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Title: Finite Mach number spherical shock wave, application to shock ignition

A converging and diverging spherical shock wave with a finite initial Mach number M{sub s0} is described by using a perturbative approach over a small parameter M{sub s}{sup −2}. The zeroth order solution is the Guderley's self-similar solution. The first order correction to this solution accounts for the effects of the shock strength. Whereas it was constant in the Guderley's asymptotic solution, the amplification factor of the finite amplitude shock Λ(t)∝dU{sub s}/dR{sub s} now varies in time. The coefficients present in its series form are iteratively calculated so that the solution does not undergo any singular behavior apart from the position of the shock. The analytical form of the corrected solution in the vicinity of singular points provides a better physical understanding of the finite shock Mach number effects. The correction affects mainly the flow density and the pressure after the shock rebound. In application to the shock ignition scheme, it is shown that the ignition criterion is modified by more than 20% if the fuel pressure prior to the final shock is taken into account. A good agreement is obtained with hydrodynamic simulations using a Lagrangian code.
Authors:
; ;  [1]
  1. University of Bordeaux, CEA, CNRS, CELIA (Centre Lasers Intenses et Applications), UMR5107, F-33400 Talence (France)
Publication Date:
OSTI Identifier:
22220651
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 20; Journal Issue: 8; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLIFICATION; AMPLITUDES; ASYMPTOTIC SOLUTIONS; CORRECTIONS; MACH NUMBER; PLASMA; PLASMA DENSITY; PLASMA SIMULATION; SHOCK WAVES; SPHERICAL CONFIGURATION