Radiation-hydrodynamic code

Radiation-hydrodynamic code

The interaction of a laser with a solid target takes place under various physical conditions depending mainly on the length of the pulse and its intensity. Let’s focus on the intensities on the order of 1 GW/cm2, when the production of plasma by laser ablation (i.e., thermal removing) of the solid target starts for relatively long pulses of length about 1 ns (one milliardth of a second), up to high-power laser systems with the intensity of 1 PW/cm2 (i.e., one and fifteen zeroes behind it in W/cm2). These intensities appear in the context of ELI mainly during the pre-pulse of an extremely intense main pulse and significantly affect the interaction (like e.g. particle acceleration and other), but they may be encountered for the high energy density physics (HEDP) and inertial thermonuclear fusion (ignition of nuclei fusion, similar to what is happening in stars, by means of an implosion) or research of the warm dense matter (WDM) similar to the conditions in the cores of planets or brown dwarfes (non-ignited stars).

The plasma is relatively dense in all the cases and the overall interaction with the laser cannot be considered as an ensemble of almost independent interactions with single particles, but rather as an interaction with a single continuum. The plasma can be approximated by a hot fluid then, where its evolution is described by the laws of hydrodynamics.

For these purposes, the state-of-the-art hydrodynamic code named PETE (Plasma Euler and Transport Equations) is being developed at ELI. It includes in addition to the description of the plasma dynamics also multiple modules for energy transport. Heat conduction is included there, but also radiative thermal transport, which is in the case of the laser plasma dominated by the radiation in the X-ray range unlike the common daily experience. This description is called radiation-hydrodynamics. A special feature of the code is that it includes what is known as the non-local heat transport, which applies to the hot electrons which weakly interact with the other particles and penetrate deeper into the plasma violating the law of heat diffusion. An indispensable part of the code is the laser absorption module, where the approaches based on the geometrical optics approximation, when the trajectory of the rays is being tracked in multiple dimensions (raytracing), and also the wave description of propagation and absorption of the laser wave in one dimension.

In addition to the physical aspects of the laser-plasma interaction, the numerical schemes for the computer simulation are being developed. In particular, the finite element method (FEM) of high order is applied, where their advantage is given by substitution of the simple discrete data by high order polynomials and as a consequence better approximation of the real profiles and utilization of the hardware resources. For this purpose, MFEM library is a major help. It is being developed in LLNL (Lawrence Livermore National Laboratories) and is a part of the modern numerical libraries generation for exascale computing. Thanks to it, the code is highly efficient, scalable from one up to three dimensions and parallelized for running on the ECLIPSE cluster.