16T Cosθ Dipole Configuration BARBARA CAIFFI on behalf of INFN team: G. Bellomo, P. Fabbricatore, S.Farinon, V. Marinozzi, A.M. Ricci , M. Sorbi and G. Volpini

Outlook Mechanics E.M. Analysis Single aperture: Steel pad Iron pad Double aperture (preliminary analysis, results to be accurately verified) Configuration 1: nominal inter-beam distance, vertical cut in the steel pad, cut at 45o in the iron yoke Configuration 2: optimized inter-beam distance, vertical cut in the steel pad, cut at 45o in the iron yoke Configuration 3: optimized inter-beam distance, vertical cut in the steel pad, horizontal in the iron yoke E.M. Analysis 3D E.M. analysis for the end without connections Conclusions and future developments

Mechanics: single aperture, steel pad Bladder & key configuration Keys length= 20 mm, xkey1=10 mm, ykey1=10 mm, interference key1= 0.1 mm, interference key2= 0.5 mm. Rectangular steel pad, cut vertically, 20-60 mm thick. Circular iron yoke, cut at 45o, 133-175 mm thick. Rectangular shaped steel pad and horizontal and vertical keys allow to decouple x and y component of pre-stress. Al alloy ANSYS model 55 mm 45o cut Iron 133 mm Vertical cut Key1 Intf=0.1 mm 20 mm SS 60 mm Key2 Intf=0.5 mm 175 mm 20 mm

Contact Pressure and Azimuthal Stress Assembly Cool Down Energization Contact Pressure [Pa] Contact Pressure [Pa] Contact Pressure [Pa] Von Mises Stress s eqv [Pa] Von Mises Stress s eqv[Pa] Von Mises Stress s eqv [Pa] seqv peak= 100 MPa s eqv peak=176 MPa s eqv peak= 179 MPa

Double aperture- configuration 1 Nominal inter-beam distance: 125 mm Bladder and Key system: Key 1 and Key 2 interference:0.6 mm Key 3 and Key 4 interference: 0.01 mm Key and Key 6 interference:0.2 mm Iron yoke cut at 45o Vertical cut in the steel pad key4 key3 key5 key2 key6 key1

Double aperture, configuration 1 Assembly Cool Down Energization Contact pressure Von Mises stress Seqvmax=143 MPa Seqvmax=162 MPa Seqvmax=194 MPa

Double aperture- configuration 2 Inter-beam distance: 104 mm Bladder and Key system: Key 1 and Key 2 interference:0.6 mm Key 3 and Key 4 interference: 0.01 mm Key 5 and Key 6 interference:0.2 mm Iron yoke cut at 45o Steel pad cut vertically key1 key2 key3 key4 key5 key6

Double aperture- configuration 2 Assembly Cool Down Energization Contact pressure Von Mises stress Seqvmax=145 MPa Seqvmax=178 MPa Seqvmax=188 MPa

Von Mises Stresses on Mechanical Structures Iron Assembly Cool down Energization sVM peak= MPa sVM peak=335 MPa sVM peak=414 MPa sVM peak=561 MPa Yield limit: >350 MPa Yield limit: >720 MPa Yield limit: >720 MPa Steel sVM peak=344 MPa sVM peak=558 MPa sVM peak=704 MPa Yield limit: 1050 MPa Yield limit: 350 MPa Yield limit: 1050 MPa

Von Mises Stresses on Mechanical Structures Ti Yield limit: 1650 MPa sVM peak=221 MPa Yield limit: 1650 MPa sVM peak=1020 MPa Yield limit: 800 MPa sVM peak=961 MPa Al alloy Yield limit: 690 MPa sVM peak=199 MPa Yield limit: 690 MPa sVM peak=631 MPa Yield limit: 480 MPa sVM peak=439 MPa

Von Mises Stresses on Mechanical Structures Ti Yield limit: 1650 MPa sVM peak=221 MPa Yield limit: 1650 MPa sVM peak=1020 MPa Yield limit: 800 MPa sVM peak=961 MPa Al alloy Yield limit: 690 MPa sVM peak=199 MPa Yield limit: 690 MPa sVM peak=631 MPa Yield limit: 480 MPa sVM peak=439 MPa

