Normal and superconducting radio-frequency cavities for high energy particle accelerators

As a starting point we begin with an introduction to the general parallel-resonant circuit as a model for the RF resonant cavity with its surface resistance, R_s, and voltage-amplification parameter, Q. Early RF cavities were of polished high purity Cu. Factors controlling the R_s of a Cu cavity are: temperature, T, operating frequency, f, and electrical resistivity, ρ, parameters associated with which are electron mean-free-path (l) and skin depth (δ). Surface resistance decreases with decreasing T and ρ in the normal skin-effect regime until a limit is reached at δ = l. Beyond this point the cavity wall enters the “anomalous-skin-effect regime” within which R_s is temperature independent and of order mΩ. To further reduce R_s and increase Q the cavity needs to be lined with or constructed from superconducting material. Currently the superconductor of choice is Nb whose BCS-based R_s (i.e. R_s^BCS) is some 3 to 4 orders of magnitude smaller than that of Cu. The R_s^BCS of the Nb cavity decreases rapidly with temperature, hence the advantage of cooling by superfluid helium. In general R_s^BCS also decreases rapidly with increase in T_c, the superconductor´s transition temperature. Thus replacing Nb with an ideal uniform coating of Nb₃Sn, for example, would in principal reduce R_s^BCS by 10⁵. Many factors can perturb the R_s of superconducting cavities and act to reduce the Q-factor, among them are: (i) Trapped magnetic flux from some external magnetic field which should expose the surface to no more than a few tens of μT, (ii) enhanced surface RF magnetic field (associated with surface defects) which limits the attainable accelerating field, (iii) effects associated with cavity shape and surface imperfections such as field emission - nd thermal breakdown. Finally the operating parameters of the LHC and the ILC are presented in terms of the accelerating properties of their SRF cavities.