Ambient magnetic field, if trapped in the penetration depth, leads to the residual resistance and therefore sets the limit for the achievable quality factors in superconducting niobium resonators for particle accelerators. Here we show that a complet
e expulsion of the magnetic flux can be performed and leads to: 1) record quality factors $Q > 2times10^{11}$ up to accelerating gradient of 22 MV/m; 2) $Qsim3times10^{10}$ at 2 K and 16 MV/m in up to 190 mG magnetic fields. This is achieved by large thermal gradients at the normal/superconducting phase front during the cooldown. Our findings open up a way to ultra-high quality factors at low temperatures and show an alternative to the sophisticated magnetic shielding implemented in modern superconducting accelerators.
We report a strong effect of the cooling dynamics through $T_mathrm{c}$ on the amount of trapped external magnetic flux in superconducting niobium cavities. The effect is similar for fine grain and single crystal niobium and all surface treatments in
cluding electropolishing with and without 120$^circ$C baking and nitrogen doping. Direct magnetic field measurements on the cavity walls show that the effect stems from changes in the flux trapping efficiency: slow cooling leads to almost complete flux trapping and higher residual resistance while fast cooling leads to the much more efficient flux expulsion and lower residual resistance.
