Jayanta Mondal, A. Roy, K. C. Mittal Accelerat or & Pulse Power Division Bhabha At omic Research Cent re Mumbai , I ndia

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1 OPI MI ZAI ON OF WALL HI CKNESS OF SUPERCONDUCI NG 700 MHZ BULK NI OBI UM AND NI OBI UM COAED OFHC COPPER CAVI I ES BY HERMAL/ SRUCURAL ANALYSI S Jayanta Mondal, A. Roy, K. C. Mittal Accelerat or & Pulse Power Division Bhabha At omic Research Cent re Mumbai , I ndia

2 I NRODUCI ON ¾he hermal\ St ruct ural Analysis has been carried out on a prot ot ype single cell Superconduct ing ellipt ical cavit y of g = 0.42 at a f requency of 700 MHz using COSMOS/ M. ¾o operat e it at low t emperat ure, t he cavit ies are cooled down f rom 300 K t o 4. 2 K in a liquid He bat h. ¾he def ormat ion and t he ef f ect ive st ress has been analyzed under t he t hermal load and t he inward He- I pressure of E+5N/ m2. ¾Resonant f requency shif t due t o t he st ruct ural def ormat ion is calculat ed using CS MI CROWAVE SUDI O/ SUPERFI SH code. MODELLI NG OF HE CAVI Y ¾A 45 0 sect ion of t he cavit y including t he beam t ube has been modeled and shown in FI G- 1. ¾he general boundary condit ions are also shown in FI G- 1. ¾Model has been generat ed cavit ies. f or bot h bulk and coat ed Copper ¾he mat erial propert ies used f or bot h t he st ruct ure are list ed in able- 1. ¾A nonlinear variat ion of t hermal conduct ivit y and specif ic heat has been t aken int o account f or bot h t he t ypes of cavit ies. ¾t he t hermal conduct ivit y of (RRR250) as a f unct ion of t emperat ure can be writ t en as, K() = (1)

3 Material Propert ies Young s (GPa) Poisson Rat io Modulus Coef f of thermal Expansion (m/ K) Density (kg/ m 3 ) coated Cu cavity E Bulk cavit y E able- I FI G- 1 hermal/ Structural Results ¾hermal\ st ruct ural result s include t he helium pressure + hermal load due t o t he cooling down of t he cavit y f rom 300 K t o 4. 2 K. ¾St ruct ural def ormat ions was det ermined f or dif f erent wall t hicknesses of 3, 4, and 5 mm respect ively. ¾ypical st ruct ural def ormat ion f or 5mm t hick coat ed Cu and bulk cavit ies is shown in FI G- 2. ¾FI G- 3 shows t he cont our plot of Von- Mises st ress f or bot h t he t ypes of cavit y of wall t hickness 5mm. coat ed Cu Cavit y bulk niobium cavit y FI G- 2

4 hermal/ Structural Results(Contnd. ) coat ed Cu Cavit y bulk niobium cavit y FI G- 3 ¾A comparat ive st udy of bot h t he t ypes of cavit y f rom t he point of view of maximum deformations in radial and axial directions and the maximum effective stresses is represented in able-2. Parameters Yielding Stress MPa Max Von- Mises Stress MPa Y- Diplace ment mm X- Displace ment mm 3mm 4mm 5mm 3mm 4mm 5mm 3mm 4mm 5mm able- 2 Coated Cu Cavity MPa Bulk Cavity 700MPa D is p la c e m e n t(c m ) dz Max. Stress 74 MPa Point of Max Deformation Z (cm) FI G- 4 dr Stress Curve 5 mm Bulk Cavity V o n -M is e s S tre s s (M P a ) ¾So f rom t he st ress point of view all the t hicknesses analyzed are suit able.

5 RF PROPERI ES hickness (mm) Parameters Undeformed deformed ¾ he RF propert ies of t he def ormed models have been calculat ed using SUPERFI SH and CS- Microwave St udio and shown in able Cu (MHz) (MHz) (MHz) able- 2 +Cu (MHz) (MHz) ¾ (resonant f requency), (transit time fac), Bpk/B0 (m/(mv/m)) +Cu (MHz) CAVI Y MODEL WI H SI FFENER AND I S EFFEC ¾ A conical st if f ener has been incorporat ed and analyzed wit h respect t o t he dif f erent posit ions at t he cavit y wall t o see it s ef f ect on t he f requency shif t and on t he ef f ect ive st ress value. ¾ At t he posit ion of (R= cm, Z= cm), t he resonant f requency shif t is minimum. ¾ he model of t he cavit y of t hickness 5mm wit h st if f ener (4mm) is shown in FI G- 5. ¾ Comput ed resonance f requency shif t s are 79 and 77 KHz f or coat ed Copper and bulk cavit y of t hickness 5mm. ¾ he t ypical plot of def ormat ion and t he st ress value wit h respect t o axial dist ance f or 5mm t hick bulk cavit y wit h st if f ener is shown in FI G- 6.

6 CAVI Y MODEL WI H SI FFENER AND I S EFFEC(Contd. ) Displacement(cm) dz Max. Stress 62 MPa Point of Max. Displacement Stress Curve With Stiffener dr Z (cm) Von-Mises Stress (MPa) FI G- 5 FI G- 6 CONCLUSI ONS ¾ he comparat ive st udy shows t hat t he bulk cavit ies have bet t er perf ormance t han t he coat ed Cu cavit ies, f rom t he point of view of hermal\ St ruct ural and RF propert ies. ¾ )RUDOOKLJK FDYLWLHVWKHRSWLPXPZDOOWKLFNQHVVLVDERXWPP But our DQDO\VLVVKRZVWKDWIRUORZ FDYLWLHVWKHVKLIWLQUHVRQDQFHIUequency is signif icant ly high f or 3mm st ruct ures. ¾ A t hickness of 5mm best replicat es t he RF propert ies at 4. 2K wit h t he original designed cavit y. ¾ Also t he 4mm t hick cavit y seems t o be alright f rom t he point of view of RF and mechanical propert ies. ¾ I ncorporat ion of st if f ener shows t hat t he f requency shif t comes down t o f ew t ens of KHz.

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