Lasers are unique tools for transporting extremely high powers over large distances, but transfer of such a power from photons to matter in small volumes is a very complicated problem. First of all, the interaction proceeds very far from equilibrium, as with photons having energy of a few electron-volts one would like to heat plasma to temperatures thousand times higher. Second, these processes are strongly nonlinear, as they correspond to transfer energies of a large number of photons to a much smaller number of charged particles in extremely small volumes and in very short time scales. Research in inertialconfinement fusion (ICF) gave a strong push for studying all these processes in detail, and now, although many issues remain to be resolved, we have quite a good understanding of how they operate in ICF conditions and what limitations and advantages they offer.
A non-modal linear hydrodynamic stability analysis of ablation waves is carried out for the first time. This analysis is performed for unsteady self-similar solutions in slab symmetry of the Euler equations with nonlinear heat conduction, using a direct-adjoint method that results from a Lagrangian-based optimization problem. Such solutions are considered in connection with inertialconfinement fusion (ICF) experiments where the hydrodynamic stability of ablative flows has been identified as a key issue to the achievement of thermonuclear burn. Inherently unsteady, these flows are compressible, highly nonuniform with a steep heat front, and bounded by a material surface and a shock front — features that are possible sources of non-modal thermo-acoustics effects. Non-modal effects are presently exhibited on a particular ablation wave solution. This finding raises the question of the existence and consequences of such effects in configurations of X-ray driven ablation that are more representative of ICF experiments, which is the object of an ongoing investigation.
IV. CONCLUSION AND OUTLOOKS
In current state-of-the-art hydrocodes to simulate the inertialconfinement fusion, a plasma state is assumed at the beginning of the interaction. All properties pertain- ing to the solid state of the ablator and fuel, as the in- sulating property, are not taken into consideration. For instance, the early absorption is modeled with inverse Bremsstrahlung whereas it is due to nonlinear processes as the multiphoton absorption resulting in electron tran- sitions from the valence band to the conduction band of dielectric materials. Such current modeling may lead to over-estimate the early absorption and lead to spurious hydrodynamic behaviors or miss the energy deposition which take place deeper in the ablator, leading to incor- rect predictions.
A Cockraft-Walton (CW) linear accelerator has been refurbished for InertialConfinement Fusion (ICF) diagnostic development. Originally manufactured by Texas Nuclear Corp. as a neutron generator 1 , it was converted for use as a fusion product source as described in Ref. 2. Since then, the device has been modified significantly to improve the quality of the source and to increase its capability and flexibility as a diagnostic development tool. In particular, the accelerator has been optimized for testing, characterizing, and calibrating nuclear diagnostics used in the national ICF program. The modifications made to the accelerator have already had an impact on the charged particle spectrometry program at the OMEGA laser fusion facility. In addition, the accelerator has been used to characterize and calibrate charged-particle diagnostics used on the Alcator C-Mod tokomak 3 . Other fusion product sources used for similar purposes exist at Colorado School of Mines and State University of New York at Geneseo. 4,5
6. K. S. Raman et al. An in-flight radiography platform to measure hydrodynamic instability growth in inertialconfinement fusion capsules at the National Ignition Facility. Phys. Plasmas, 21:072710, 2014.
7. P. J. Schmid. Nonmodal stability theory. Annu. Rev. Fluid Mech., 39:129–162, 2007. 8. R. Marshak. Effect of radiation on shock wave behavior. Phys. Fluids, 1(1):24–29, 1958. 9. C. Boudesocque-Dubois, S. Gauthier, and J.-M. Clarisse. Self-similar solutions of unsteady
optical phonons into consideration has been derived in or- der to describe electron collisions when the ablator is in the solid state. Electron collisions when the ablator is in the plasma state are described considering both electron-neutral and electron-ion collisions. For the latter, a modified Coulomb logarithm has been used in order to account for screening ef- fects, showing a good agreement when compared to ab ini- tio calculations. By coupling these two collision frequencies with a four-step fragmentation model for polystyrene abla- tor, which describes the successive chemical dissociations of polystyrene leading to a carbon-hydrogen mixture, an effec- tive collision frequency valid over the whole range of tem- peratures reached in inertialconfinement fusion experiments has been obtained. This effective collision frequency has been compared to a generic collision frequency used to describe the solid-to-plasma transition of the ablator. Relatively large dif- ferences in behavior and amplitude depending on temperature are observed but the timescale of solid-to-plasma transition should not be strongly modified as it mainly depends on the photo-ionization rate. However, larger modifications of ther- mal and hydrodynamic responses are expected since they are driven by the electron collision frequency due to laser heating. In addition, this effective collision frequency has been used to evaluate the thermal conductivity for temperatures above 1 eV. When compared to a thermal conductivity obtained by ab initio calculations, good agreements have been observed for temperatures larger than 10 eV. But below 10 eV, a smaller conductivity was found, coming from the consideration of the chemical fragmentation of the ablator, which could lead to a more important laser imprint.
