1. Rossana Bonomi Rossana.Bonomi@cern.ch ESS Cryomodule Status Meeting, 9/1/2013

2. Short Cryomodule ESS Cryomodule Status Meeting, 9/1/2013

3. Simulation tool Mathcad semi- analytical model * One dimensional Mesh with 22 nodes 3 series of nodes (inner wall, outer wall, gas) * Based on O. Capatina ‘s presentation: http://indico.cern.ch/getFile.py/access?contribId=3&resId=1&materialId=slides&co nfId=86123 ESS Cryomodule Status Meeting, 9/1/2013

4. Geometry DWT length= 300 mm Inner wall diameter= 100 mm Cu sputter thickness= 4 um Inner wall thickness= 1.5 mm Outer wall thickness= 2 mm Wall cross section= 1152 mm 2 Antenna diameter= 44 mm ESS Cryomodule Status Meeting, 9/1/2013

5. Boundary conditions Cold flange temperature= 2 K Warm flange temperature= 300 K Antenna temperature= 330 K Inlet gas temperature= 4.5 K (1 bar) Inlet gas mass flow= 40 mg/s Convection coefficient= 40 W/m 2 /K

6. Material properties Th-mech properties function of temperature Solids: Cryocomp Fluid (helium): Hepak ESS Cryomodule Status Meeting, 9/1/2013 Outer wall Inner wall Copper RRR=30

7. Material properties Radiative properties function of temperature Copper on wall ESS Cryomodule Status Meeting, 9/1/2013 Cuivre poli mequanique from “Cryogenie” 1995 – Blue book

8. Temperature profiles Results are comparable with FE 2D simulations (Comsol) Heat load at bath: < 0.5 W RF power: around 10 W Antenna radiation load: around 1 W Inner wall No COOL 40 mg/s He Outer wall Inner wall Gas

9. RF power distribution RF currents node position is critical.. 704 MHz, 50 ohm Power: 1 MW p Duty cycle: 10% Current: = 200 A p RF currents ESS Cryomodule Status Meeting, 9/1/2013

10. RF power distribution RF currents ESS Cryomodule Status Meeting, 9/1/2013 RF currents node position is critical.. currents power

11. Sensitivity analysis: RF node No cooling ESS Cryomodule Status Meeting, 9/1/2013 Shift [mm] P rf [W] Q rad [W] Q bath [W] 023.6880.75324.381 1024.8630.76724.799 2025.9400.78525.110 5027.7380.84025.159 10024.6820.82323.034 CF

12. Sensitivity analysis: RF node Gas cooling with 40 mg/s ESS Cryomodule Status Meeting, 9/1/2013 Shift [mm] P rf [W] Q rad [W] Q bath [W] 0 10.2081.3460.104 1011.4251.3540.121 2012.6601.3600.155 5015.5311.3690.338 10014.1361.3490.538 CF

13. Sensitivity analysis: Mass flow ESS Cryomodule Status Meeting, 9/1/2013 Mass flow (mg/s) Qheater (W) Prf (W) Qrad (W) Qbath (W) 0023.6880.75324.381 3032.72212.5421.4610.151 4049.66910.2081.3460.104 5063.6299.6671.2840.103 RF node @ cold flange (shift = 0)

14. Conclusions ESS Cryomodule Status Meeting, 9/1/2013 Mathematical tool can be tuned to simulate different geometries and cryo fluids Looking forward to the mock-up test for confirmation of this model..and to suggestions ! THANK YOU !

16. Operating conditionValue Beam current/pulse lenght40 mA/0.4 ms beam pulse 20 mA/0.8 ms beam pulse cryo duty cycle4.11%8.22% quality factor10 x 10 9 5 x 10 9 accelerating field25 MV/m Source of Heat LoadHeat Load @ 2K Beam current/pulse lenght40 mA/0.4 ms beam pulse20 mA/0.8 ms beam pulse dynamic heat load per cavity5.1 W20.4 W static losses<1 W (tbc) power coupler loss at 2 K<0.2 W HOM loss in cavity at 2 K<1<3 W HOM coupler loss at 2 K (per coupl.) <0.2 W beam loss1 W Total @ 2 K8.5 W25.8 W SPL operational conditions

17. (Figure from: « An Introduction to Cryogenics », Ph.Lebrun, CERN/AT 2007-1) He refrigerationHe Liquefaction Thermodynamic efficiency of gas cooling Electrical power for liquefaction of 1 g/s helium: 6200 W el Carnot COP @ 4.5 K: 66 W el /W th 1 g/s liquid helium is equivalent to 100 W th @ 4.5 K * * U. Wagner s presentation: http://cdsweb.cern.ch/record/808372/files/p295.pdf ESS Cryomodule Status Meeting, 9/1/2013

18. Thermodynamic efficiency of gas cooling Comparison with other ways of cooling (heat intercepts, self-sustained cooling) 990 @ 2 K, 220 @ 9 or 4.5 K, 16 @ 80 K CaseQ @ 2K [W] P [W el ] Q @ 9K [W] P [W el ] Q @ 80K [W] P [W el ] vapours rate [g/s] Q equiv. @ 4.5K [W] (1g/s=100W) P [W el ] Total power [Wel] A) No intercept 12.612,375 -- -- - B) 1 optimised intercept @ 80K 2.22,178 -- 44.6714 -- - 2,892 C) 2 optimised intercepts @ 80K & 9K 0.181783.270430.6490 -- - 1,372 D) 4.5K self-sustained vapour cooling 0.0330- - - -0.0202440470 E) He vapour cooling (4.5K-300K) 0.1099- -- -0.044880979 F) He vapour cooling (4.5K-300K), RF power on 0.50495- - - -0.0448801,375 G) No He vapour cooling, RF power on 2221,780 -- - -000 ESS Cryomodule Status Meeting, 9/1/2013

19. (B) 1 Heat intercept Q @ 2K 300K x1x1 L Q @ 80K

20. (C) 2 Heat intercepts Q @ 2K 300K Q @ 8K Q @ 80K L x1x1 x2x2

21. (D) He vapour cooling 300K 4.5K Q in g/s L attenuation factor

22. Geometry

24. Mesh CF WF