Shock wave formation in radiative plasmas.

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 thick and thin 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 thick and thin 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.

Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equations of state.

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equations of state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when γ>2 or it weakens them when γ<2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1+sqrt[2]. Results have been validated with numerical simulations performed with the FLASH code.

Magnetic flux conservation in an imploding plasma.

The theory of magnetic flux conservation is developed for a subsonic plasma implosion and used to describe the magnetic flux degradation in the MagLIF concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)10.1063/1.3333505]. Depending on the initial magnetic Lewis and Péclet numbers and the electron Hall parameter, the implosion falls into either a superdiffusive regime in which the magnetization decreases or a magnetized regime in which the magnetization increases. Scaling laws for magnetic field, temperature, and magnetic flux losses in the hot spot of radius R are obtained for both regimes. The Nernst velocity convects the magnetic field outwards, pushing it against the liner and enhancing the magnetic field diffusion, thereby reducing the magnetic field compression and degrading the implosion performance. However, in the magnetized regime, the core of the hot spot becomes magnetically insulated and undergoes an ideal adiabatic compression (T∼R^{-4/3} compared to T∼R^{-2/3} without magnetic field), while the detrimental Nernst term is confined to the outer part of the hot spot. Its effect is drastically reduced, improving the magnetic flux conservation.