material

When the beam hits on the collimator, the temperature grows up on the surface. The energy deposit on the surface (J/g) can be expressed by,  

$$W_e = N_e \cdot { dE \over{dX} }(ev \cdot {cm^2 \over g }) \cdot {1. \over a} \cdot 1.6 \times 10^{-19} ({J \over eV} )$$ (1)

where N_e particles hit on the surface area of a (cm²). The thermal energy due to a temperature rise ($\delta T$) is given by,  

$$W_T = 3 \cdot {6.02 \times 10^{23} \over A} \cdot 1.38 \times 10^{-23} ({J \over K}) \cdot \delta T,$$ (2)

where, A is an atomic mass number. The temperature rise due to the energy deposit can be obtained by W_T = W_e. Apparently, a material with smaller atomic number is better for the collimator if its melting temperature is high enough. The relevant properties of several atoms are listed in table 1. Carbon seems to be the best on this point. Is it true?

 

$$\rho$$ material A X₀ T_melt T_boil T_stress

$$^\circ C ^\circ C ^\circ C$$ g / cm³ cm

C 12 2.25 18.8 3700 4800 < 2500

Ti 47.9 4.51 3.56 1660 3277 < 1000

W 183.8 19.24 0.35 3410 5900 ?

Cu 63.5 8.93 1.43 1080 3000 < 180

Fe 55.8 7.87 1.76 1535 2750 ?