Proof-of-principle demonstration of Nb₃Sn superconducting radiofrequency cavities for high Q applications Open Access

Superconducting radiofrequency (SRF) cavities are electromagnetic resonators used to generate large electric fields for accelerating charged particle beams in applications such as light sources,^1,2 neutron sources,^3,4 and colliders.^5,6 The small surface resistance R_s of the superconducting material on the surface of the cavities minimizes the power dissipated in the walls by surface currents, allowing the cavities to operate with up to 100% duty factor even at high fields. However, the superconducting materials require operation at cryogenic temperatures, where thermodynamic efficiency is small. As a result, high duty factor particle accelerators with many cavities require a large cryogenic plant, with cost on the order of 100 million USD and power requirements on the order of a megawatt (see, for example, the planned Linac Coherent Light Source (LCLS) II¹ or the Cornell ERL²).

A number of alternative superconductors are under investigation to reduce cryogenic costs,^7,8 but, to date, performances have not been strong enough to justify the replacement of niobium, the standard material used in state-of-the-art SRF accelerators. One very promising material is Nb₃Sn, which has critical temperature T_c = 18 K, approximately twice that of niobium, allowing Nb₃Sn cavities to have exceptionally high quality factor Q₀—which indicates extremely small dissipation—at a given temperature. It also meets many other important criteria for SRF cavities, including: ability to fabricate the material with a high degree of uniformity over a large, complex geometry; ability to clean the superconductor using known methods; and reasonably large coherence length ξ.⁹ 

Pioneering research into Nb₃Sn for SRF applications began in the 1970s and involved many laboratories.^10–16 An important program to highlight is that of University of Wuppertal, in which niobium cavities with shape and frequency appropriate for particle accelerator applications were coated with a thin layer of Nb₃Sn.¹⁷ These cavities achieved high quality factor Q₀ at small accelerating electric fields E_acc, but strong Q-slope (decrease in Q₀ with field) was observed, preventing the cavities from being useful in applications. This degradation was consistently observed to occur when the peak surface magnetic field H_pk reached the lower critical field H_c1 of the Nb3Sn coating.^18,19 This led to a hypothesis that Nb₃Sn cavities would be limited by strong losses caused by the penetration of flux beginning at H_c1.^18,20

A Nb₃Sn SRF program began at Cornell University in 2009, building on the work of previous researchers. After demonstrating the ability to reliably fabricate high quality Nb₃Sn coatings on small samples²¹ via the vapor diffusion process,²² single cell 1.3 GHz niobium cavities were coated and tested. Early results²³ showed high Q₀ at accelerating fields significantly higher than those achieved by Wuppertal and for peak surface magnetic fields significantly higher than H_c1. This showed that H_c1 is not a fundamental limit for SRF cavities, but the maximum fields achieved were still somewhat smaller than are generally used in applications, and it had not been established if this result was reproducible. In this paper, results are presented, demonstrating (1) reproducible high Q₀ on the order of 10¹⁰ at 4.2 K, (2) reproducible sustaining of this high Q₀ to useful gradients ∼14 MV/m, and (3) reproducible H_pk significantly higher than H_c1 with no strong degradation, showing that it is not a limit. The impact of these results on future high duty factor accelerators is discussed.

A single cell 1.3 GHz ERL-shape²⁴ cavity, which shall be called cavity 1, was coated with Nb₃Sn at Cornell. After RF performance evaluation, it received a buffered chemical polish (BCP) to remove several micrometers of material from the surface, exposing the niobium of the substrate. The cavity was then coated and evaluated again. This process was repeated twice more for a total of four coatings. Details of the coating procedure and apparatus are discussed elsewhere.²⁵ A second single cell 1.3 GHz cavity with TeSLA shape,²⁶ cavity 2, was prepared with electropolish (EP), coated, and evaluated. The performance curves of these coatings are presented in Fig. 1.

In each case, Q₀ at 4.2 K on the order of 10¹⁰ was maintained to E_acc above 10 MV/m, where the cavities were limited by quench. The average quench field was 14 MV/m, and the average Q₀ at quench was 8 × 10⁹. In one coating, a maximum field of 17 MV/m was achieved. Moderate Q-slope was observed in each case, but it is far less strong than that observed by Wuppertal researchers.

The BCS material parameters from each coating were extracted from measurements of Q₀ and resonant frequency as a function of temperature T, as described in Ref. 27. The results are shown in Table I, along with critical fields calculated from the material parameters. In each case, H_pk at the quench field is significantly higher than H_c1, further demonstrating that it is not a fundamental limit for these cavities.²⁸ 

Next, we consider implications of these results for high duty factor SRF accelerators that would benefit from reduced power consumption. If the surface resistance is approximately constant over the cavity surface, Q₀ is related to R_s according to Q₀ = G/R_s, where G is a constant that depends only on the geometry of the cavity (G is 272 Ω for cavity 1 and 278 Ω for cavity 2). R_s is often separated into two components: the temperature-dependent BCS resistance R_BCS, which can be calculated from BCS theory given material parameters, frequency, and temperature,³² and the temperature-independent residual resistance R_res, which is determined by factors such as impurity content and trapped flux.³³ At a given field, Q₀ increases exponentially due to the BCS component as the temperature is decreased below T_c, then Q₀ levels off as R_BCS becomes smaller than the constant R_res. R_BCS was calculated for the material parameters of the first coating of cavity 1 in Table I, and the corresponding Q₀ is plotted in Fig. 2, along with Q₀ vs T data measured during the experiment. At low T, R_res dominates, and at high T, the penetration depth is large, allowing magnetic field to leak into the normal conducting niobium substrate, resulting in lower Q₀ than predicted for a fully Nb₃Sn layer.

