Thermal stability and long term hydrogen/deuterium release from soft to hard amorphous carbon layers analyzed using in-situ Raman spectroscopy. Comparison with Tore Supra deposits

The thermal stability of 200 nm thick plasma enhanced chemical vapor deposited a-C:H and a-C:D layers ranging from soft to hard layers has been studied and compared to that of deposits collected on the Tore Supra tokamak plasma facing components by means of in-situ Raman spectroscopy. Linear ramp heating and long term isotherms (from several minutes to 21 days) have been performed and correlations between spectrometric parameters have been found. The information obtained on the sp 2 clustering has been investigated by comparing the G band shift and the 514 nm photon absorption evolution due to the thermal treatment of the layer. The effects of isotopic substitution have also been investigated.Comment: appears in Thin Solid Films, Elsevier, 201

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method

We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L^2 norm of a perturbed solution relative to the shock wave is bounded above by the L^2 norm of the initial perturbation.Comment: 17 page

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page

Integrated modelling of Ion Cyclotron Resonant Heating in toroidal system

An integrated model capable of self-consistent Ion Cyclotron Resonant Heating (ICRH) simulations has been developed. This model includes both full shaping and pressure effects, warm contributions to the dielectric tensor, pressure anisotropy and finite orbit width. It evolves the equilibrium, wave field and full hot particle distribution function until a self-consistent solution is found. This article describes the workings of the three codes VMEC, LEMan and VENUS and how they are linked for iterated computations in a code package we have named SCENIC. The package is thoroughly tested and it is demonstrated that a number of iterations have to be performed in order to find a consistent solution. Since the formulation of the problem can treat general 3D systems, we show a quasi-axisymmetric stellarator low power test case, and then concentrate on experimentally relevant Joint European Torus (JET) 2D configurations. (C) 2010 Elsevier B.V. All rights reserved

The Dependence of the Damping Rate of Medium-n Toroidal Alfvén Eigenmodes on the Edge Plasma Elongation in JET

This paper reports the first quantitative analysis of the measurements of the damping rate (gamma/omega) for stable Alfvén Eigenmodes (AEs) with toroidal mode number (n) in the range |n|=3-15 as function of the edge plasma elongation (kappa95). We find that the damping rate gamma/omega vs. kappa95 for medium-n Toroidal AEs, with n=3 and n=7, increases for increasing elongation, i.e. its scaling vs. kappa95 follows the same trend previously measured and explained theoretically for the n=1 and n=2 TAE modes. Theoretical analysis of the measurements for the n=3 TAEs has been performed using the LEMan code. The results are in good agreement (within a factor 2) for all the magnetic configurations where there is only a very minor up/down asymmetry in the poloidal cross-section of the plasma. These experimental results further confirm the possibility of using the edge shape parameters as a real-time actuator for control of the stability of alpha-particles driven AEs in burning plasma experiments, such as ITER