Frequency dependence of trapped flux sensitivity in SRF cavities

Abstract

In this letter, we present the frequency dependence of the vortex surface resistance of bulk niobium accelerating cavities as a function of different state-of-the-art surface treatments. Higher flux surface resistance per amount of trapped magnetic field-sensitivity-is observed for higher frequencies, in agreement with our theoretical model. Higher sensitivity is observed for N-doped cavities, which possess an intermediate value of electron mean-free-path, compared to 120 • C and EP/BCP cavities. Experimental results from our study showed that the sensitivity has a non-monotonic trend as a function of the mean-free-path, including at frequencies other than 1.3 GHz, and that the vortex response to the rf field can be tuned from the pinning regime to flux-flow regime by manipulating the frequency and/or the mean-free-path of the resonator, as reported in our previous studies. The frequency dependence of the trapped flux sensitivity to the amplitude of the accelerating gradient is also highlighted.

Simple model for the rf field amplitude dependence of the trapped flux sensitivity in superconducting rf cavities

“…Recent investigations have also focused on the frequency dependence of the effect of trapped magnetic flux [7] confirming and integrating older results [3]. In this paper we will present a simple model based on a nonlinear extension of the classical Gittelman and Rosemblum (GR) model [14], originally introduced to describe dissipations in thin films due to the motion of a rigid flux-lattice under the effect of an RF current as in a forced linear oscillator.…”

“…In different words, these models can only describe the term 0 fl R but do not provide a description of 1 fl R . In the following we will extend the basic GR model, introducing an ad hoc non-quadratic pinning potential (nonlinear pinning force) in order to reproduce the linear rf B field amplitude dependence experimentally observed by many authors [3], [5], [6], [7]. We should mention that a recent different approach also attempts at explaining the dependence on rf B , by making use of a mean-field collective pinning potential [24].…”

“…where 0 rf B is the RF field amplitude, 0 B is the trapped external field, 0 fl R is the zero RF field trapped flux sensitivity and 1 fl R is the RF slope of the sensitivity. The first term is typically dominating in the case of bulk niobium cavities, although the second term can become of a comparable order of magnitude at high RF fields, in particular for high-frequency cavities [6], [7]. Interestingly, it was found that cavities made with the sputter thin film technology of niobium on a copper substrate (Nb/Cu) were much less sensitive to the ambient magnetic field, usually because of a much smaller 0 fl R compared to bulk Nb cavities [5], [6].…”

Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity

“…Whereas most of the data shown in Figs. 15-17 are for 1.3 GHz cavities, there are also three data points each for 650 MHz, 2.6 GHz and 3.9 GHz elliptical cavities [17]. It should be pointed out that in Refs.…”

“…We also thank Dr. Mattia Checchin for providing the data in Ref. 17 and Dr. Matthias Liepe for providing us with the correction factor for the data in Ref. 15.…”