1. Benjamin Lepers IPHC Strasbourg, WP2 Euronu 12/05/2010
Thermal study
Benjamin Lepers
IPHC Strasbourg, WP2 Euronu
12/05/2010

2. Outline
Transient model
Resistivie loss
Next steps.

3. Transient model
heat source term is calculated with Fluka for 4MW power beam and 4.5GeV proton kinetic energy
P is the power at some location per second; the power for the target during 1 pulse is:
The spatial heat source distribution is multiplied by a train of square pulse of duration 4micro s and periodicity 20 ms.

4. Transient heat equation:
Boundary conditions: insulation and convection cooling on the surface of the target cylinder.
Tf=293K, h=5000W/(m K)

6. Resistive loss
Assume that most of the current is flowing between the external radius and the skin depth.
Calculate the AC resistance
For aluminium at f=5000Hz

7. Resistive loss; model
Use ampere law and vector potential formulation:

8. Boundary conditions:
z=0, 0.78: rot(A)=0, tangential components of the magnetic potential are set to 0 (magnetic insulation)
R=re, surface current: Js=I0/(2Pi r)

10. Results Radius(mm) 18 15 11 Resistance[Ohm/m]*10^-4 2.96 3.58 4.97
Power_cal[kW/m]20°C
Power density[kW/cm3]
61.9
0.49
74.9
0.72
103.9
1.37
Power_model[kW/m]20°C
61.6
74.6
103.6
Power_cal[kW/m]200°C
80.9
0.64
98.2
0.94
137.2
1.82
Power_model[kW/m]200°C
81.9
99.4
138.9
Aluminium

11. Results Radius(mm) 18 15 11 Power_cal[kW/m]20C 57.3 69.3 96.3
Power_model[kW/m]20°C
57.5
69.5
96.4
Power_cal[kW/m]200°C
91.8
111.6
156.7
Power_model[kW/m]200°C
11.6
156.4
Beryllium

13. Cooling, realistic h values, cooling design.
Next steps
Include resistive loss and heat source term from the beam in one model.
Cooling, realistic h values, cooling design.