I. I NTRODUCTION
M EGAJOULE-CLASS laser facilities are devoted to the study of nuclear fusion by inertialconfinement (ICF). Work is in progress both in the US (National Ignition Facility, NIF)  and in France (Laser Megajoule, LMJ) , and they will need plasma diagnostics to perform high neutron yield ex- periments. Such complex radiation environments can be found in existing facilities such as the Large Hadron Collider (LHC) , in other facilities currently being developed such as the In- ternational Thermonuclear Experimental Reactor (ITER) , and in future projects such as the High Power laser Energy Re- search (HiPER)  or the Laser Inertial Fusion Energy (LIFE) . The different technologies usable for these diagnostics have been identified. Work is currently in progress to improve the tol- erance of the different subsystems’ response to the harsh radia- tion environments associated with such experiments , .
Figure 3: Example of a target and a laser pulse shape used in ICF direct-drive. Reprinted from [ 7 ]. (MCF) and an inertialconfinement (ICF). In the next, we describe only the latter confinement technique given that this doctoral thesis is inspired by issues encountered in ICF.
In ICF [ 7 – 10 ], a capsule composed by a low-Z material called ablator covers the core of a DT fuel. The latter is turn divided in a cryogenic (solid) outer part and an inner DT gas. A high-power, nanosecond laser driver uniformly illuminates the target, in order to ablate the outer shell. The ablated material presents in form of plasma due to its high temperature. As a reaction to the ablation, the so-called rocket effect occurs: a shock wave propagates inward and implodes the capsule up to temperatures and densities necessary to ignite the fuel. Several configurations of ICF have been investigated. They can be divided in two main categories: indirect- drive approach, in which the target is placed inside a cylindrical metallic hohlraum and it is compressed by the x-rays produced by laser-hohlraum interaction, and direct-drive approach, where the lasers directly irradiate a spherical capsule. In the following sections, we describe in more details some characteristics of direct-drive ICF given that it represents the framework of this thesis.
Inertialconfinement fusion (ICF) [ 1 ] uses lasers or other drivers such as pulsed-power devices or particle accelerators to implode a shell of cryogenic deuterium and tritium (DT). Laser light can be directly incident on the capsule surface (direct drive) or converted into x-rays (indirect drive) through a high-Z enclosure (hohlraum). The shell is imploded to high velocities of hundreds km/s to achieve high central temperatures and areal densities [ 2 ]. The hot spot (∼5–10 keV) is a low-density (30–100 g/cm 3 ) core and is surrounded and tamped by a cold (200–500 eV) near Fermi-degenerate dense (300–1000 g/cm 3 ) fuel layer. Fusion alphas produced in the hot spot deposit their energy primarily through collisions with plasma electrons further enhancing the temperature and fusion reaction rate (alpha heating). Under certain conditions of pressure, temperature, and confinement time, alpha heating initiates a burn wave in the surrounding dense shell, leading to fusion energy outputs greatly exceeding the thermal and kinetic energy supplied to the DT fuel by the implosion [ 2 ]. Alpha heating is essential for ignition and energy gain in nuclear fusion.
4 CPHT, CNRS, ´ Ecole Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau,
(Received xx; revised xx; accepted xx)
Most amplified initial perturbations are found for an unsteady compressible ablation flow with nonlinear heat conduction that is relevant to inertialconfinement fusion (ICF). The analysis is carried out for a self-similar base flow in slab symmetry which is descriptive of the subsonic heat wave bounded by a leading shock front, that is observed within the outer shell, or ablator, of an ICF target during the early stage, shock transit phase, of its implosion. Three dimensional linear perturbations as well as distortions of the flow external surface and shock front are accounted for. The optimisation is performed by means of direct-adjoint iterations. The derivation of a continuous adjoint problem follows from the Lagrange multipliers method. The physical analysis of these optimal perturbations reveals that nonmodal effects do exist in such an ablation flow and that transient growth may dominate the flow stability until the end of the shock transit phase, even at short wavelengths which are held as innocuous from the classical standpoint of the ablative RichtmyerMeshkov instability. Perturbations are not only amplified in the ablation front, but in the whole flow which is found to be especially sensitive to perturbations in the compression region. This fact points out ablator bulk inhomogeneities as the most detrimental defects regarding the shock transit phase of an ICF implosion.
