Brookhaven Science Associates U.S. Department of Energy Neutrino Factory / Muon Collider Collaboration Meeting March 17-19, 2008, FNAL, Batavia, IL Target.

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Brookhaven Science Associates U.S. Department of Energy Neutrino Factory / Muon Collider Collaboration Meeting March 17-19, 2008, FNAL, Batavia, IL Target Simulations Roman Samulyak Department of Applied Mathematics and Statistics Stony Brook University and Brookhaven National Laboratory U.S. Department of Energy, Collaborators: Jian Du, Wurigen Bo

Brookhaven Science Associates U.S. Department of Energy 2 Talk Outline n Distortion of the mercury jet entering magnetic field n Simulation of the mercury jet – proton pulse interaction. n Conclusions and future plans

Brookhaven Science Associates U.S. Department of Energy 3 Jet entering 15 T solenoid FronTier code: Explicitly tracked material interfaces Multiphase models MHD in low magnetic Reynolds number approximation

Brookhaven Science Associates U.S. Department of Energy 4 Previous Results (2005) Aspect ratio of the jet cross-section. I B = 15 T V0 = 25 m/s

Brookhaven Science Associates U.S. Department of Energy 5 B = 15 T V0 = 25 m/s Previous Results (2005) Aspect ratio of the jet cross-section. II 0.10 rad, z = 0: Aspect ratio = 1.4

Brookhaven Science Associates U.S. Department of Energy mrad tilt angle z = 0 cm z = 20 cm z = 40 cm z = 50 cm z = 30 cm z = 60 cm Aspect ratio = 1.4 in the solenoid center Confirmation: Independent studies by Neil Morley, UCLA, HiMAG code

Brookhaven Science Associates U.S. Department of Energy 7 R. Samulyak et. al, Journal of Computational Physics, 226 (2007), Comparison with the theory

Brookhaven Science Associates U.S. Department of Energy 8 Confirmed MERIT setup

Brookhaven Science Associates U.S. Department of Energy 9 V = 15 m/s, B = 15 T Jet trajectory Bz ByJet distortion

Brookhaven Science Associates U.S. Department of Energy 10 V = 20 m/s, B = 15 T Jet distortion Jet trajectoryBz By

Brookhaven Science Associates U.S. Department of Energy 11 Comparison: V = 15 and 20 m/s, B = 10 and 15 T Jet distortion vp1 vp2 vp3

Brookhaven Science Associates U.S. Department of Energy 12 Simulations only qualitatively explain the width of the jet in different view ports. Experimental data V = 15 m/s, B = 10TV = 20 m/s, B = 10T B = 15T

Brookhaven Science Associates U.S. Department of Energy 13 Jet - proton pulse interaction. Evolution of models. Phase I: Single phase mercury (no cavitation) n Strong surface instabilities and jet breakup observed in simulations n Mercury is able to sustain very large tension n Jet oscillates after the interaction and develops instabilities Jet surface instabilities

Brookhaven Science Associates U.S. Department of Energy 14 We evaluated and compared homogeneous and heterogeneous cavitation models: Homogeneous model Heterogeneous model (resolved cavitation bubbles) Two models agree reasonably well Predict correct jet expansion velocity Surface instabilities and jet breakup not present in in simulations Jet - proton pulse interaction. Phase II: Cavitation models

Brookhaven Science Associates U.S. Department of Energy 15 If jet does not develop surface instabilities, the jet expansion is strongly damped in 15 T magnetic field (radial current are always present). Experimentally confirmed in MERIT. The linear conductivity model predicts strong stabilizing effect of the magnetic field Stabilizing effect of the magnetic field is weaker if conductivity models with phase transitions are used (~ 20 % for Bruggeman’s model) Jet - proton pulse interaction Phase II: Cavitation models in magnetic field

Brookhaven Science Associates U.S. Department of Energy 16 Jet - proton pulse interaction Phase III: Search of missing physics phenomena Why surface instabilities and jet breakup are not observed in simulations with cavitation? Possible Cause: Turbulence nature of the jet Microscopic mixture and strong sound speed reduction of the homogeneous model (separation of phases is important) Unresolved bubble collapse in the heterogeneous model Bubble collapse is a singularity causing strong shock waves Other mechanisms?

Brookhaven Science Associates U.S. Department of Energy 17 Bubble collapse (singularity) is difficult to resolve in global 3D model. Multiscale approach to bubble collapse Multiscale approach: Step 1: Accurate local model precomputes the collapse pressure Step 2: Output of the local model serves as input to the global model

Brookhaven Science Associates U.S. Department of Energy 18 Step 1: 1D bubble collapse Radius vs. Time Pressure Profile at t = ms

Brookhaven Science Associates U.S. Department of Energy 19 Bubble collapse near the jet surface causes surface instability The growth of the spike is not stabilized by the magnetic field This is unlikely to be the only mechanism for surface instabilities Step 2: 2D and 3D simulations of the collapse induced spike t = 0 t = ms t = ms

Brookhaven Science Associates U.S. Department of Energy 20 This was the real state of the jet before the interaction with protons Initial instability (turbulence) of the jet This was initial jet in previous numerical simulations (in 2D and 3D) The obvious difference might be an important missing factor for both the jet flattening effect and interaction with the proton pulse.

Brookhaven Science Associates U.S. Department of Energy 21 Major numerical development allowed us to obtain the state of the target before the interaction by “first principles” Simulation of the jet - proton pulse interaction is in progress 3D jet naturally growing from the nozzle