Magnesium diboride coated bulk niobium: a new approach to higher acceleration gradient

Abstract

Bulk niobium Superconducting Radio-Frequency cavities are a leading accelerator technology. Their performance is limited by the cavity loss and maximum acceleration gradient, which are negatively affected by vortex penetration into the superconductor when the peak magnetic field at the cavity wall surface exceeds the vortex penetration field (H_vp). It has been proposed that coating the inner wall of an SRF cavity with superconducting thin films increases H_vp. In this work, we utilized Nb ellipsoid to simulate an inverse SRF cavity and investigate the effect of coating it with magnesium diboride layer on the vortex penetration field. A significant enhancement of H_vp was observed. At 2.8 K, H_vp increased from 2100 Oe for an uncoated Nb ellipsoid to 2700 Oe for a Nb ellipsoid coated with ~200 nm thick MgB₂ thin film. This finding creates a new route towards achieving higher acceleration gradient in SRF cavity accelerator beyond the theoretical limit of bulk Nb.

Introduction

Particle accelerators are our main window to explore particle physics and understand the early universe. Bulk niobium superconducting radio frequency (SRF) cavities are the leading accelerator technology, and in the last 2 decades, their performance has been improved to being very close to the theoretical limit. New materials and/or approaches are needed to further improve the performance and reduce the cost of SRF cavities^1,2. In this work, we studied the magnesium diboride (MgB₂) coated bulk niobium and showed the coated SRF cavities have the potential to reach 30% higher acceleration gradient than the state of the art Nb cavities.

The technology of SRF cavities is based on the Meissner effect, characterized by the expulsion of magnetic field from a bulk superconducting material. In type II superconductors, such as Nb, the Meissner state can only be sustained up to a certain magnetic field, above which flux will penetrate the material in the form of vortices. In the presence of an RF excitation these vortices will oscillate, producing dissipation that drastically reduces the quality factor (Q), thus rendering the cavity useless. The limiting factor is the maximum accelerating gradient (E_acc), which is related to the maximum magnetic field parallel to the cavity surface that can be sustained without vortex penetration (H_vp). In thermodynamic equilibrium, H_vp of a bulk superconductor in the absence of demagnetizing effects is equal to the lower critical field (H_c1). However, surface barriers may preclude the vortex entry, allowing the Meissner state be retained under metastable conditions up to a higher superheating field H_sh³. The best Nb cavities have E_acc 50 MV/m at temperature T~2 K (the operating temperature of the SRF cavities at f > 500 MHz), corresponding to H_vp,Nb~2000 Oe⁴, which is very close to the ideal limit set by the intrinsic material properties, H_sh,Nb(2 K) ≈ 2280 Oe⁵.

To increase H_vp, Gurevich proposed coating the inside of Nb cavities with multilayers of thin superconducting films separated by insulating layers². The idea is that the superconducting films will partially screen the cavity magnetic field, reducing it to a value lower than H_vp,Nb at the internal surface of the Nb wall. We will focus on the simplest case of a SRF cavity coated with a single layer of superconductor, because this S-I-S structure already exhibits all the relevant physics and detailed theoretical analyses of its shielding effect have recently been performed with various approaches^6,7,8,9.

The principle of operation of the S-I-S structure involves two concepts. First, when the thickness of the superconducting film (d_S) is comparable to or smaller than the penetration depth (λ), H_c1 for field parallel to the surface increases. This is because the internal field is nonzero everywhere within the thin film, thus the free energy cost of shielding the external field by a screening current is lowered and vortex penetration does not become favorable until a higher field. For instance, if H is applied on both sides of a film with d_S ≪ λ, H_c1 increases from the bulk values H_c1 ∝ Φ₀/λ² to H_c1 ∝ Φ₀/d_S² (here Φ₀ = 2.07 × 10⁻⁷ Gcm² is the flux quantum). The situation is somewhat different when the field is only applied on one side⁶, but also in this case H_c1 for a thin film is substantially enhanced, resulting in a higher H_vp for the film-coated Nb cavity¹⁰. The second concept is that the screening (reduction) of the field produced by the film is ΔH~d_SJ, where the superconducting current density (J) depends on the details of the geometry but cannot exceed the superconducting depairing current density (J_d) in the film, J_d~H_c/λ, where H_c is the thermodynamic critical field (H_c > H_c1 in type II superconductors). It is clear from the previous considerations that if d_S is too large there is no enough H_c1 enhancement and if it is too small H_vp is only increased by a small amount ΔH, so there must be some optimum d_S that produces the largest H_vp. T. Kubo^9,11 has shown that, when the simple estimate of an exponential decay of the magnetic field from the film surface is replaced by the simultaneous solution of the Maxwell and London equations in the complete S-I-S structure with the appropriate boundary conditions, H_vp depends on the properties of both the coating layer and bulk superconducting materials, on d_S, and on the thickness of the insulating layer (d_I). In particular, these studies show that the shielding effect still exists for d_I = 0, that is, without an insulating layer between the thin film and the niobium underneath. In this paper we provide the first experimental demonstration of the concept, by showing that a Nb SRF cavity coated with a single MgB₂ layer could sustain a higher H_vp, above the theoretical limit given by the H_sh for Nb. This could lead to SRF cavities with higher accelerating gradients.

