1 EUROnu design System target + horn First thermal calculations on the target made of aluminium G. Gaudiot 02/06/2010 Strasbourg

2 Introduction The thermal inputs on the target and the horn : - beam on the walls of the horn - external conductor ~ 48 kW - internal conductor, cone ~ 15 kW - internal conductor, small pipe ~ 80 kW - Joule effect in the horn conductors significant value only in the small pipe (« waist ») ~ 10 kW (for 6 cm diameter) - deposited power in the target > 200 kW

3 study of the target which receives most of the heat Previous calculations with a target made of graphite, cooling by an important flux of helium gas temperature : about 1000°C Target in aluminium : maximal temperature °C does a water cooling allow to maintain this value for a power of 200 kW ? → very simple model in a permanent working.

4 First model of a target in aluminium axi symetric mm R mm 3,5 W/mm 3 1,5 W/mm 3 total : 220 kW hc = 5000 W/m².K t ∞ 18°C (water spray) Hypothesis : as we want a maximal temperature of 200 °C, the exchange by rayonnement is not considered

5 Temperature distribution in the target Maximal temperature 1726 °C !

6 With ridges on external radius 5 8 exchange area + 60% max. temperature : 1476 °C diminution of the power density 1,7 W/mm 3 in a cylinder Ø 20 long. 400 (214 kW) → 1171 °C 0,44 W/mm 3 in a cylinder Ø 40 long. 400 (221 kW) → 853 °C → impossibility to cool the target with water sprays only

7 Just a mechanical idea water flowing inside pipes : we can reach coefficients of heat-transfer hc > W/m².K water output water input square target !? long drillings ?

°C 1319 °C maximal temperatures hc = W/m².K t∞ 18°C Ø8 2x Ø6 P = 3,5 W/mm 3 in Ø10 et 1,5 W/mm 3 between Ø10 and Ø20

9 maximal wetted area flowing water target Ø 40 mm internal conductor of the horn water sprays

W/m².K W/m².K Axi symetrical model target + internal horn wall maxi 1082 °C Temperature distribution for 200 kW (3,5 et 1,5 W/mm 3 )

11 « manual » calculation on a transversal section T max T 1 T p R 1 R e Volume power Pv (per unit of length P vl ) λ T ∞ hc T max – T 1 = P vl / 4π.λ T 1 – T p = P vl. ln(R e /R 1 ) / 2 π.λ T p - T ∞ = P vl / 2π.R e.hc Pv = W l = 0,4 m P vl = W/m R e = 0,02 m R 1 = 0,005 m λ = 170 W/m.K (alloy of aluminium) hc = W/m².K T max – T 1 = 234,1 °C T 1 – T p = 648,9 °C T p - T ∞ = 397,9 °C T max - T ∞ = 1280,9 °C material (λ) material (λ) R e, hc ←┐ R e /R 1 ←┘ parameters

12 It is impossible to keep a low target temperature with water cooling if : we don’t reduce the power density (for exemple by using at the same time 4 systems target + horn) we don’t put the cooling closer to the area of maximal power density may be, we don’t use a better thermal conductor Consider the other material parameters (density, …) in order to reduce the total deposited power in the target

13 Possible improvements Thermal transfer by phase change : hc > 10 5 W/m².K Tp - T ∞ = 39,8 °C pour hc = 10 5 W/m².K Diminution of the target diameter, where the density is maximal → to reduce ln(R e /R 1 ) and T 1 Water sprays in front ? → to cool the impact of the beam is it acceptable for physics ? Other materials for a system target + horn (or for target only) Beryllium melting point : 1285 °Cλ = 210 W/m.K AlBeMet (62 % Be 38% Al) melt. point : 1082 °C« solidus 645 °C

14 Beryllium (= glucinium) light, density : 1,85 rigidity : + 50% / steel high mechanical strength → used in aeronautics but difficult welding : - welding and electron beam welding : high conductivity of Be and extensive grain growth result in brittle joint. acceptable, if mechanical strength is not very important - brazing in argon, the best joining technique dusts (machining) and vapours very toxic AlBeMet® (Brush Willman) low density too, high elastic modulus 193 GPa (almost the same as steel) and welding by the same technologies than aluminium.

15 Phase diagram of aluminium – beryllium system (Elliott, IITRI)

16 General concept for a steady state regime without considering the pulses Mechanical design Material properties and manufacturing technology → acceptable temperature Energy deposition in the target Energy deposition in the magnetic horn (waist) Definition of the water cooling Calculations : - temperature distribution - thermal strain - stresses

17 Next actions thin curtain of water under high pressure in front of the target → effectiveness ? design of a setup of sprinklers very close to the target → important coefficient of transfer (thermal study by Benjamin Lepers and help by an engineering school) answer to the question : is AlBeMet better than aluminium for the target (point of vue of technology, not only in theory) ? influence of pulses

18 3D Model from the drawings of the CERN horn prototype Drawing by S. Rangod (2001) Modelizing by Valeria Zeter (IPHC)

19 Aim to have a parameterized 3D model in order to make multiphysic calculations.

20 EUROnu - la corne prototype du CERN S.Rangod 15/05/2001

21 EUROnu - la corne vue d’ensemble sprinklers, not represented water inlets water outlet

22 EUROnu- la Corne outer electrical skin inner electrical skin waist jacket inner conductor connection flange

23 EUROnu - la corne Quelques détails screw shaped neck water inlets glass insulator disc water inlets

24 Plaque alimentation corne_Version LAL

25 Vue éclatée de la plaque d’alimentation

26 Electrical connections, strip-lines