Double aperture- configuration 3 Nominal inter-beam distance: 104 mm Bladder and Key system: Key 1 interference:0.5 mm Key 2 interference:0.6 mm Key 3 and Key 4 interference: 0.01 mm Key 5 interference:0.2 mm Key 6 interference:0.25 mm Horizontal cut in iron yoke Vertical cut in steel pad key1 key2 key3 key4 key5 key6

Double aperture- configuration 3 Assembly Cool Down Energization Contact pressure Von Mises stress seqvmax= 156 MPa seqvmax= 166 MPa seqvmax= 191 MPa

Von Mises Stresses on Mechanical Structures Assembly Cool down Energization sVM peak= 651MPa sVM peak= 743MPa sVM peak= 857 MPa Yield limit: >350 MPa Yield limit: >720 MPa Yield limit: >720 MPa Steel sVM peak= MPa sVM peak= 684 MPa sVM peak= 575 MPa sVM peak= 760 MPa Yield limit: 350 MPa Yield limit: 1050 MPa Yield limit: 1050 MPa

Von Mises Stresses on Mechanical Structures Ti Yield limit: 800 MPa sVM peak= 1110 MPa Yield limit: 1650 MPa sVM peak= 236 MPa Yield limit: 1650 MPa sVM peak= 1020 MPa Al alloy Yield limit: 690 MPa sVM peak= 193 MPa Yield limit: 690 MPa sVM peak=185 MPa Yield limit: 480 MPa sVM peak= 385 MPa

Von Mises Stresses on Mechanical Structures Ti Yield limit: 800 MPa sVM peak= 1110 MPa Yield limit: 1650 MPa sVM peak= 236 MPa Yield limit: 1650 MPa sVM peak= 1020 MPa Al alloy Yield limit: 690 MPa sVM peak= 193 MPa Yield limit: 690 MPa sVM peak=185 MPa Yield limit: 480 MPa sVM peak= 385 MPa

Single aperture, iron pad Al alloy 55 mm 45o cut Iron Key1 Intf=0.1 mm Vertical cut 133 mm iron 60 mm Key2 Intf=0.5 mm 175 mm Keys length= 20 mm, xkey1=10 mm, ykey1=10 mm, interference key1= 0.1 mm, interference key2= 0.5 mm. Rectangular steel pad, cut vertically, 20-60 mm thick. Circular iron yoke, cut at 45o, 133-175 mm thick. Rectangular shaped steel pad and horizontal and vertical keys allow to decouple x and y component of pre-stress.

Single aperture, iron pad Assembly Cool Down Energization Contact pressure Von Mises stress Seqvmax=124 MPa Seqvmax=172 MPa Seqvmax=187 MPa

Single aperture, iron pad Assembly Cool down Energization Von Mises stress on iron pad and yoke are below yield strength of the new proposed iron material

3D E.M. Analysis Roxie Model- side opposite to the connections The 3D model includes also the iron yoke, but here only the coil is shown.

NORMAL 3D INTEGRAL RELATIVE MULTIPOLES 3D Harmonic Analysis Preliminary optimization based on geometrical parameters in the end has been performed. B3 B5 B7 B9 B11 NORMAL 3D INTEGRAL RELATIVE MULTIPOLES b 1: 10000.00000 b 3: 4.89034 b 5: 5.30343 b 7: 1.99606 b 9: 0.97365 b11: 0.74835 Bn(10-4B0) Zpos [mm]

Conclusions and further developments Double aperture mechanical configurations have been investigated: Configuration1: nominal inter-beam distance (125 mm), vertical cut in the rectangular steel pad, cut at 45o in the iron yoke. Requirements on stress on conductors and on mechanical structures are fulfilled, though contact pressure in particular for 1st layer is not sufficient. Configuration2: inter-beam distance =104 mm, vertical cut in the rectangular steel pad, cut at 45o in the iron yoke. Requirements on stress on conductors and on mechanical structures are fulfilled, as well as contact pressure. Configuration3: inter-beam distance =104 mm, vertical cut in the rectangular steel pad, horizontal cut in the iron yoke. Requirements on stress on conductors are fulfilled, as well as contact pressure. Stress on mechanical structures, and in particular in the iron are higher than the limit. The feasibility of an iron pad has been investigated, giving good results on single aperture. Still to be implemented on double aperture. 3D E.M. analysis of the integrated harmonics has been performed with Roxie for the side opposite to the connections. Even if the result is still preliminary, harmonics are already quite optimized.