The increase of H_c1 in thin films for H//surface is a well-established and well understood effect¹⁰, and can be readily observed using a SQUID magnetometer. As H is increased from 0 at a fixed temperature, the initial Meissner state is characterized by a linear m(H) dependence m_M = −(V_eff/4π)H. Here V_eff is the effective superconductor volume, which is smaller than the geometrical volume V due to the field penetration near the surfaces. At H_c1, m(H) deviates from the linear dependence, signaling vortex penetration. The H_c1 enhancement in thin MgB₂ films has been studied previously using this technique¹². V_eff for δ ≪ λ is very small, thus the experimental resolution of the magnetometers is a serious limiting factor for these measurements.

However the second concept of Gurevich proposal, namely that a thin film can sustain a ΔH between both of its surfaces, cannot be tested using the approach described above because both surfaces of the film are exposed to the same ambient field. In this paper we propose a novel approach that overcomes this fundamental limitation, and concomitantly also solves the resolution and alignment problems (see supplementary information). We have fabricated macroscopic-sized ellipsoids and coated them with MgB₂ films. The Meissner effect in the film screens the entire ellipsoid volume from the applied field, so a ΔH develops between the internal and external film surfaces. Here the field is outside of the ellipsoid rather than inside as in a real SRF cavity, thus we call it the “inverse cavity” concept. We use ellipsoids because the demagnetizing effects and boundary conditions are well defined, and in the Meissner state the external field at the ellipsoid surface is parallel to the surface everywhere, the same as in real SRF cavities.

The Nb ellipsoids have the nominal semi axes a = 4 mm, b = c = 2.5 mm, made from the same bulk material as presently used in SRF cavities. The measurements were performed in a Quantum Design MPMS SQUID magnetometer. When the applied field H is parallel to the i axis (i = a, b, c) the calculated “Meissner slope” is m_M,i/H = −V/[4π(1 − N_i)] = −ab²/[3(1 − N_i)], where N_i are the demagnetizing factors, such that N_a < N_b = N_c and N_a + N_b + N_c = 1.

Figure 1a shows the schematic of the H_vp measurement. Most results in this paper were measured with the applied magnetic field parallel to the long axis of the ellipsoid (top). However, the field alignment to the short axis (bottom) was also measured to confirm the results taking into account the different demagnetizing factors for the two field directions. Figure 1b presents m vs. H at several temperatures for a bare Nb ellipsoid shown in the inset. For each T, the sample was cooled from above T_c = 9.3 K to T in H = 0 (zero field cooling, ZFC) before the m vs. H measurement. The Meissner slope does not change with T because the variation of the effective superconductor volume due to the change in λ(T) is too small compared to the dimensions of the ellipsoid. The solid line in this figure corresponds to the predicted m-H relationship for the ellipsoid with a = 4 mm and b = c = 2.5 mm in the Meissner state. The m vs. H curves at T = 5 K for the Nb ellipsoid are shown in the inset of Fig. 1c for both H||a and H⊥a. From the slopes of both orientations m_M,a/H and m_M,b/H, we obtained N_a = 0.1880 and N_b = N_c = 0.4060. The ellipsoid volume was calculated to be V = 0.1062 cm³, in excellent agreement with the designed value (from the weight of this particular ellipsoid we had determined V = 0.1048 cm³).

Figure 1

(a) Schematic of the vortex penetration field measurement. (b) ZFC m-H curves of bare Nb ellipsoid at different temperatures. (c) <B>-H curves of bare Nb ellipsoid at different orientations. (d) Typical ZFC m-T curve of bare Nb ellipsoid under 1000 Oe applied field. Arrow signals the temperature where H_vp equals the applied field. (e) Comparison of H_vp obtained from both methods.

