[en] In this paper we shall use the Random Walk procedure to accelerate the tracking of the particles which have a large number of collision events. This method is based on the approximation of Fleck's transport equation by a diffusion equation using the multiple scale technique. The chapter is organized as follows: In Sec. I we derive the transfer equation satisfied by a Monte-Carlo particle and the corresponding diffusion equation, the explicit solution of which is known in a sphere. We calculate the probability of escaping from the sphere and the probability of remaining inside at the end of the time step in Sec. 2. We study some criteria for the validity of this approximation in Sec. 3, using Monte-Carlo calculations in the sphere. Numerical results are given in Sec. 4

[en] We study different Monte-Carlo methods for solving radiative transfer problems, and particularly Fleck's Monte-Carlo method. We first give the different time-discretization schemes and the corresponding stability criteria. Then we write the temperature variance as a function of the variances of temperature and absorbed energy at the previous time step. Finally we obtain some stability criteria for the Monte-Carlo method in the stationary case

[en] We approximate Fleck's radiative transfer equation by a diffusion equation using the multiple scales technique. The validity criterium (and the value of a few parameters) are empiricaly evaluated by numerical computations. Then the diffusion equation is used in Fleck's Monte-Carlo method in order to move directly the photons in highly collisionnal medium. With this method, called ''Random Walk'', the computational time may be highly reduced in opaque medium

[en] The nominal configuration of inertial confinement fusion with the Laser Megajoule (LMJ) uses a cylindrical hohlraum with two polar holes for the entrance of 60 laser quads. But the LMJ facility makes it possible to use a spherical hohlraum with more than two holes. We have studied two alternate configurations, in which 56 and 44 laser quads enter a spherical hohlraum through four and six holes respectively, with the same wall surface as in the nominal cylindrical hohlraum. We have estimated the intrinsic and random radiation asymmetries on the nominal capsule A1040 in these two configurations. (authors)

[en] To ensure the robustness of the LMJ target against experimental uncertainties, a wide parametric study is necessary. The FC12 hydrodynamic radiative code allows complete but too long simulations. In this paper, we present a faster and simplified code, named SYMCAL, which calculates the capsule irradiation symmetry. For weak parametric variations, we adjust SYMCAL by a non-predictive method, based on three FCI2 calculations. By post-processing SYMCAL and FCI2 results with a simple model of hot spot deformation, we obtain a 10% precision of SYMCAL compared to FCI2. (authors)

[en] The sensitivity of LMJ capsule yield to experimental uncertainties is currently being studied. We are perfecting a computing line based on a radiation view factor code which will allow us to achieve the probability of non-ignition as a function of the standard deviations of the random experimental parameters. To illustrate this approach, we give preliminary results with 18 parameters: 6 pointing errors, 6 power imbalances, 4 target imperfections and 2 off-centring errors (capsule in hohlraum and target in laser chamber). The effects of off-centring errors on standard deviation of hot spot deformation are two times greater than pointing errors effects. (authors)

[en] This work addresses the analytical calculation of the irradiation coming from a cylindrical surface to a spherical one. This exact solution of the x-ray transport equation allows one to connect the emitted and the received fluxes, expanded as Fourier modes, by coefficients called Fourier view factors. Such a calculation is well suited to a symmetry study in the Laser Megajoule configuration [P.-A. Holstein, M. Andre, M. Casanova et al., C. R. Acad. Sci. Paris 1, 693 (2000)] where a cylindrical hohlraum and a spherical capsule are irradiated. Indeed, this 60 quad laser system induces an azimuthal asymmetry of the hohlraum lighting depending on the laser focal spot size. Thus, the Fourier view factors allow one to express the modes of the capsule irradiation as functions of the elliptic spot dimensions

[en] The Laser Megajoule (LMJ) facility is under construction and will deliver up to 2 MJ of 0.35 μm light in 240 beams. Four similar beams are now available on the Ligne d'Integration Laser (LIL) facility, and the first LIL plasma experiments were completed this winter. On this paper, we will focus on LMJ design studies in indirect-drive configuration. Different capsules with CH(Ge) ablator are studied. Laser plasma instabilities will be smaller in 250 eV targets whereas 350 eV capsules will be more tolerant to initial roughness. A global model enables us to minimize these risks inside possible laser domain. Our nominal design A1040 has similar margins regarding these two uncertainties. LMJ ignition studies aim to quantify more precisely these risks with specific codes and experiments on Omega and LIL facilities. 2D-hydrodynamic instability simulations were performed with different CH and DT roughness. Sensitivity of hydro instability growth to DT gas density, which depends on the cryogenic temperature, is evaluated with a 1D-mixed model. The same target, with graded dopant instead of uniform one, is less sensitive to ablator roughness. Low mode deformations of the DT shell are estimated at maximum velocity. The main causes of deformation are CH thickness defects for modes 1-2 and intrinsic X-ray non-uniformities for modes 4-10. Effects of random errors as laser mis pointing, imbalance and hohlraum geometrical defects are fewer, according to LMJ specifications. Intrinsic and random radiation asymmetry due to a tetraedrical hohlraum compatible with direct-drive configuration (beams at angles of 49 degree centigree from the vertical shifted at 78 degree centigree) has been estimated. The comparison of second and third harmonic light potentialities is in progress. (Author)

[en] For the Inertial Confinement Fusion, the different problems to be studied are: DT burning, shell implosion and hydrodynamic instabilities, spherical symmetry of the shell given by the X-rays produced in a hohlraum and laser-plasma interaction. One of the requirements is that the shell stay essentially spherical up to the end of the implosion. In these conditions, 2-D simulations show a gain of 10 in a realistic configuration. The Rayleigh-Taylor instabilities occurring during the shell implosion grow first in the linear regime for which we have some models and experimental results. But the saturation mechanism reduces the final amplitude significantly. By using a simple but global model, we determine an operating domain of the LMJ, taking into account a 25% margin for laser energy. (author)

[en] Our study is in line with the robustness of the LMJ target and the definition of safety margins. It is based on the determination of the 'acceptable gain', defined as 75% of the nominal gain. We have tested the sensitivity of the gain to physical and numerical parameters in the case of deteriorated implosions, i.e. when implosion conditions are not optimized. Moreover, we have simplified the radiative transport model, which enabled us to save a lot of computing time. All our calculations were done with the Lagrangian code FCI2 in a very simplified configuration. (authors)