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We derive expressions for shock formation based on the local curvature of theflow characteristics during dynamic compression. Given a specific ramp adiabat,calculated for instance from the equation of state for a substance, the idealnonlinear shape for an applied ramp loading history can be determined. Wediscuss the region affected by lateral release, which can be presented incompact form for the ideal loading history. Example calculations are given forrepresentative metals and plastic ablators. Continuum dynamics (hydrocode)simulations were in good agreement with the algebraic forms. Exampleapplications are presented for several classes of laser-loading experiment,identifying conditions where shocks are desired but not formed, and where longduration ramps are desired.

Shock formation and the ideal shape of ramp compression waves