Although the applied field is uniform, due to the demagnetizing effects the total external field is not. In the Meissner state the total external field at the surface of the ellipsoid is parallel to the surface everywhere, and its magnitude varies along the surface, being zero at the poles and reaching a maximum at equator H_eq = H/(1 − N_i), where i = a, b. (see Fig. 1a). Consequently, vortex penetration starts at the equator. As seen in the Fig. 1c, the average magnetic induction <B_i> = 4π(1 − N_i)(m − m_M)/V of the ellipsoid starts to deviate from zero at the same H_eq for both H||a and H||b orientations. We define the vortex penetration field H_vp as when <B> increases above the noise. The noise level increases with H, reaching about ±2 G at 1.5 kG, which negatively impact the accuracy of the H_vp(T) measurement¹³. This high noise level could be originated from the superconducting magnet in the magnetometer when it was charged between 1000 and 5000 Oe with fine steps¹⁴.

An alternative approach to measure H_vp is to apply a field H < H_vp(T) after ZFC and then measure m(T). A result is shown in Fig. 1d. As T increases, m initially remains constant at the Meissner value until the vortex penetration occurs, which is signaled by a sudden reduction of the absolute value of m when H = H_vp(T). Figure 1e summarizes the H_vp(T) results obtained from both m(H) and m(T) measurements. The left and right vertical axes in Fig. 1e show the value of H and H_eq for first vortex penetration respectively. The error bars in Fig. 1e stand for the H_vp variation when using 5 G and 1 G <B> criterion. The results suggest that the m-T approach is a preferred method for the H_vp measurement. At high field, it is more accurate than the m-H technique mainly due to the elimination of the flux creep effect from the superconducting magnet. At low H it is comparable to the m-H technique. Therefore, the m-T technique was used to measure H_vp of a bare Nb ellipsoid and two MgB₂ thin film-coated Nb ellipsoids in this work. From Fig. 1e we find that at T~2 K vortex penetration starts at H_eq~2200 Oe, very close to the ideal limit H_sh,Nb(2 K) ≈ 2280 Oe, confirming the high quality of the Nb used in our study.

The MgB₂ thin film coating of Nb ellipsoids was performed using hybrid physical-chemical vapor deposition (HPCVD)¹⁵. Two Nb ellipsoids were coated with MgB₂ layers of 100 nm (Nb100) and 200 nm (Nb200), respectively. Figure 2a shows an SEM image taken at the equator of the ellipsoid Nb100. The film is polycrystalline with grain size of ~1 μm. The MgB₂ layer covered the entire ellipsoid uniformly without pinholes. An optical image of Nb200 is presented as the inset to Fig. 2b. Figure 2c shows the m-T curves for the bare Nb ellipsoid and the Nb ellipsoids coated with 100 nm and 200 nm MgB₂ layers for 1500 Oe applied field. The onset of vortex penetration are marked with black arrows in the figure. With an increasing temperature, vortices penetrate into the bare Nb ellipsoid at 3.76 K. This temperature increases to 5.11 K and 5.21 K for the Nb100 and Nb200 ellipsoid, respectively. By repeating the m-T measurements, the temperature dependence of H_vp can be obtained.

Figure 2

(a) SEM image taken on the Nb100 ellipsoid. (b) optical image of Nb200 ellipsoid (c) m-T curves comparisons between Nb ellipsoids with different thicknesses of MgB₂ coating. ZFC to 1.8 K then apply 1500 Oe field. Arrows indicate the H_vp of each sample. (d) Comparison of H_vp-T curves measured on Nb ellipsoids. Data points in the blue box corresponds to the 3 curves in Fig. 2(c). The actual H field at the ellipsoids equator is calculated on the right y-axis.

Figure 2d summarizes the H_vp(T) curves for the bare Nb ellipsoid, Nb100, and Nb200. The three data points within the blue box correspond to the 3 curves in Fig. 2c. The H_vp(T) of Nb200 is about 400 Oe higher than the bare Nb ellipsoid in the temperature range from 1.8 K to the T_c of Nb. This increase is approximately constant because the properties of MgB₂ do not change significantly in this temperature range (T < T_c/4). The maximum field at the equator that our inverse cavity can sustain before vortex penetration is indicated on the right vertical axis. At T~2.8 K it is ~2600 Oe, about 500 Oe above the bare Nb ellipsoid.

