Maximum screening field and the optimum parameters of superconductivity

multilayers for resonator cavities

Alex Gurevich

Old Dominion University,

Department of Physics and Center for Accelerator Science,

Norfolk, VA 23529, USA

The Sixth International Workshop on THIN FILMS AND NEW IDEAS FOR SRFOctober 6 –8, 2014 Legnaro National Laboratories (Padua) ITALY

Supported by the US Department of Energy, HEP under grant No. DE-SC0010081

Multilayer coating

Nb

insulating layers

higher-TcSC: NbN, Nb3Sn, etc

Magnetic screening of the Nbcavity without vortex penetration

Multilayer coating of SC cavities: alternating SC and I layers with d <

The breakdown field could be increased up to the superheating field Hs of the coating: 450 mT for Nb3Sn

07.0ln

22

01

d

dHc

No thermodynamically stable parallel vortices due to the enhancement of Hc1

in thin films with d < (Abrikosov, 1964)

AG, APL. 88, 012511 (2006)

The idea has caused a lot of excitement and misinterpretations (Hc1 = 0, Hc1 is not important, Hs is reduced not increased, “unmanageable” dissipation, etc, S. Posen et al., 2014)

Recent progress

Experimental evidences of the enhancement of the parallel Hc1 in thin filmsL. Civale, T.K. Worthington, A. Gupta, Phys. Rev. B 48, 7576 (1993).

C. Antoine, et al Phys. Rev. ST-AB 13, 121001 (2010).

T. Tajima, et al. J. Phys. Conf. Ser. 234, 012043 (2010); AIP Conf. Proc. 1435, 297 (2012).

DB Beringer, C Clavero, T Tan, XX Xi, WM Roach, RA Lukaszew IEEE Trans. Appl. Supercond. 23, (2013)

Increasing the high-field performance and reduction of surface resistance by a NbN overlayer

C.Z. Antoine, J.-C. Villegier, G. Martinet, APL 102, 102603 (2013).WM Roach, DB Beringer, Z Li, C Clavero, RA Lukaszew, IEEE Trans. Appl. Supercond. 23 (2013)

What’s next?

Is there an optimum thickness of layers which maximizes the breakdown field? ✔

If yes, how far can the maximum screening field Hm be increase by multilayers? Can the optimized Hm exceed the superheating field of the layer? ✔

Do we know how to select is the best layer material? Can we just use a dirty Nb

✔ Are the insulating layers really necessary to protect the cavity and to suppress

strong dissipation caused by local penetration of vortices at defects? ✔

Outline

There is an optimum thickness of multilayers at which it can screen the magnetic field exceeding the superheating field of both Nb and the layer material.

ML provide best protection of cavities against surface defects which lower the Bean-Livingston barrier and open gates for local penetration of vortices.

Dielectric layers are instrumental to suppress vortex dissipation and dendritic thermomagnetic avalanches which trigger the cavity quench.

Implementation of the optimized Nb3Sn or NbN multilayers could double the maximum accelerating gradient, pushing it above 100 MV/m.

Pnictides could potentially quadruple the accelerating gradient.

New opportunities of using dirty Nb multilayers to push Hm up to 280-300 mT

GL superheating field

Meissner state can only exist below the superheating field H < Hs

Periodic vortex instability as the current density Js = H/ at thesurface reaches the depairing current density Jd = Hs/

Hernandez and Dominguez, PRB 65, 144529 (2002)

GL calculations of Hs(Matricon and Saint-James, 1967, Chapman 1995)

Bs »1.2Bc, k @1,

Bs » 0.745Bc, k >>1

Bs decreases as the surface gets dirtier and κ = λ/ξ increases.

Nb

At H = Hs the magnetic surface barrier for penetration of vortices vanishes

Superheating field at T << Tc

GL is not applicable. Calculation ofHs requires solution of microscopic BCS/Eilenberger equations

clean limit (bad): gap vanishes at H < Hs

dirty limit (good): gap remains finite at H = Hs

Lin and Gurevich, PRB 85, 054513 2012

clean

dirty

Only Hs(0) = 0.84Hc at κ >> 1 has been calculated in the clean limit (Galaiko 1966, Catelani and Sethna, 2008)

and for arbitrary impurity concentration(Lin and Gurevich, 2012)

Possible multilayer materials

Materi

al

Tc (K) Hc [T] Hc1

[mT]

Hc2[T] [nm]

[meV]

Nb 9.2 0.2 170 0.4 40 1.5

pnictid

es

30-55 0.5-0.9 30 >100 200 10-20

Nb3Sn 18 0.54 50 30 85 3.1

NbN 16.2 0.23 20 15 200 2.6

MgB2 40 0.43 30 3.5-60 140 2.3;

