Simulation of High-Power Liquid Metal Jet Targets Roman Samulyak

1. 2014 MAP Winter Meeting December 3 – 7, SLAC, CA Simulation of High-Power Liquid Metal Jet Targets Roman Samulyak AMS Department, Stony Brook University and Computational Science Center Brookhaven National Laboratory

2. Talk Outline • Computational methods and codes • Front tracking and FronTier code (FT) • Smooth Particle Hydrodynamics (SPH) • New Lagrangian particle method • Summary of results • Entrance of mercury jet into solenoid • Interaction of mercury jet with proton pulses • Influence of MHD on the mercury splash • Other liquid metals

3. Computational Methods: Front Tracking • Front tracking is a hybrid Lagrangian-Eulerian method for systems with sharp discontinuities in solutions or material properties FronTieris a parallel 3D multiphysics code based on front tracking • Compressible and incompressible fluid dynamics • MHD in low magnetic Reynolds number approximation • Flow in porous media • Complex EOS, phase transition and cavitation models (N-1) dimensional Lagrangian mesh (interface) Volume filling rectangular mesh (Eulerian Coord.) (i,j)

4. Particle-based Methods I: SPH • A parallel smoothed particle hydrodynamics (SPH) hydro code has been developed • Collection of solvers, smooth kernels, EOS and other physics models (cavitation) • Exact conservation of mass (Lagrangian code) • Natural (continuously self-adjusting) adaptivity to density changes • Capable of simulating extremely large non-uniform domains • Ability to robustly handle material interfaces of any complexity • Scalability on modern multicore supercomputers

5. Particle-based Methods II: New Lagrangian Particle Method • While completely suitable for the target hydro problem, SPH may not be accurate for other classes of problems (in particular MHD) • SPH is an accurate discretization for the system of Lagrange equations for the collection of SPH particles (not exactly equivalent to the fluid dynamics equations) • SPH is accurate for systems that are driven by global conservations laws (target is an example), but not always accurate for wave dynamics problems • We understood deficiencies of SPH and developed a new Lagrangian particle method that dramatically improves the accuracy of SPH • In addition to target-type problems, that new method is beneficial for many other free surface flows or very non-uniform systems (astrophysics / cosmology, high energy density matter) • The method was broadly verified / validated (submitted J. Comput. Physics paper)

6. Summary of Simulation Studies

7. Deformation of Mercury Jet Entering Solenoid • Performed MHD simulations of mercury jet entering solenoid under different angles • Demonstrated fattening of the jet • Agreement with theoretical predictions using expansion series • Small angle between the jet and solenoid axis was used in MERIT experiment 2 4 6 8 10 12 14 -50 -40 -30 -20 -10 0 10 20 30 40 50 Transverse B, kGauss, vs longitudinal coordinate, cm

8. Experimental images of mercury splash at t = 0.88, 0.125, 0.7 ms after impact of 12 teraproton beam (A. Fabich) Experimental device Validation: Simulation of mercury thimble experiments SPH simulation results at t = 0.5 and 0.7 ms

9. Interaction of jets with proton pulses • Performed simulations of jets with cylindrical and elliptic (MHD-deformed) cross-sections • Investigated the muon collider vs neutrino factory beam power regimes • MHD effects; light metal jets etc • Strong dependence on cavitation (minor jet disruption without cavitation) • In a typica example below, velocities of the mercury disruption reach: ~110 m/s (shorter axis), ~40 m/s (longer axis)

10. Summary of Jet Splash Simulations: Energy Deposition in Muon Collider vs Neutrino Factory Beam: 8 GeV, 4 MW, 3.125e15 particles/s, r.m.s. rad = 1.2 mm Neutrino Factory: 150 bunches / s 6.67 ms interval 20.8 teraproton per bunch Muon Collider: 15 bunches / s 66.7 ms interval 208 teraproton per bunch • Energy deposition calculated by MARS code • Thermodynamic response calculated by Equation of State • Accurate mercury EOS model based on experimental and theoretical thermodynamic data from Sandia • Maximum pressure (estimate): Muon Collider: Pmax = 110 kbar Neutrino Factory: Pmax = 11 kbar

11. Brief Summary of Jet Splash Disruption Velocities Neutrino Factory: velocities is in the range of 15 - 35 m/s, with some small droplets reaching velocities of the order of 40 - 50 m/s Muon collider: main jet fragments disperse with the velocity of 90 - 110 m/s with some droplets reaching much higher velocities Gallium targets: density of gallium is 6.1 g/cc and the sound speed is 2879 m/s. Gallium jet splash was comparable to the mercury splash with muon collider beam parameters Neutrino factory: 0.35 ms (top) and 1 ms (bottom) after interaction with beam Muon collider: 0.35 ms after interaction with proton beam

12. MHD Simulation of the Mercury Splash • Demonstrated stabilizing effect of the magnetic field • Magnetic field reduces the amount of cavitation and velocity of filaments • Reasonable agreement with MERIT experiments on disruption velocities 0T 15T Mercury jet surface at 150 microseconds after the interaction with 12 teraproton pulse. Left: MERIT experimental image (15T) Right: FronTier simulation

13. Growth of surface filaments No magnetic field Energy deposition in elliptic jet (neutrino factory) B=10T

14. Summary • Developed new computational methods and parallel codes for multiphase problems (in particular suitable for high power targets) • Unique front tracking MHD code • Smooth Particle Hydrodynamics code • New Lagrangian particle method and parallel code • Developed accurate EOS and cavitation models • Performed simulations of hydrodynamic aspects of high power liquid metal jet targets • Entrance of mercury jet into solenoid • Interaction of mercury jet with proton pulses • Influence of MHD on the mercury splash • Other liquid metals (gallium) • Reasonable agreement with available experimental data