As an additional test of our inverse cavity concept we deposited MgB₂ films of thickness d_S = 100; 200 and 300 nm on non-superconducting molybdenum ellipsoids. For details of the measurements and analysis, see the supplementary material. For the three samples we measured m(H) at several T with H||a. The Meissner slopes indicate that the full volume of the ellipsoids is screened, implying that the field at the MgB₂-Mo interface is zero. At H_vp(T) the field at the interface becomes nonzero and spreads inside the Mo. The obtained H_vp(T) curves are shown in Fig. 3a. They extrapolate to zero at the T_c of the MgB₂ films (~38.1; 38.6 and 38.7 K respectively).

Figure 3

(a) The dependence of H_vp of the MgB₂/Mo samples on temperature. H_vps of Mo100 and Mo300 are almost overlapped. (b) Maximum H difference shieled by a single layer of MgB₂ versus the field inside the MgB₂ shell for Mo200 at 1.8 K and 5 K.

As described in detail in the Supplementary Materials, we found out that in all cases H_vp at the equator is lower than the prediction for the enhanced H_c1, and that the field penetration occurs when the screening current is large enough to eliminate the surface barrier. The fact that H_vp in the MgB₂ coated Mo ellipsoids is determined by J rather than H_c1 is good news for cavity applications, because it implies that H_vp is the limit for the difference in field that can be sustained between both surfaces of the film, not for the absolute value of the field. This is fully consistent with our main experimental finding, namely that by adding an MgB₂ coating we have been able to increase H_vp by about 500 Oe on top of the already large penetration field of Nb.

We performed additional studies on the Mo200 ellipsoid to estimate how high H_vp could potentially be obtained. After applying a field H_int at a temperature above the T_c of MgB₂ (which penetrates homogeneously into the Mo), we cooled down to a measurement T and subsequently increased H. We observed an initial linear m(H) Meissner dependence, indicating that screening currents develop in the MgB₂ that shield the internal Mo volume from the external field variation. Eventually the surface barrier disappears and the field penetrates when the difference between the outside and the inside field, ΔH = H − H_int, reaches a value ΔH_vp, as summarized in Fig. 3b. The remarkable result is that ΔH_vp > 0 even for H_int well above the maximum operating fields of Nb cavities. This implies that the operating field of a cavity could be increased by ΔH_vp/(1 − N_a) by internally coating it with this MgB₂ film. For instance, Fig. 3b shows that if a hypothetical cavity were able to sustain H_vp~4000 Oe, at 1.8 K, then this MgB₂ film would further increase that H_vp by ~200 Oe.

Our results demonstrate three important facts. First, it is indeed possible to increase the H_vp of the Nb material used in the state-of-the-art SRF cavities by a substantial amount (~600 Oe) by coating it with a thin superconducting film that screens vortex penetration. Second, it is technically possible to deposit a thin MgB₂ film with appropriate properties for this purpose on curved bulk Nb. Third, a single layer of superconducting thin film can reduce the magnetic field felt by the bulk material under it. These three facts are enough to demonstrate that it is possible to increase the H_vp of existing Nb SRF cavities by ~600 Oe. The superconducting shielding current density at the equator of Nb200 is estimated to be J~ΔH/d~10⁷ A/cm², as compared to J_d~10⁸ A/cm² reported for MgB₂ thin films¹⁶, therefore the maximum ΔH that a MgB₂ thin film can shield has not been reached. Further, a superconductor/insulating multilayer coating proposed by Gurevich would achieve even higher shielding field ΔH_total with MgB₂ films.

Methods

Deposition of MgB₂ thin film on Nb ellipsoids

The MgB₂ films were deposited by Hybrid Physical-Chemical Vapor Deposition (HPCVD) technique¹⁵. The schematic of the deposition technique is presented in Extended Data Fig. 1(a). By heating magnesium pellets above melting temperature and letting magnesium vapor react with boron from the decomposition of diborane gas, this technique has produced the films with the highest quality on both single crystal and metallic substrates^17,18. In this work, MgB₂ film was deposited at 730 °C in 40 Torr hydrogen atmosphere. The boron source was 20 sccm 5% diborane in hydrogen solution, which gave a growth rate of 55 nm/min. Each ellipsoid was coated three times with rotating 120 degree between each coating to achieve uniform coating. During the first deposition, a piece of 5 × 5 mm² silicon carbide (SiC) substrate is put aside of the ellipsoid as a reference for thickness calibration. The nominal thickness of MgB₂ layer coated on the ellipsoid refers to the film thickness on the SiC substrate.