The current state-of-the-art preparation to achieve the highest Q₀ in niobium SRF cavities is nitrogen doping.³⁴ Also plotted in Fig. 2 is Q₀(T) predicted by BCS theory for nitrogen-doped niobium, based on material parameters from a cavity in Ref. 35 at 16 MV/m, the planned operating gradient for cavities in both LCLS-II and the Cornell ERL.

To achieve high Q₀ in Nb cavities, it is necessary to cool the liquid helium bath to around 2 K. Nb₃Sn offers high Q₀ at considerably higher temperatures, even close to 4.2 K, the boiling point of liquid helium at atmospheric pressure. Operation near atmosphere would simplify cryogenic plants, reducing infrastructure costs. In addition, operation at higher temperatures can significantly reduce AC power requirements. The efficiency of a cryogenic plant is determined by the inverse coefficient of performance (COP⁻¹), which is strongly temperature dependent.^36,38 For example, for a bath temperature of 2 K, approximately 830 W of input power is needed to remove 1 W of heat. At 4.2 K, COP⁻¹ is on the order 240 W/W, a factor of 3.5 smaller than the 2 K value.

The AC power required to cool a cavity is given by

where R_a is the shunt impedance, R_a/Q₀ is a constant that depends only on the geometry of the cavity, and L is the active length of the cavity. It is illustrative to present cavity performance in terms of $PAC/Eacc2$ instead of Q₀, as this allows direct comparison of real cryogenic requirements even between different operating temperatures. By additionally presenting performance in terms of $PAC/Eacc2$ per cell, cavities with similar shapes but different numbers of cells can be compared.

In Fig. 3, $PAC/Eacc2$ per cell vs E_acc is shown for the fourth coating of cavity 1. In addition, the E_acc at which H_pk = H_c1 extracted in Table I is shown in the shaded region, the width of which takes into account uncertainty. No strong increase in the required P_AC is observed at this field, illustrating that H_c1 is not a limiting field for this cavity. Moderate Q-slope is observed, which measurements at other temperatures suggest is due to an increase in R_res. However, even with this Q-slope, the $PAC/Eacc2$ per cell of the Nb₃Sn cavity at 16 MV/m is still smaller than that of the LCLS-II and the Cornell ERL target values, which are also shown in the figure. The Nb₃Sn cavity exceeds the specifications for both accelerating gradient and cryogenic efficiency for these planned high duty factor projects.

Fig. 4 presents $PAC/Eacc2$ per cell as a function of temperature. Both Nb₃Sn and Nb curves are shown, calculated from BCS theory. For the Nb cavity, calculations were performed using the BCS material parameters for nitrogen-doped niobium that were used in Fig. 2, together with the specified R_res = 5 nΩ for LCLS II. For the Nb₃Sn cavity, material parameters from the fourth coating of cavity 1 were used in the calculation, and three different values of R_res are shown: 9 nΩ corresponds to E_acc values ∼1 MV/m, 29 nΩ corresponds to E_acc values ∼16 MV/m, and 3 nΩ corresponds to an extremely small R_res value measured in a Wuppertal cavity at low fields.¹⁹ 

The figure shows the potentially large reduction in P_AC for Nb₃Sn compared to Nb at optimal temperatures. With the R_res of cavity 1 at 16 MV/m, the power requirements at 4.2 K are approximately equal to that of Nb at 2 K, the planned operation temperature of LCLS-II. With increased development, it is expected that R_res values can be improved, as they have been with Nb cavities. If the low field R_res value of 9 nΩ can be maintained out to 16 MV/m, the power consumption would be decreased to approximately one third of the LCLS-II specification. If R_res can be further decreased to 3 nΩ, power consumption would be smaller than one seventh of the specification.

In this paper, results were presented from five Nb₃Sn coatings of single cell 1.3 GHz SRF cavities. High Q₀ at 4.2 K was maintained reproducibly out to medium fields, with an average quench field of 14 MV/m and an average Q₀ at quench of 8 × 10⁹. For the coating with the best performance, the quench field was 17 MV/m, higher than the operating gradient specifications of several near future high duty factor SRF accelerators (LCLS-II¹ and PIP-II³⁷), ∼16 MV/m. The required AC power for this Nb₃Sn cavity was compared to that of nitrogen-doped niobium cavities. The higher T_c of Nb₃Sn allows it to have high Q₀ even at high temperatures where thermodynamic efficiency is higher. As a result, the cavity was able to meet the power requirements of planned high duty factor facilities. Continued development is expected to reduce R_res and in turn the power consumption of Nb₃Sn cavities, making them a very promising technology for future high Q₀ SRF accelerators. Future research will also focus on reliably achieving this performance level in multicell cavities as well as increasing quench fields for higher gradient applications.

This work was supported by NSF Career Award No. PHY-0841213, NSF Award No. PHY-1416318, DOE Award No. ER41628, and the Alfred P. Sloan Foundation.