7.1

YBCO 93 1.4 10 >100 150 20

Large gap Δ (good for SRF) is usually accompanied by low Hc1 (bad for SRF)

Very small surface

resistance at H < Hc1

(Q = 1010-1011)

Q drop due to vortex

dissipation at H > Hc1

Nb has the highest Hc1

but not Hc:

Raise RF critical field

above Hc1(Nb) using

higher Hc materials which

have low Hc1

London screening of parallel field

London equation for the magnetic field h(x)eiωt

in a multilayer on a thick SC substrate in the external field Heiωt

Boundary conditions: continuity of the magnetic and electric field at x = d:

continuity of magnetic field continuity of electric field

The rf electric field is:

T. Kubo, Y. Iwashita, and T. Saeki, APL 104, 032603 (2014).

AG, 2014 unpublished

London Solutions

Solutions for the screening filed at di << ds:

Important parameters

where c and b are given by:

for the SC substrate (Nb) with λ0 < λ, both c and k are positive

J(x)/

J(0)

Breakdown of the Meissner state occurs at the surface of either ML or Nb where the current densities J(0) = h’(0) and J(d) = h’(d) are maximum

Current counterflow induced by the substrate

Current density in the layer J(x) = - h’(x):

Current density at the surface J(0) is reduced by the substrate with λ0 < λ:

The conterflow induced by the substrate reduces the current density at the ML surface, allowing the Meissner state in the ML to survive up to fields exceedingthe superheating field Hs for a semi-infinite SC

For a thick ML with d >> λ, the maximum field Hm is limited by Hs: optimum thickness dm at which Hm exceeds both Hs and Hs0

AG, unpublished, 2014

Optimum thickness

The Meissner state is stable if the screening current densitity at the surface of both the ML and the substrate is smaller than the depairing limit:

J(0) < Jd = Hs/λ and J(d) < Jd0 = Hs0/λ0

for Hs = 2Hs0 and k = ½,dc = ln[μ + (μ2 – k)1/2 ]

The Meissner state is below both blue and red lines.

The crossing point defines the optimum thickness dm

for maximum Hm which exceeds the superheating fields of both the layers and the substrate

The assumption that the breakdown of the Neissner state is caused by the rf field but not current (T. Kubo, Y. Iwashita, and T. Saeki, APL 104, 032603 (2014)) underestimates Hm

Maximum screening field

The maximum screening field Hm corresponds to d = dm for which

Hm at the optimum thickness exceeds the bulk superheating fields of both Nb and the layer material. For λ >> λ0, practically for λ > 160 nm for a SC layer on the Nbcavity with λ0 = 40 nm, Hm approaches the limit

Let us evaluate Hm for a ML on clean Nb with λ0 = 40 nm and Hs0 = 1.2Hc = 240 mT(the GL result for clean Nb) and different layer materials, such as Nb3Sn, NbN, pnictides, and also dirty Nb

AG, unpublished, 2014

Estimates of Hm and dm

Nb3Sn: Hs = 0.84Hc = 454 mT and λ = 120 nm (moderately dirty):

Hm = 507 mT, dm = 1.1λ = 132 nm

doubles the superheating field of clean Nb

Ba0.6K0.4Fe2As2, Tc = 38 K, Hc = 0.9T, Hs =756 mT, λ = 200 nm

Hm = 930 mT, dm = 1.78λ = 356 nm.almost quadruples the superheating field of clean Nb

dirty Nb layer: Hc = 200 mT, Hs = 170 mT, l = 2 nm, and λ =λ(ξ0 /l)1/2 = 180 nm

Hm = 288 mT, dm = 0.44λ = 79 nm.20% gain as compared to Hs = 240 mT of clean Nb

Surface barrier and vortex penetration at H > Hc1

Meissner current pushes the vortex in the bulk

Attraction of the vortex to its antivortex image pushes the vortex out of the superconductor

H0

b

J

image

to ensure

J = 0

])2([)( 01

/

00 HHbHeHbG cv

b

H = Hc1

H < Hc1

H > Hc1

H = Hc

b

G

Thermodynamic potential G(b) of the vortex:

Meissner Image

Vortices have to overcome the surface barrier even at H > Hc1 (Bean & Livingston, 1964)

BL barrier at an ideal surface disappears only at the overheating field H = Hs

Surface materials defects open gates for local penetration of vortices at H < Hs

Penetration of vortices in a thick film

Once a vortex breaks through a defect, it triggersa magnetic flux avalanche

in the bulk at H > Hc1

Penetration of many vortices causes heating and a dendritic thermo-magnetic flux jump

