx 1$ g/cm$^2$, and $G>2000$ at $H\rho_0 \approx 5$ g/cm$^2$. To evaluate the ignition energy $E_{\mathrm{ig}}$ of cylindrical targets, the quasi-1D model, limiting trajectories of $\alpha$-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence $E_{\mathrm{ig}} \sim \rho_0^{-2}$ and gives $E_{\mathrm{ig}} = 160$ kJ for $\rho_0 = 100\rho_s \approx 22$ g/cm$^3$.

Abstract:
Fast Ignition Inertial Confinement Fusion is a variant of inertial fusion in which DT fuel is first compressed to high density and then ignited by a relativistic electron beam generated by a fast (< 20 ps) ultra-intense laser pulse, which is usually brought in to the dense plasma via the inclusion of a re-entrant cone. The transport of this beam from the cone apex into the dense fuel is a critical part of this scheme, as it can strongly influence the overall energetics. Here we review progress in the theory and numerical simulation of fast electron transport in the context of Fast Ignition. Important aspects of the basic plasma physics, descriptions of the numerical methods used, a review of ignition-scale simulations, and a survey of schemes for controlling the propagation of fast electrons are included. Considerable progress has taken place in this area, but the development of a robust, high-gain FI `point design' is still an ongoing challenge.

Abstract:
The results from 2.5-dimensional Particle-in-Cell simulations for the interaction of a picosecond-long ignition laser pulse with a plasma pellet of 50-$\mu m$ diameter and 40 critical density are presented. The high density pellet is surrounded by an underdense corona and is isolated by a vacuum region from the simulation box boundary. The laser pulse is shown to filament and create density channels on the laser-plasma interface. The density channels increase the laser absorption efficiency and help generate an energetic electron distribution with a large angular spread. The combined distribution of the forward-going energetic electrons and the induced return electrons is marginally unstable to the current filament instability. The ions play an important role in neutralizing the space charges induced by the the temperature disparity between different electron groups. No global coalescing of the current filaments resulted from the instability is observed, consistent with the observed large angular spread of the energetic electrons.

Abstract:
Fusion energy due to inertial confinement has progressed in the last few decades. In order to increase energy efficiency in this method various designs have been presented. The standard scheme for direct ignition and fast ignition fuel targets are considered. Neutrons, electrons and photons transport in targets containing different combinations of Li and Be are calculated in both direct and fast ignition schemes. To compress spherical multilayer targets having fuel in the central part, they are irradiated by laser or heavy ion beams. Neutrons energy deposition in the target is considered using Monte Carlo method code MCNP. A significant amount of neutrons energy is deposited in the target which resulted in growing fusion reactions rates. It is found that Beryllium compared to Lithium is more important. In an introductory consideration of relativistic electron beam transport into central part of a fast ignition target, we have calculated electron energy deposition in highly dense D-T fuel and Beryllium layer of the target. It has been concluded that a fast ignition scheme is preferred to direct ignition because of the absence of hydrodynamic instability.

Abstract:
Ion beam requirements for fast ignition are investigated by numerical simulation taking into account new effects such as ion beam divergence not included before. We assume that ions are generated by the TNSA scheme in a curved foil placed inside a re-entrant cone and focused on the cone apex or beyond. From the focusing point to the compressed core ions propagate with a given divergence angle. Ignition energies are obtained for two compressed fuel configurations heated by proton and carbon ion beams. The dependence of the ignition energies on the beam divergence angle and on the position of the ion beam focusing point have been analysed. Comparison between TNSA and quasi-monoenergetic ions is also shown.