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

2. 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

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

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

6. diminution of the power density
With ridges on external radius 5
exchange area % 8
max. temperature : °C
diminution of the power density
1,7 W/mm3 in a cylinder Ø 20 long (214 kW) → °C
0,44 W/mm3 in a cylinder Ø 40 long (221 kW) → °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
square target !?
water input
long drillings ?

8. 2x Ø6
hc = W/m².K t∞ 18°C Ø8
1647 °C °C maximal temperatures
P = 3,5 W/mm3 in Ø10 et 1,5 W/mm3 between Ø10 and Ø20

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

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

11. « 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
R Re
Pv = W l = 0,4 m Pvl = W/m
Re = 0,02 m R1 = 0,005 m λ = 170 W/m.K (alloy of aluminium) hc = 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/R ←┘ parameters

12. 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

13. 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

14. 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.

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