  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 complete expulsion of the magnetic flux can be performed and
leads to: 1) record quality factors $Q > 2\times10^{11}$ up to accelerating
gradient of 22 MV/m; 2) $Q\sim3\times10^{10}$ 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.