The deuterium-tritium (D-T) γ -to-neutron branching ratio [ 3 H(d,γ ) 5 He/ 3 H(d,n) 4 He] was determined under
inertial conﬁnement fusion (ICF) conditions, where the center-of-mass energy of 14–24 keV is lower than that in previous accelerator-based experiments. A D-T branching ratio value of (4.2 ± 2.0) × 10 −5 was determined by averaging the results of two methods: (1) a direct measurement of ICF D-T γ -ray and neutron emissions using absolutely calibrated detectors, and (2) a separate cross-calibration against the D- 3 He γ -to-proton branching ratio
Airbus Operations S.A.S., 31060 Toulouse, France
Advanced large-wing-span aircraft result in more structural flexibility and the potential for instability or poor handling qualities. These shortcomings call for stability augmentation systems that entail active structural control. Consequently, the in-flight estimation of wing shape is beneficial for the control of very flexible aircraft. This paper proposes a new methodology for estimating flexible structural states based on extended Kalman filtering by exploiting ideas employed in aided inertial navigation systems. High-bandwidth-rate gyro angular velocities at different wing stations are integrated to provide a short-term standalone inertial shape estimation solution, and additional low-bandwidth aiding sensors are then employed to bound diverging estimation errors. The proposed filter implementation does not require a flight dynamics model of the aircraft, facilitates the often tedious Kalman filtering tuning process, and allows for accurate estimation under large and nonlinear wing deflections. To illustrate the approach, the technique is verified by means of simulations using sighting devices as aiding sensors, and an observability study is conducted. In contrast to previous work in the literature based on stereo vision, a sensor configuration that provides fully observable state estimation is found using only one camera and multiple rate gyros for Kalman filtering update and prediction phases, respectively.
Rodney O. Fox
Department of Chemical and Biological Engineering, Iowa State University, Ames, Iowa 50011-1098, USA
(Received 22 February 2019; published 16 October 2019)
A theoretical model of liquid and particle random fluctuations is proposed for gravity- driven flows of inertial homogeneous suspensions. It is based on a paradigm assuming that fluctuations of both liquid velocity and particle slip velocity are driven by fluctuations of the phase indicator function. It is shown that this model accurately predicts the energy of the fluctuations of both the fluid and particle phases measured in a homogeneous solid- liquid fluidized bed over a wide range of particle volume fractions, from 10% to 45%. DOI: 10.1103/PhysRevFluids.4.102301
Ce goût pour la variété, hérité de la tradition baroque espagnole (l’insertion des chansons populaires était déjà pratiquée par Lope de Vega) fait donc ressortir, d’une certaine manière, la concentration de l’écriture de Lagarce. La dispersion de l’écriture se signale par une tendance à la fragmentation monologique, mais le chœur n’est plus extérieur à l’action, dès lors que le commentaire de la parole, la retouche corrective du personnage par lui-même, sont devenus le thème même du drame. L’usage du vers libre crée une forme de lyrisme atténué, significative peut-être du désir de sublimer formellement l’aspect étouffant du conflit familial. Si les énoncés disent la même désunion, si la parole réflexive enferme chacun dans sa solitude, l’ensemble des personnages subit toutefois la loi du style de leur auteur, si bien que la forme dramatique recrée, malgré tout, une sorte de fraternité dans l’énonciation. On pourrait ainsi généraliser à toutes les pièces travaillées par la dialectique du confinement l’analyse proposée par Adèle Chaniolleau et Julie Sermon à propos du Pays lointain : « un lieu discursif et choral se crée, au-delà du dialogue, une forme d’entente musicale qui dépasse les antagonismes premiers » 32 .
with k x > 0. Making use of fluidization law ( 1 ) and identity ( 2 ), Eqs. ( 13 ) and ( 14 ) provide an analytic relation between the velocity variances of particles and fluid, with a single parameter for each component, k z and k x . Equation ( 7 ) provides the relations for the liquid velocity variance.
Note that the assumption of inertial regime does not seem to have been necessary so far for the development of the above equations, since the particle Reynolds (or Archimedes) number is only involved in the fluidization law, which is valid over a full range of Reynolds (or Archimedes) numbers. However, the particle Reynolds number needs to be large enough to ensure that the velocity disturbances generated by each particle vanish at a distance of the order of the particle diameter.