A simple model of a strong shock driven by a spherical or cylindrical piston

Ryutov, D. D.

doi:10.1063/5.0051264

A simple model of a strong shock driven by a spherical or cylindrical piston

Journal Article · Fri Jul 16 00:00:00 EDT 2021 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0051264· OSTI ID:1825859

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Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

A simple model of piston-driven spherical and cylindrical shocks is suggested. The model is based on a consistent use of two factors: (a) an almost uniform pressure across the shocked layer and, (b) continuous geometrical stretching of the surface elements of the expanding piston. It turns out that for a uniform pre-shock medium the gas between the piston and the shock behaves essentially as an incompressible fluid. An algebraic equation for the shock vs piston position is obtained. Detailed evaluation of the accuracy of the proposed solution shows that its accuracy is a few percent for the adiabatic index γ = 5/3 (as in ideal plasma). A closed-form solution describing enhancement of a weak ambient magnetic field by the shock is presented. The proposed model of piston-driven shocks goes beyond the classical self-similar solutions in that it: (1) naturally covers an early, non-asymptotic dynamics and its transition to asymptotic regime; (2) allows for smooth radial density variation of an ambient gas of the form of bumps, dimples or ramps between two constant values; and (3) allows for smooth temporal variation of piston velocity of the form of bumps, dimples, or ramps. Furthermore, this simple and versatile model provides some new insights into a classical hydrodynamical problem.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1825859

Alternate ID(s):: OSTI ID: 1808338

Report Number(s):: LLNL-JRNL--820731; 1032411

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 28; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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A simple model of a strong shock driven by a spherical or cylindrical piston

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