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

Overview Model studied Comparing structure within and without weld Numerical noise

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

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

Overview Model studied Comparing structure within and without weld Numerical noise

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

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

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

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.

Overview Model studied Comparing structure within and without weld Numerical noise

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