First thermal calculations on the target made of aluminium EUROnu design First thermal calculations on the target made of aluminium 15/04/2010 G.Gaudiot

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

maximal temperature 150 - 200°C 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 150 - 200°C does a water cooling allow to maintain this value for a power of 200 kW ? → very simple model in a permanent working.

First model of a target in aluminium axi symetric R mm hc = 5000 W/m².K t∞ 18°C (water spray) 30 10 5 0 200 400 500 mm 3,5 W/mm3 1,5 W/mm3 total : 220 kW Hypothesis : as we want a maximal temperature of 200 °C , the exchange by rayonnement is not considered

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

diminution of the power density With ridges on external radius 5 exchange area + 60% 8 max. temperature : 1476 °C diminution of the power density 1,7 W/mm3 in a cylinder Ø 20 long. 400 (214 kW) → 1171 °C 0,44 W/mm3 in a cylinder Ø 40 long. 400 (221 kW) → 853 °C → impossibility to cool the target with water sprays only

Just a mechanical idea water flowing inside pipes : we can reach coefficients of heat-transfer hc > 20000 W/m².K water output square target !? water input long drillings ?

2x Ø6 hc = 20000 W/m².K t∞ 18°C Ø8 1647 °C 1319 °C maximal temperatures P = 3,5 W/mm3 in Ø10 et 1,5 W/mm3 between Ø10 and Ø20

maximal wetted area water sprays flowing water target Ø40 mm internal conductor of the horn

Axi symetrical model target + internal horn wall 5000 W/m².K 20000 W/m².K maxi 1082 °C Temperature distribution for 200 kW (3,5 et 1,5 W/mm3)

« manual » calculation on a transversal section Volume power Pv (per unit of length Pvl) λ Tmax – T1 = Pvl / 4π.λ T1 – Tp = Pvl . ln(Re/R1) / 2 π.λ Tp - T∞ = Pvl / 2π.Re.hc T∞ hc Tmax T1 Tp R1 Re Pv = 2.105 W l = 0,4 m Pvl = 5.105 W/m Re = 0,02 m R1 = 0,005 m λ = 170 W/m.K (alloy of aluminium) hc = 10000 W/m².K Tmax – T1 = 234,1 °C T1 – Tp = 648,9 °C Tp - T∞ = 397,9 °C Tmax - T∞ = 1280,9 °C material (λ) material (λ) Re , hc ←┐ Re/R1 ←┘ parameters

we don’t put the cooling closer to the area of maximal power density 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

Possible improvements Thermal transfer by phase change : hc > 105 W/m².K Tp - T∞ = 39,8 °C pour hc = 105 W/m².K Diminution of the target diameter , where the density is maximal → to reduce ln(Re/R1) and T1 Water sprays in front ? → to cool the impact of the beam no doubt , not acceptable Other materials for a system target + horn Beryllium melting point : 1285 °C λ = 210 W/m.K AlBeMet (62 % Be 38% Al) melt. point : 1082 °C «   solidus 645 °C

Beryllium (= glucinium) high mechanical strength → used in aeronautics 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.

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

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