Shock formation and the ideal shape of ramp compression waves.
We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long-duration ramps are desired.
Swift
Damian C
DC
Condensed Matter and Materials Division,Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA. dswift@llnl.gov
Kraus
Richard G
RG
Loomis
Eric N
EN
Hicks
Damien G
DG
McNaney
James M
JM
Johnson
Randall P
RP