Stability analysis of double ablation fronts in inertial confinement fusion
Javier Sanz Recio1,2 and Carlos Yañez2,31Institute of Laser Engineering, Osaka University, Osaka 565-0871, Japan2

E. T. S. de Ingenieros Aeronáuticos, Universidad Politécnica de Madrid, Spain

3CELIA, Université Bordeaux 1, Talence, France

The Rayleigh-Taylor instability (RTI) in inertial confinement fusion (ICF) is critical for theachievement of appropriate implosions. In the direct-drive approach, a shell of cryogenic
deuterium and tritium (DT) is accelerated to high velocities (~400 km/s) by directed laser
irradiation of the target surface. During this imploding acceleration phase, the compressedmaterial is ablated off the surface (ablation front) into low-density expanding plasma. The
plasma blowoff (light fluid) accelerates the compressed material (heavy fluid) radially inwards,
and this is the standard situation for the occurrence of the Rayleigh-Taylor instability. In thiswork the linear stability theory of double ablation fronts is developed for direct-drive inertial
confinement fusion targets, and the so-called electron-radiative ablation front (Shinsuke Fujioka
et al., Phys. Rev. Lett. 92, 195001 (2004)) [1] is studied with a self-consistent model.
Actual target capsule designs comprise a core of thermonuclear fuel (mixture of DT gas)
which is enclosed by two layers behaving as ablators, mainly the outer one. Inner layer (arounda hundred of microns) is made up of cryogenic DT ice, which is often solidified around the thinmain ablator (few tens of microns thickness). Selection of the material that provides the best
performances to achieve the ultimate goal of ICF has been object of numerous studies in recentyears. First experiences were carried out using a thin plastic (CH) overcoat. Both, cryogenic DTand plastic foam matrix form a wetted foam layer (CD) [2]. The small amount of CH in wetted
foams leads to enhanced absorption of the laser light and better performance over pure DT ice
targets. Since the thin CH overcoat is quickly ablated off in the early stages of the driving laser
pulse, the main ablator is hydrogenic and the DT ice plays both roles of ablator andthermonuclear fuel. The choice of hydrogenic ablators is motivated by their relatively lowdensity, that permits them achieve high ablation velocities with low in-flight aspect ratio, andtherefore exhibit good hydrodynamic stability [3,4]. However, recent cryogenic implosion
experiments on the OMEGA laser have shown that hydrogenic ablators exhibit a low thresholdfor the two-plasma decaying (TPD) instability leading to elevated levels of hot electron preheat
for ignition-relevant laser intensities of 1015 W/cm2 and 351 nm wavelength [5]. This preheat
implies not achieving the onset of ignition requirements on high total area densities and high hot
spot temperatures. If hydrogenic ablators are excluded as viable ablators due to excessive
preheat, then alternative choices need to be explored. Two decisive facts motivate the study ofusing moderate-Z ablators such as SiO2 and CH or CD doped with moderate-Z elements. Firstly,
although the utilization of moderate-Z ablators can be suspected of worsening hydrodynamic
stability, a recent work shows the contrary [1] indicating that the use of brominated plastic foils
significantly improves the hydrodynamic stability properties by reducing the growth of the RTI.
Secondly, a recent direct-drive implosion experiment in the OMEGA Laser Facility [6] using
glass ablators (SiO2) suggests that the use of this moderate-Z ablator reduces target preheat.
Therefore, moderate-Z ablators are less affected by the TPD instability. A crucial peculiarity ofablation fronts formed from moderate-Z ablators is the importance of radiative energy flux thatdrives the appearance of a second ablation front. This structure of two separated ablation fronts,
called double ablation (DA) front, was confirmed also in the simulations carried out in [1].
The one-ablation front linear theory of ablative RTI has been extensively studied over thepast forty years [7]. Roughly speaking, linear models can be divided into two main types. First,
there are the sharp boundary models (SBM). They consider the ablation surface as a zerothickness interface and homogeneous flow at both sides of it. Problem is not mathematicallyclosed and a closing assumption is necessary to solve it. Recent generalized SBM avoids thisdifficulty by keeping the model with one free parameter, the density jump across the ablation
front [8]. This unknown parameter depends on the structure of the front and its determination
requires the prescription of a characteristic length inherent to the ablation process. With anadequate choice of such a length, supported by the analysis of the sophisticated self-consistentmodels, the SB models yield results in good agreement with the numerical calculations and withthe self-consistent models. The just-mentioned self-consistent models are the second type ofanalytic linear theories. These models start from studying the temperature and density profiles
in the ablation front region, for, next, imposing over those profiles linear perturbations, which
are analyzed, numerical [9] or analytically [10], in order to complete the study. Nevertheless,analytic theories of both types reported in the literature are all based on a temperature singlegroup model, which are not able to properly reproduce the hydrodynamic profiles of DA fronts.
Therefore, existing models are not adequate to determine the RT growth rate of imploding shells
with DA fronts. The aim of this work is to develop a first approach to a linear stability theory
for DA fronts.

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