LARP Technology Quadrupole Review US LHC Accelerator Research Program bnl - fnal- lbnl - slac Supporting FEA for TQC I. Novitski LARP Technology Quadrupole Review Nov 29 – Dec 1

TQC Design and Model Skin Yoke Collar Coil Control spacer Near Splice - P d S h i m n t c g K y I b z w s f B u M Skin Yoke Collar Coil Control spacer Near Splice Coil midplane shim Body area LJ area Splice area LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Model Material Properties, Boundary Conditions and Loads 1. Assembly at room temperature 300K DRcoil TQC01 TQC02 Stress in the coil pole block controled by material placed in the groove During skin welding the yoke-to-collar interference at the coil parting plane compresses coil radially Rsh Prestress in the coil during collaring generated at midplane by coil-to-coil interference, Mp shim The yoke outer mid-plane gap (contact elements) is always open after skin welding (Sk). 2. Cool down from 300K to 1.9K Material properties 3. LF at 1.9K , B=233T/m Fx=1.44MN/m Fy=-2.19MN/m Small reaction forces at pole of the first layer should remain Coil peak stress should be less than 165-170MPa at all loads (based on TQS model result, 2D model singularities). Stress in all structural elements should be below yield point. LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Coil saz: 300K:162MPa, 1.9K:144MPa, B233Tm:146MPa TQC Baseline Design with G10 in the pole groove, Mp=0.15mm,Rsh=0.075mm,St=0-0,Sk=0.3mm 67mm -109mm -129mm -100MPa -95MPa -9MPa -58MPa -42MPa -8MPa 162MPa 144MPa 146MPa -64mm -260mm -228mm Bmax 233T/m 300K 1.9K 44mm -178mm -191mm +9MPa DRcoil 160-190MPa 270-320MPa 280-340MPa Coil saz: 300K:162MPa, 1.9K:144MPa, B233Tm:146MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-01 Real Body Model with epoxy in the groove, Mp=0. 075mm,Rsh=0 TQC-01 Real Body Model with epoxy in the groove, Mp=0.075mm,Rsh=0.05mm,St=0.05-0,Sk=0,3mm -42MPa 21mm -37MPa -161mm -13MPa -36MPa -24MPa -7MPa -37mm 55MPa 57MPa 66MPa -238mm 1.9K I=8kA 300K 38mm -194mm +9MPa Training start DRcoil +70MPa -162mm +26MPa +3MPa +12MPa +2MPa +11MPa saz 107MPa -196mm 85MPa 66MPa +26MPa +11MPa I=14kA 233T/m I=12kA I=9kA -193mm +12MPa 12kA slow training 9kA slow training Coil saz: 300K:66MPa, 1.9K:55MPa, B233T/m:107MPa Separation starts at 9kA, quenches, consistent with observed training behavior LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-01 Real LJ Model with epoxy, Mp=0. 075mm,Rsh=0. 075mm,St=0 TQC-01 Real LJ Model with epoxy, Mp=0.075mm,Rsh=0.075mm,St=0.05mm-0,Sk=0.3mm -47MPa -53MPa -171mm 16mm -25MPa -38MPa -31MPa -15MPa 83MPa -53mm 67MPa -251mm 78MPa 300K 1.9K I=8kA 35mm -200mm -17MPa Training start DRcoil +36MPa -194mm +15MPa -10MPa +3MPa -10MPa +20MPa 111MPa -217mm 93MPa 84MPa +15MPa I=14kA 233T/m I=12kA I=9kA +3MPa -216mm 12kA slow training -5MPa 9kA slow training Coil saz No separation up to 12kA, no quenches, consistent with observed training behavior LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Model for TQC-01 Splice Area with Stainless Steel Yoke -247mm -5mm Extreme parameters Mp=0.075mm Rsh=0.075mm St=0.05mm Sk=0.4mm -57mm -331mm 300K 1.9K -155mm 21mm Coil saz: 300K-142MPa 1.9K -153MPa Not a problem area LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-01 Model near Splice Area with Stainless Steel Yoke Mp=0.075mm Rsh=0.125mm St=0.05mm Sk=0.3mm Coil seqv: 300K-163MPa 1.9K -175MPa 300K 1.9K Coil seqv