RF Superconductivity and the Superheating Field Hsh

1
RF Superconductivityand the Superheating Field
Hsh

• James P. Sethna, Gianluigi Catelani, and Mark
  Transtrum

• Radio Frequency cavity
• Oscillating E(t) to accelerate particle bunches
• Maxwell implies oscillating H(t)
• Best shaped cavities E/H 36 MV/(m G)

• Superconducting RF cavity
• Lower losses
• Limited by maximum of H(t) in cycle
• Each superconducting material
• has maximum possible Hsh

2
Metastability and Nucleation

• Raindrops the Liquid-Gas Transition

Metastable energy barrier B droplet nucleation R2
surface tension cost R3 bulk energy gain
Superheating like 110 humidity
Unstable spontaneous separation at Tsp linear
stability theory sinusoidal threshold dr e
exp(i k?z) lowers energy
Tsp
k
Tc
Gas phase metastable for Tc gt T gt Tsp, spinodal
temperature
3
Superconductors and magnetic fields
Type I (Pb)

• Whats the superheating field?

Coherence length Decay of Y
Energy gain
Type II (Nb and Nb3Sn)
Energy cost
Penetration depth Decay of H

• Type II superconductors
• L gt x
• Magnetic flux lattice H gt Hc1

RF cavity operating conditions already above
Hc1 Vortex nucleation slower than RF frequency
(GHz)
Can we calculate the phase diagram for Hsh?
4
Metastability threshold and Hsh

• Why is there a barrier to vortex penetration?

How to calculate Hsh?
Why a superheating field?

• Field where barrier vanishes
• Linear stability analysis
• determines nucleation
• mechanism vortex array

x

• Theories of superheating field
• Line nucleation
• HshHc /k
• discouraging, but wrong
• Ginsburg-Landau theory Hsh 0.745 Hc
• Eilenberger equations Hsh 0.84 Hc
• Eliashberg equations (hard!)

Barrier
Lgt x
Costly core x enters first gain from field L
later
5
Theories of superconductivity

• Validity versus complexity

6
Theories of superconductivity

• Validity versus complexity

• Eilenberger Equations
• Valid at all temperatures
• Assumes D(r), H(r) vary slowly
• Greens function f, g
• Vortex core collapse??

Eilenberger equation results

• Eliashberg equations
• Needs electronic structure
• Never done before for Hsh

7
Theories of superconductivity

• Validity versus complexity

kF

• Bogoliubov-deGennes equations
• Pairs all k, -k
• Local equations for quasiparticle eigenstates
• We solved for vortex core states, predicted
  split peak
• Sum over all quasiparticle states to get
  self-consistent y(r), H(r)

n
Experiment verified our theoretical prediction of
split peak away from vortex center
Quasiparticle density of states at different
distances from vortex center
Shore et al.
Hess et al.