1. Case study 5 RF cavities: superconductivity and thin films, local defect… 1 Thin Film Niobium: penetration depth Frequency shift during cooldown. Linear representation is given in function of Y, where Y = (1-(T/T C ) 4 ) -1/2 Q1 : What can explain the variation of frequency observed ? It traduces the evolution of R S with temperature : which directly arises from the variation of the penetration depth with T. In the two-fluid model  is expected to follow the relationship:

2. 2 Thin Film Niobium: local defect * Case study 5 Q2~ 3x10 10 Q1~ 1.5x10 10 Q3 : explain qualitatively the experimental observations. Because locally the film is in bad thermal contact with copper, it is not enough cooled and its surface resistance increases

3. 3 Bulk Niobium: local defects Q6 : regarding the previous questions, and the field distribution in these cavities, how can you explain the multiple observed Q-switches ? Because of the size of the cavity there is a large variation of the magnetic field on the surface from the top to the bottom of the cavity. If the surface is not well polished and present a distribution of poor superconducting small areas, the defect situated close to the high magnetic field area will transit first, then the location of the “hot spot” will progressively get closer to the high electrical field part. Note : first curve (red dots) was better until the first Q-Switch @ ~ 4MV/m. We do not know why. It can be due to a slight difference in the He temp., or the ignition of a field emitter (if X-rays a measured simultaneously) After 40 µm etching After 150 µm etching Case study 5 MP Barrier Typical behavior of quench : when cavity becomes norm. cond. The frequency changes and the power cannot go in any more => the cavity cools down and becomes SC again, powers go in, etc… The cavity is still tuned, i.e. SC

4. 4 Bulk Niobium: steps @ GB 2D RF model Q7. What conclusion can we draw about: The influence of the lateral dimensions of the defect? Its height ? A step induces an increase of the local field. When H increases (shape factor ↑) one reaches a “saturation “. The lateral dimension plays a minor role The influence of the curvature radius? The small the angle of curvature the highest the field enhancement factor The behavior at high field? In the saturation region, at high field, the field enhancement factor is still increases, but not so rapidly. It depends only on the shape factor H/R What happens if the defect is a hole instead of bump (F<<L) ? In this model, if the “hole” becomes too narrow, the field cannot enter it => no field enhancement factor Case study 5 H

5. 5 Q8.- do these calculation change the conclusion from the precedent simplified model ? The curvature radius indeed plays a major role. The lateral dimension plays a minor role in the field enhancement factor, but impacts the dissipation -what prediction can be done about the thermal breakdown of the cavity? The breakdown is solely due to the dramatic heating of the defect that suddenly overcome the overall dissipation -why is this model underestimating the field enhancement factor and overestimating the thermal dissipations? Because it is a 2D model : the defect is treated like if it was an infinite wall. In case of finite dimension the shape factor gets higher, inversely the dissipation would be reduced if coming only from a finite obstacle. Steps @ GB w. realistic dimension RF only Case study 5

6. 6 Steps @ GB w. realistic dimension RF + thermal Case study 5 Q9 Comment these figures. If the dissipation is correctly evacuated to the helium bath, it is possible to maintain SC state up to a certain field, but a slight increase of field (a few 0.1 mT) induces thermal runaway)and transition of the whole superconducting material The amount of power that can be transferred to the bath is limited by interface transfer. A higher field can be reached with a good thermal transfer What will happen if we introduce thermal variation of  and/or R S.  tends to increase with T, but this effect will be compensated by the increase of R S with T What happen if we increase the purity of Nb ?, why ? Increase of the purity of Nb allows to reduce the interstitial content which acts as scattering centers for (thermal) conduction electrons. It increases the thermal conductivity and allows to better transfer the dissipated power, hence to get higher field for an “equivalent” defect. Comment : the quench happens on the defect edge both because of morphologic field enhancement and temperature enhancement : thermomagnetic quench at H<H C and T< T C