may reach >200MPa at 1.9K if count on parameters variation due to collared coil OD elliptical shape (measured after disassembly). Cable stress sensitivity Coil m-p shim 10-12 MPa/25mic Collar-yoke radial shim 20-25 MPa/25mic Skin shrinkage after welding 3-4 MPa/25mic Normalized Ic vs. transverse pressure for all samples tested at 12 T. LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Summary for TQC-01 Coil prestress was generally lower than expected due to difference from design parameters: Epoxy in the pole groove (~30MPa, possible yielding of pole) Bigger size of two control spacers (attempt to correct calculated yoke asymmetry during assembly) Smaller coil midplane shim Coil seqv near splice area may reach >200MPa at 1.9K if parameter variations due to collared coil OD elliptical shape are considered (measured after disassembly). TQC Baseline TQC-01 as built (Body) 300K 1.9K 14kA 12(14)kA Pressure at Inner pole, MPa -100 -95 +/-9 -47 -53 +15(+36) Pressure at Outer pole, MPa -58 -42 -8 -38 -31 +3(+20) Max azim. stress, MPa 162 144 146 83 67 93(111) Coil dR at pole up, mm -109 -129 16 -171 (-194) Coil dR at midplane, mm -64 -260 -228 -251 (-217) Coil dR at pole near yoke split, mm 44 -178 -191 35 -200 (-216) LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-02 Model Features G10 in the pole groove Possible glued pole inserts Full round collars Wider collar radial support Full length iron yoke LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-02 Model (LJ) with G10, Mp=0.15mm,Rsh=0.075mmF,St=0-0,Sk=0.3mm -100MPa -95MPa 42mm -124mm -20MPa -145mm -75MPa -60MPa -20MPa 169MPa 168MPa 173MPa -64mm -266mm -236mm Bmax 233T/m 300K 1.9K 29mm -39MPa -233mm -249mm -1MPa DRcoil 170-210MPa 290-350MPa 280-330MPa Coil saz: 300K:169MPa, 1.9K:168MPa, B233Tm:173MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-02 Model (Body) with G10, Mp=0.15mm,Rsh=0.075mmF,St=0-0,Sk=0.3mm -100MPa -95MPa 58mm -109mm -20MPa -134mm -75MPa -60MPa -20MPa 170MPa 164MPa 167MPa -67mm -266mm -236mm Bmax 233T/m 300K 1.9K 33mm -39MPa -222mm -209mm +/-2MPa DRcoil 170-210MPa 290-345MPa 280-330MPa Coil saz: 300K:170MPa, 1.9K:164MPa, B233Tm:167MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Model for TQC-02 Near Splice Area with Iron Yoke -150mm 21mm Mp=0.075mm Rsh=0.075mm St=0 Sk=0.3mm -74mm -269mm -256mm -8mm DRcoil Coil seqv: 300K-125MPa 1.9K -116MPa Stresses reduced to safe level LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

Model for TQC-02 Splice Area with Iron Yoke 24mm -136mm Mp=0.075mm Rsh=0.075mm St=0 Sk=0.3mm -55mm -256mm 17mm -224mm DRcoil Coil saz: 300K-132MPa 1.9K -133MPa Stresses at safe level LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC

TQC-02 Summary saz at splice area is 133MPa/1.9K TQC Baseline TQC-02 (LJ) 300K 1.9K 14kA Pressure at Inner pole, MPa -100 -95 +/-9 -20/-1 Pressure at Outer pole, MPa -58 -42 -8 -75 -60 -20/-39 Max azim. stress, MPa 162 144 146 169 168 173 Coil dR at pole up, mm 67 -109 -129 42 -124 -145 Coil dR at midplane, mm -64 -260 -228 -266 -236 Coil dR at pole near yoke split, mm 44 -178 -191 29 -249 -233 Increase contact area of yoke upon collars : Reduced coil bending Increase coil prestress for second layer Increased skin stress by ~15MPa Full length iron yoke: Coil seqv near splice area is 125MPa/300K and saz at splice area is 133MPa/1.9K LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC