The measured niobium surface resistance in a nine-cell superconducting cavity plotted as a function of TC / T. Here T is the temperature of the helium bath and TC = 9.2 K the critical temperature of niobium. The residual resistance of 3 nΩ corresponds to a quality factor Q0 = 1011.
of a cell is chosen such that the field direction has inverted when the relativistic bunch has moved to the next cell. This is fulfilled for a cell length equal to half the radio-frequency wavelength,
The quality factor of a cavity is defined as the ratio of the resonance frequency to the width of the resonance curve:
Q0 = f0 / Δf. It is inversely proportional to the surface resistance and amounts to Q0 > 1010 for niobium cavities at 2K. In principle the quality factor should stay constant when the field in the cavity is raised from zero to an upper limit which is reached when the radio-frequency magnetic field approaches the critical magnetic field of the superconductor. For niobium at 2K the critical field is Bc ≈ 200 mT, corresponding to a maximum accelerating field Eacc ≈ 45 MV/m. In practice, however, the excitation curve Q0 = Q0(Eacc) usually ends at a lower field due to “dirt effects” such as contamination of the inner cavity surface or field emission of electrons. By applying the cleanroom techniques of the semiconductor industry during the assembly and preparation of the cavities one can almost achieve the physical limit of the superconducting material.
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