Q1: When the cavity is cooled down the conductivity of the superconducting layer increases and the penetration depth decreases making the cavity electromagnetically smaller . This makes the frequency higher.

Q2:

=

In the bulk Nb the penetration depth is 39nm at 1,3GHz.

Purity, mean free path length l, coherence length : => 0.5 which was possibly done on purpose to minimize the Rs

presentation prepared by

Stephane Gabouien

Natalia Glowa

Miguel Lozano

Rolf Wegner

Q3: Q= Local defect dissipates power and lowers the Q due to the local heating when field is increased.

Q4/Q5:The drop of Q0 is due to the defect. As we are in superconducting state, . At 1.2MV/m, quench occurs due to the hot spot and . In this case PS=PN. =2mW. Then

The size of the defect for the higher field (at 7,3cm from the equator) is:

Then at the equator, by making a “regle de 3” the size of defect at the center is

Q6 :1- After 40 µm etching there still are some defects remaining in the cavity that are affected by the RF creating multipacting and local micro quenches. As shown on the second black plot, at the maximum E field level the maximum cooling capacity of the cryosytem is reached. The entire cavity quenches shortly and the RF power is reflected. So the cavity cools down and becomes superconducting again.

2- After 150 µm etching all the impurities have been removed and the plot shows a very nice and typical Q drop when the E field increases. We also see some Xrays increasing with the E field as expected .

𝐻𝑚𝑎𝑥

𝐻 0=1+0.59 𝑥(𝐻𝑅 )

0.5x

Q7 1-According to the formula the effect of the lateral dimension of the defect is very small . This is confirmed by the different plots of the first picture . 2-According equation added to the transparency the effect of the defect’s height is more important than the lateral dimension. See red equations. The higher the height, the higher the Hmax 3-Radius is the most important factor . The smaller (sharper shape) it is the bigger the Hmax. 4- For the high field (saturation regime), F and L don’t play any role. Only the ratio H/R play a role. 5-If F<<L the equation shows that it will be transparent for the magnetic field. The latter does not penetrate into the Hole, Hmax/H0 ~ 1

Q8 1- In this model, only one bump is taking into account. Then F can be considered infinite. The model gives a good estimation

2-The thermal breakdown of the cavity is more violent for bigger defect radius. For all cases the power dissipated in the grain exceeds the power of the cavity above 95% of Hc 3-This model is a 2D model and is not taking into account the 3D surface of the grain in terms of heat dissipation and field enhancement.

R H Hmax/H01 11 2.9568096 11 1.798864

20 11 1.43755650 11 1.276735

Q9:

In the left cases the cavity stays superconductive and reaches an stable thermic situation .On the other hand in the examples on the right side we see a fast quench trigger by the hot spot when the field increases only 0.1 mT .

From the bottom to the top we see increasing thermal conductivities that increase the level of power that the cavity can take before quenching . Due to this we also see a bigger temperature spread in different points of the cavity.

K increases with the temperature. So heat can be better removed lowering the temperature spread in the cavity at a constant power. In this situation more power can be applied to the cavity before quench occurs.

If we increase the purity of the Nb the thermal conductivity and the electrical resistivity increase . This two effects are contradictory and have to be investigated to see which one dominants for the material purity and working point.