1. LHC Beam screen: impact of the weld on the wakes
Preliminary analysis
E. Metral, G. Rumolo, B. Salvant, C. Zannini

2. Overview Model studied Comparing structure within and without weld
Numerical noise

3. Model studied LHC design as it is built and installed
In this step we are only interested to understand the effect of the weld .
weld

4. Model studied
a=46.4 mm
b=36.8 mm
w=2 mm
L=1m w b a L

5. Overview Model studied Comparing structure within and without weld
Numerical noise

6. Comparing within and without weld
For a displacement in x of 5 mm the horizontal dipolar wake with weld seems to be five time larger than the wake without weld

7. Horizontal dipolar wake with weld versus displacement
The displacement is considered negative if it is in the direction opposite the weld
The horizontal dipolar wake with weld for a displacement in x of -5 mm seems to be twenty-five time larger than the wake with weld for a displacement in x of 5 mm

8. For a displacement in x of -5 mm the horizontal dipolar wake with weld seems to be five time smaller than the wake without weld

9. Changing the transverse dimension of the weld w
Ssteel corresponds to w/2
Increasing the transverse dimension of the weld the horizontal dipolar wake increase almost linearly.

10. Overview Model studied Comparing structure within and without weld
Numerical noise

11. Numerical noise
The high value of conductivity that we need to simulate determines a very small signal and then the simulation results (longitudinal wake) are very noisy. The transverse wakes are obtained integrating this wake using the Panofsky-Wenzel theorem. In the frame of these issues can we consider reliable the results shown previously?
To verify the correctness of the results we can simulate the worst case for the noise: the structure without weld. We can simulate the structure with two different conductivity high and low conductivity and then rescaling the results at the same conductivity and compare them. The results obtained with low conductivity are more reliable because the numerical noise is insignificant. To obtain a good comparison it means that even though the signal is very noisy the code is able to make a good integration and we can be more confident of the results obtained.
Sigmacopper is the conductivity of the cold Copper σ=1.82e9 S/m
Decreasing the conductivity the results increase as the square root of the conductivity