# Presentation: 710683

## 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, *_[rosamu@bnl.gov](mailto:rosamu@bnl.gov)_
- Collaborators: **Jian Du, Wurigen Bo**

## Talk Outline

-  Distortion of the mercury jet entering magnetic field
-  Simulation of the mercury jet – proton pulse interaction.
-  Conclusions and future plans

## Jet entering 15 T solenoid

- FronTier code:
-  Explicitly tracked material interfaces
-  Multiphase models
-  MHD in low magnetic Reynolds number approximation

## Previous Results (2005) Aspect ratio of the jet cross-section. I

**B = 15 T****V0 = 25 m/s**

## Previous Results (2005) Aspect ratio of the jet cross-section. II

**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**

## Confirmation:  Independent studies by Neil Morley, UCLA, HiMAG code

**100 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**

## Comparison with the theory

**Comparison with the theory**

## MERIT setup 

**MERIT setup **

## V = 15 m/s,  B = 15 T

**V = 15 m/s,  B = 15 T**

- Jet trajectory

- Bz

- By

- Jet distortion

## V = 20 m/s,  B = 15 T

**V = 20 m/s,  B = 15 T**

- Jet distortion

- Jet trajectory

- Bz

- By

## Comparison: V = 15 and 20 m/s,  B = 10 and 15 T

**Comparison: V = 15 and 20 m/s,  B = 10 and 15 T**

- Jet distortion         vp1       vp2      vp3

## Experimental data 

**Experimental data **

**V = 15 m/s,  B = 10T **

**V = 20 m/s,  B = 10T **

**B = 15T **

**B = 15T **

## Jet - proton pulse interaction. Evolution of models.

**Jet - proton pulse interaction. Evolution of models.**
**Phase I: Single phase mercury (no cavitation)**

-  Strong surface instabilities and jet breakup observed in simulations
-  Mercury is able to sustain very large tension
-  Jet oscillates after the interaction and develops instabilities

- Jet surface instabilities

## Jet - proton pulse interaction. 

-  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**

## Jet - proton pulse interaction 

-  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**

## Jet - proton pulse interaction 

**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?**

## Multiscale approach to bubble collapse 

**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

## Step 1: 1D bubble collapse 

**Step 1: 1D bubble collapse **

***Radius vs. Time***

***Pressure Profile at  t =0.0035 ms***

## Step 2: 2D and 3D simulations of the collapse induced spike 

-  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 = 0.0035 ms                 t = 0.0070 ms

## Initial instability (turbulence) of the jet 

**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.

## 3D jet naturally growing from the nozzle 

-  Simulation of the jet - proton pulse interaction is in progress

**3D jet naturally growing from the nozzle **