Two-dimensional radiation hydrodynamic simulations of high-speed head-on collisions between high-density plasma jets
Authors: Yang Meng-Qi , Wu Fu-Yuan , Chen Zhi-Bo , Zhang Yi-Xiang , Chen Yi , Zhang Jin-Chuan , Chen Zhi-Zhen , Fang Zhi-Fan , Rafael Ramis , Zhang Jie ,   Key Laboratory of Laser Plasma, Ministry of Education, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China,   Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China,   IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China,   E.T.S.I. Aeronautica y del Espacio, Universidad Politecnica de Madrid, Madrid 28040, Spain
Published: August 2022

<sec>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.</sec><sec>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/cm<sup>3</sup>). 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/cm<sup>3</sup>, 30 eV and 300 km/s, respectively, the colliding plasma density can reach more than 300 g/cm<sup>3</sup>. This is very favorable for the following fast electron heating process in the double-cone ignition (DCI) scheme.</sec><sec>The issue about quantum degeneracy after collision is discussed in this work. Under the typical initial conditions of plasma jets in DCI scheme (<inline-formula><tex-math id="M1">\begin{document}$100\,\,\rm{km}/\mathrm{s}\leqslant {V}_{0}\leqslant 500\,\,\rm{km}/\mathrm{s},10\,\,\rm{eV}\leqslant {T}_{0}\leqslant 100\,\,\rm{eV},10\,\,\mathrm{g}/\mathrm{c}\mathrm{m}^3\leqslant {\rho }_{0}\leqslant 50\,\,\mathrm{g}/\mathrm{c}\mathrm{m}^3)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M1.png"/></alternatives></inline-formula>, both quantum degenerate plasma and classical non-degenerate plasma can be obtained in a temperature range between <inline-formula><tex-math id="M2">\begin{document}$ 0.3{T}_{F} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M2.png"/></alternatives></inline-formula> (Fermi temperature) and <inline-formula><tex-math id="M3">\begin{document}$ 3{T}_{F} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220948_M3.png"/></alternatives></inline-formula>. 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.</sec>