One-dimensional magneto-hydrodynamics simulation of magnetically driven solid liner implosions on FP-1 facility

As an important cylindrical-convergent drive technology, magnetically driven solid liner implosion has been widely used in the high energy density physics (HEDP) experiments for different researches, such as the properties of condensed matter at an extreme pressure, the hydrodynamic behaviors of imploding systems, and the properties and behaviors of dense plasmas. On the 2.2 MA FP-1 facility (with a rise time of 7 s), implosions of aluminum liners and their impact on target liners are studied experimentally for exploring the applications of instability and ejecta mixing. A one-dimensional Lagrangian codeMADE1D is developed to study liner implosions numerically, which is based on magneto-hydrodynamics model with material strength, wide-range equation of state, Lee-More conductivity, and SCG (Steinberg, Cochran and Guinan) constitutive model. The code is based on the finite difference method. The finite difference equations are written in the covariant form for both Cartesian and cylindrical coordinates which enables the accurate simulation of different load geometries. Numerical results, such as the simulated velocity and radius at inner surface of the liner and target, agree well with the measurements. It shows that FP-1 has the ability to accelerate a 0.5 mm thick aluminum liner with an initial radius of 1.5 mm to a speed of more than 1.1 km/s, and the corresponding velocity of inner surface is more than 1.5 km/s due to the cylindrical convergence effect. In our calculation, most of the liner keeps solid throughout the implosion, though its outer surface is melted due to the Ohmic heating. A cylindrical converging shock about 8-10 GPa can be obtained by setting a target with an initial radius of 8-11 mm inside the liner coaxially. The numerical results show that since the imploding liner is fully magnetized when it impacts the target, the shock and the corresponding reflect release wave run faster than in the unmagnetized target. This means that the target will spall near the liner-target interface, though they are impedance-matched acoustically. The movement of the shocked target can be affected by the pre-filled gas inside. Increasing the gas pressure makes the target lose its velocity quickly, and the rebound radius increases as well. By adjusting the load design and gas pressure appropriately, we can obtain the right implosion process to meet the study requirement.