Shock Wave Formation in Radiative Plasmas

TL;DR

This paper investigates the formation and evolution of weak radiative shocks in plasmas, deriving conditions for optically thin and thick regimes, supported by simulations and providing benchmarks for radiative hydrodynamic codes.

Contribution

It introduces a theoretical framework using a Burgers-type equation to analyze radiative shock formation, including conditions for different optical regimes and scaling laws.

Findings

Weak shocks become optically thick over time below a Boltzmann number threshold.

Optically thin solutions are linked to overdense layers in the plasma.

Scaling laws for shock formation time and width are established.

Abstract

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thin and thick regions alternate to form a radiatively-driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work, we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equation that governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thin and thick solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive test-case has been designed to benchmark radiative hydrodynamic codes.