RF breakdown in multilayer coatings a possibility to

RF breakdown in multilayer coatings: a possibility to break the Nb monopoly Alex Gurevich National High Magnetic Field Laboratory, Florida State University "Thin films applied to Superconducting RF: Pushing the limits of RF Superconductivity" Legnaro National Laboratories of the ISTITUTO NAZIONALE DI FISICA NUCLEARE, in Legnaro (Padova) ITALY, October 9 -12, 2006.

Motivation • Why Nb? BCS surface resistance: Rs 4 exp (- /k. BT) Minimum Rs implies maximum , that is, maximum Tc 1. 87 /k. B and minimum London penetration depth Nb 3 Sn has maximum Tc and minimum to provide the optimum Rs Exceptions: • Does not work for the d-wave high-Tc superconductors for which Rs T 2 due to nodal lines in (k) = 0. • Two gap Mg. B 2 with 2. 3 me. V 7. 2 me. V: Tc is proportional to , while Rs exp (- /k. BT) is limited by Vanishing (k) = 0 along [110] directions in HTS

Background KEK&Cornell Best KEK - Cornell and J-Lab Nb cavities are close to the depairing limit (H Hc = 200 m. T) How far further can rf performance of Nb cavity be increased? Theoretical SRF limits are poorly understood …

Superconducting Materials Very weak dissipation -M Very weak dissipation at H < Hc 1 (Q = 10101011) Q drop due to vortex dissipation at H > Hc 1 Strong vortex dissipation 0 Hc 1 Hc Hc 2 H Higher-Hc SC Nb Material Tc (K) Hc(0) [T] Hc 1(0) [T] Hc 2(0) [T] (0) [nm] Pb 7. 2 0. 08 na na 48 Nb 9. 2 0. 17 0. 4 40 Nb 3 Sn 18 0. 54 0. 05 30 85 Nb. N 16. 2 0. 23 0. 02 15 200 Mg. B 2 40 0. 43 0. 03 3. 5 140 YBCO 93 1. 4 0. 01 100 150 Nb has the highest lower critical field Hc 1 Thermodynamic critical field Hc (surface barrier for vortices disappears)

2 Single vortex line • Core region r < where (r) is suppressed B 2 • Region of circulating supercurrents, r < . r • the. Each vortex carries flux quantum 0 Important lengths and fields • Coherence length and magnetic (London) penetration depth λ For clean Nb, Hc 1 170 m. T, Hc 180 m. T

Surface barrier: How do vortices get in a superconductor at H > Hc 1? J Two forces acting on the vortex at the surface: H 0 image to ensure J = 0 G - Meissner currents push the vortex in the bulk - Attraction of the vortex to its antivortex image pu the vortex outside b Thermodynamic potential G(x 0) as a function of the p Meissner H < Hc 1 H = Hc 1 H > Hc 1 H = Hc x 0 Image Vortices have to overcome the surface barrie even at H > Hc 1 (Bean & Livingston, 1964) Surface barrier disappears only at the overhe field H = Hc > Hc 1 at which the surface J beco the order of the depairing current density

Vortex in a thin film with d < London screening is weak so 2 2 B = - 0 (r) Vortex field in a film decays over the length d/ instead of (interaction with many images) Vortex free energy as a function of the position x 0 Self-energy Magnetic energy G. Stejic, A. Gurevich, E. Kadyrov, D. Christen, R. Joynt, and D. C. Larbalestier, Phys. Rev. B 49, 1274 (1994) Lorentz force x 0

Enhanced lower critical field and surface barrier in films Use thin films with d < to enhance the lower critical field Field at which the surface barrier disappears Example: Nb. N ( = 5 nm) film with d = 20 nm has Hc 1 = 4. 2 T, and Hs = 6. 37 T, Much better than Hc = 0. 18 T for Nb

How one can get around small Hc 1 in SC cavities with Tc > 9. 2 K? AG, Appl. Phys. Lett. 88, 012511 (2006) Higher-Tc. SC: Nb. N, Nb 3 Sn, etc Multilayer coating of SC cavities: alternating SC and insulating layers with d < Higher Tc thin layers provide magnetic screening of the bulk SC cavity (Nb, Pb) without vortex penetration Nb, Pb For Nb. N films with d = 20 nm, the rf field can be as high as 4. 2 T ! Insulating layers No open ends for the cavity geometry to prevent flux leaks in the insulating layers

How many layers are needed for a complete screening? H 0 = 2 T Hi = 50 m. T Example: N Nb 3 Sn layers with d = 30 nm 0 = 65 nm and Hc 1 = 2. 4 T Peak rf field H 0 = 2 T < Hc 1 Internal rf field Hi = 50 m. T (high-Q regime) Nb d N = (65/30)ln(40) = 8 Strong reduction of the BCS resistance by Nb 3 Sn layers due to larger and shorter :

A minimalistic solution H 0 = 324 m. T Hi = 150 m. T A Nb cavity coated by a single Nb 3 Sn layer of thickness d = 50 nm and an insulator layer in between If the Nb cavity can withstand Hi = 150 m. T, then the external field can be as high as d Lower critical field for the Nb 3 Sn layer with d = 50 nm and = 3 nm: Hc 1 = 1. 4 T is much higher than H 0 A single layer coating more than doubles the breakdown field with no vortex penetration, enabling Eacc 100 MV/m

Global surface resistance layer bulk Nb 3 Sn coating of thickness L = 50 nm, RNb 3 Sn(2 K) 0. 1 RNb Screen the surface of Nb cavities using multilayers with lower surface resistance

Why is Nb 3 Sn on Nb cavity much better than Nb 3 Sn on Cu cavity? vortices H(t) H Nb Cu w Nb 3 Sn/Nb cavity is much better protected against small transverse field components than Nb 3 Sn/Cu cavity Meissner state persists up to H < Hc 1(Nb) Meissner state is destroyed for small H < (d/w)Hc 1(Nb 3 Sn) << Hc 1(Nb 3 Sn) due to large demagnetization factor w/d 103 -105

Vortex penetration in a screen Dynamic equation for a vortex Vortex flight time and energy release For a 30 nm Nb 3 Sn film, 10 -12 s, much shorter than the rf period 10 -9 s Maximum rf field at which the surface barrier disappears: Nb 3 Sn coating more than doubles vortex penetration field for Nb

Analytical thermal breakdown model T Tm H(t) coolant Ts T 0 d x Thermal runaway due to exponential increase of Rs(T) Kapitza thermal flux: q = (T, T 0)(T – T 0) For a general case of thermal quench, see Gurevich and Mints, Reviews of Modern Physics 59, 941 Equations for Tm and Ts

Maximum temperature BCS + residual surface resistance Ri Since Tm – T 0 << T 0 even Hb, we may take and h at T = T 0, and obtain the equation for H(Tm):

Thermal feedback stability for multilayers Breakdown field as a function of the total overlayer thickness L Here s = exp(-2 L/ ), r = R 0/Rb, = 0/ b • 50 nm Nb 3 Sn overlayer triples Q at low field • 100 nm overlayer more than doubles thermal breakdown field

Conclusions: • Multilayer S-I-S coating could make it possible to take advantage of superconductors with much higher Hc, than those for Nb without the penalty of lower Hc 1 • Strong increase of Hc 1 in films allows using rf fields > Hc of Nb, but lower than those at which flux penetration in grain boundaries may become a problem • Strong reduction of BCS resistance because of using SC layers with higher (Nb 3 Sn, Nb. N, etc) • The significant performance gain may justify the extra cost.