Head-on collisions of plasma jets are common hydrodynamic phenomena in astrophysical and laser-plasma interaction processes. Deriving scaling relationships between colliding plasmas and initial conditions of plasma jets is of great significance in optimizing the design and the data analysis of the relevant experiments. Double-cone ignition (DCI) scheme is an excellent platform for studying plasma jets’ collision, since the collision between high-speed, high-density plasma jets can be easily generated and characterized in both simulations and experiments.

In this work, we employ the upgraded two-dimensional arbitrary Eulerian-Lagrange (ALE) program MULTI-2D to simulate the collision process of plasma jets with high speed (≥100 km/s) and high density (≥10 g/cm³). Using the database obtained from the simulations, hydrodynamic scaling laws describing the collision process of plasma jets are derived by the Bayesian inference method in machine learning. The Bayesian inference method not only has the parameter estimation function of traditional least square method, but also possesses other potential advantages such as giving the probability distribution of estimated parameters. Numerical results show that the collision of plasma jets with open boundaries is easy to form an isochoric plasma distribution with high-density. Increasing the initial density and velocity of the plasma jet is helpful in enhancing the density and temperature of the colliding plasma. Increasing the initial temperature of plasma jet is beneficial to achieving colliding plasmas with a higher temperature, while leading plasma density and pressure to decrease after head-on collision. When the initial density, temperature and velocity of the plasma jets are set to be 15 g/cm³, 30 eV and 300 km/s, respectively, the colliding plasma density can reach more than 300 g/cm³. This is very favorable for the following fast electron heating process in the double-cone ignition (DCI) scheme.

The issue about quantum degeneracy after collision is discussed in this work. Under the typical initial conditions of plasma jets in DCI scheme (100\,\,\rmkm/\mathrms\leqslant V_0\leqslant 500\,\,\rmkm/\mathrms,10\,\,\rmeV\leqslant T_0\leqslant 100\,\,\rmeV,10\,\,\mathrmg/\mathrmc\mathrmm^3\leqslant \rho _0\leqslant 50\,\,\mathrmg/\mathrmc\mathrmm^3), both quantum degenerate plasma and classical non-degenerate plasma can be obtained in a temperature range between 0.3T_F (Fermi temperature) and 3T_F . By comparing the plasma temperature with the Fermi temperature of the collision, the criterion for achieving quantum degenerate plasma or non-degenerate plasma under given initial conditions is obtained with the help of the derived hydrodynamic scaling laws. The criterion shows that higher initial velocity, higher temperature and lower density of plasma jets are required if we want to obtain non-degenerate plasma after collision.