1. Temperature Distribution Study of Composite Germanium Detector
M.Wolf, J.Kojouharova, T.Engert, J.Gerl, J.Groß, H.-J.Wollersheim
1. Motivation
2. Physics
Electromechanical cooler with single Ge detector
X-Cooler II cooling engine
(ORTEC)
A composite Germanium (Ge) detector containing three encapsulated Ge crystals
The temperature distribution is governed by the following equation
The boundary condition at the cooling contact of the detector is
The radiative heat flux between the cold thermal shield surrounding the Ge array and the room temperature cryostat is the dominating process and is given by
Germanium detectors are operated at low temperatures between 77 K and 120 K
Ta – room temperature
λ - thermal conductivity
ε - surface emissivity of thermal shield
Tcf – cold contact temperature
σ - Stefan-Boltzmann constant
ρ - mass density
c - specific heat capacity
Can X-COOLER II cool down a composite Ge detector?
3. Simulation
Influence of the surface emissivity ε of the thermal shield on the heat loss and the maximal temperature of composite detector
Surface temperature distribution of a single Ge-detector
Surface temperature distribution of composite Ge-detector
0.02
0.82
78.14
0.04
1.64
79.27
0.06
2.45
80.41
0.08
3.27
81.54
0.10
4.09
82.68
0.12
4.91
83.81
0.14
5.72
84.94
The calculated heat loss of 2.5 W is an estimate for the cooling power of the X-COOLER II engine.
The heat loss is
- 5.7 W for ε=0.14 (blank aluminum surface)
- 2.5 W for ε=0.06 (polished aluminum surface)
4. Conclusion
The present study with the COMSOL MULTIPHYSICS Model „Surface to Ambient” shows that a suitable thermal shield may substantially reduce the thermal energy transfer thus the present cooling engine should be well suited for a composite Ge detector.