Poor thermal conductivity of Nb3Sn: a 2-3 μm thick film doubles the thermal impedance of the Nb cavity wall, facilitating local overheating and branching vortex avalanches

H

λλ

H

A defect locally weakens the surface barrier whichvanishes at

J(0) > βJd β < 1

Thin dielectric layers provide the strongest possible pinning of vortices, blocking propagation of vortex avalanches

Penetration of vortices in a thin multilayer

Parallel Hc1 in a thin film multilayer is irrelevant (no longer a problem)

I layer intercepts propagating vortex loops,turning them into two short vortices of opposite polarity. No propagation in the bulk if h(d) < Hc1

Great reduction of the RF vortex power q localized in a thin S layer. Upper limits of q and the amplitude of V-AV oscillations um

Nb3Sn: ρn = 0.2 μΩm, d/λ = 0.2, κ = 20, λ = 100 nm, β = 1/2, ν = 2GHz

For Nb3Sn, um ≈ 4 μm, and q ≈ 2 μW

Unlike thick Nb3Sn films (d > 1-2 μm), a thin ML only slightly (by ≈ 5%) increases the thermal Impedance of the cavity wall. No deterioration of thermal quench stability.

Magnetic flux penetration in superconductors

Smooth

flux penetration and

remagnetization in a

Nb single crystal

Dendritic flux penetration:

magnetic microavalanches

(mostly at low T)

MgB2

U. Oslo and UW websites

Vortex sandpile.

Nonlinear magnetic

flux diffusion

Positive feedback

between flux motion

and Joule heating

Thermomagnetic

instability

Dendritic pattern

formation

What happens if vortex avalanches are not stopped (MO image of Nb film by M.Welling and R. Wijngaarden, U. Amsterdam)

Looks familiar?

snowflake

Dendritic instability

during solidification growth

Viscous liquid fingering

Diffusion-limited

aggregation

bacterial “snowflakes”

Theory of dendritic flux penetration

Coupled equations for the temperature T and electric field E

t

ETJE

EETJTt

TC

),(

),(

0

2

E

JJc Two characteristic times:

- tm = 0L2/ - time of magnetic flux diffusion

- th = CL2/ - time of thermal diffusion

Thermal bistability and nonlocal flux diffusion

Turring instability in a reaction-diffusion systems

Nonequilibrium dendritic structures

Aranson, Gurevich, Vinokur, Phys. Rev. Lett. 87, 0976003 (2001); 94, 037002 (2005).

Becomes particularly violent at low temperatures < 4 K as the specific heat C(T) = C0T3 decreases

Dendritic flux propagation in a film with surface defects

EM nonlocalityfacilitates branching instability

Giant magnetic avalanche in the defect free region

Several successive waves of dendritic flux propagation

Aranson, Gurevich, Vinokur,

Phys. Rev. Lett. 87, 94, 037002 (2005).

Supersonic propagation at low temperatures

How to protect cavities from vortex avalanches?

βHs

Hc1

Maximum field which satisfies the necessarystability margin

but now Hs and Hs0 are re-defined as follows

The onset of vortex penetrationreduced by defects (β < 1)

The onset of vortex penetrationreduced by defects (β < 1)

Conservative stability margin: even in the worst case scenario vortex hotspots are only localized in a thin surface layer and do not propagate in the bulk

Other conservative assumptions, β = ½ and Hc1 = 170 mT for numerical estimates

Estimates of Hm and dm for β = ½ and Hs0 = 170 mT

Nb3Sn: Hs = 0.84Hc = 454 mT and λ = 120 nm (moderately dirty):

Hm = 273 mT, dm = 96 nm

20% higher than for thick Nb3Sn

Ba0.6K0.4Fe2As2, Tc = 38 K, Hc = 0.9T, Hs =756 mT, λ = 200 nm

Hm = 588 mT, dm = 310 nm.more than doubles the superheating field of clean Nb

Conservative stability margin against penetration of vortices

Conclusions

• Multilayers can be optimized in such a way that they can screen the magnetic field exceeding the superheating fields of both the layer material and substrate

• Can push the accelerating gradients over 100 MV/m

• S-I-S multilayers provide best protection of cavities against local penetration of vortices

• Significant reduction of vortex dissipation and suppression of thermomagnetic avalanches as compared to thick films or uncoated cavities

• Lots of materials to play with (Nb3Sn, NbN, pnictides)

• Key material challenges are: weak-linked grain boundaries, second phase precipitation and the broadening of the gap peaks in the density of states by impurities and inhomogeneities

• New opportunities to use a 89-90 nm thick dirty Nb overlayer on a thin (few nm) dielectric layer deposited onto the Nb cavity