UPDATE ON THE COUPLED THERMO- AND MAGNETO- MECHANICAL STUDY OF THE HORN

1. UPDATE ON THE COUPLED THERMO- AND MAGNETO- MECHANICAL STUDY OF THE HORN Cracow University of Technology Institute of Applied Mechanics P. Cupial, A. Wroblewski EUROnu Project P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

2. New results covered • Thermomechanical results for the beam power of 1.3 MW for • the baseline geometry • Coupled magneto-solid analysis of a simplified model of the • horn • New horn geometry as provided by C. Bobeth • Our part of the report is well advanced P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

3. 48.2 kW 67kW 14.9kW 78.7kW 4MW, 2.2 GeV proton beam Update of thermomechanical study of the horn – beam power 1.3 MW The magnitudes of energy deposition for a 4MW beam shown have been rescaled proportionally for the beam power of 1.3 MW. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

4. Update of thermomechanical study of the horn – beam power 1.3 MW Themomechanical results were presented during the annual meeting in Strasbourg. This is a nonlinear analysis and the results do not scale with the beam power. Some new results are discussed for the beam power of 1.3 MW. Temperature distribution in the horn for the specified energy deposition. The case of one horn with 1.3 MW beam power. Maximum temperature 350 K should be acceptable. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

5. Update of thermomechanical study of the horn – beam power 1.3 MW Cooling water flow velocity. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

6. Temperature distribution for a cooling system without water spray – beam power 1.3 MW Very high temperature – especially on the front plate. Convection coefficient drops for the case without a water spray. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

7. Z Y X -493180 -383585 -273989 -164393 -54798 -438383 -328787 -219191 -109596 0 Coupled magneto-solid analysis of a simplified plane model of the horn Assumption – cylindrical geometry with infinite length along the axis (plane-strain assumption) Previous study used the analytically calculated magnetic field and the analytical expression for the magnetic pressure (which is only valid for a simplified geometry) P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

8. Coupled magneto-solid analysis of a simplified model of the horn Plane model of the horn: 300 kA current flows in the positive axial direction in the inner conductor and returns through the outer conductor. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

9. Results of static analysis Magnetic flux vs. radius. Good agreement with analytical solution, but additional accuracy studies are needed. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

10. Hoop and axial stress vs. radius, respectivelly in the inner and outer conductor. The higher absolute value corresponds to the hoop stress. Inner conductor is in compression (maximum hoop stress about 7 MPa). P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

11. Response to a single current pulse – coupled magneto-solid results Dynamic stress due to a rectangular current pulse of magnitude 300 kA and 100 s duration: On the inner conductor: 10 MPa On the outer conductor: 2.5 MPa The stress levels calculated using the coupled-field analysis are very comparable to those obtained with the magnetic pressure method. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

12. 3D model of the horn used in the magneto- solid analysis Coupled magneto-solid analysis is more versatile as it is capable of handling complex geometries. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

13. New horn geometry as proposed by C. Bobeth The thermo- and magneto-mechanical studies have been initiated for this new geometry. Especially the non-linear analysis of the cooling system requires considerable effort. P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010

14. Status of the report in Krakow (P.Cupiał and A. Wróblewski) • The results are available for the (old?) baseline geometry. The thermomechanical study using the new geometry has just started. • Sections almost finished on: horn cooling; thermo- and magneto-mechanical dynamic analysis. The description is for the baseline geometry and 1.3 MW beam power with the graphite target. • Section still under development: horn and target integration conceptual drawings. • For future work: should the design with AlBeMet target be considered from the mechanical point of view? P.Cupial, A.Wroblewski, Update on coupled thermo- and magneto-mechanical analysis of the horn EUROnu WP2 Cracow meeting, 14.10.2010