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RF Superconductivity and the Superheating Field H sh

RF Superconductivity and the Superheating Field H sh. R adio F requency cavity Oscillating E ( t ) to accelerate particle bunches Maxwell implies oscillating H ( t ) Best shaped cavities: E/H = 36 MV/(m G). James P. Sethna, Gianluigi Catelani, and Mark Transtrum.

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RF Superconductivity and the Superheating Field H sh

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  1. RF Superconductivityand the Superheating Field Hsh • Radio Frequency cavity • Oscillating E(t) to accelerate particle bunches • Maxwell implies oscillating H(t) • Best shaped cavities: E/H = 36 MV/(m G) James P. Sethna, Gianluigi Catelani, and Mark Transtrum • Superconducting RF cavity • Lower losses • Limited by maximum of H(t) in cycle • Each superconducting material • has maximum possible Hsh

  2. Metastable energy barrier B droplet nucleation R2 surface tension cost R3 bulk energy gain Metastability and Nucleation “Superheating” like 110% humidity Raindrops: the Liquid-Gas Transition Unstable spontaneous separation at Tsp linear stability theory sinusoidal threshold dr ~ e exp(i k·z) lowers energy Tsp Tc k Gas phase metastable for Tc > T > Tsp, spinodal temperature

  3. x L Type I (Pb) Coherence length: Decay of Y Energy gain Superconductors and magnetic fields Type II (Nb and Nb3Sn) Energy cost Penetration depth: Decay of H What’s the superheating field? • Type II superconductors • L > x • Magnetic flux lattice H > Hc1 RF cavity operating conditions already above Hc1 Vortex nucleation slower than RF frequency (GHz) Can we calculate the phase diagram for Hsh?

  4. How to calculate Hsh? Why a superheating field? Metastability threshold and Hsh • Field where barrier vanishes • Linear stability analysis • determines nucleation • mechanism: vortex array x Why is there a barrier to vortex penetration? • Theories of superheating field • Line nucleation • Hsh~Hc /k • discouraging, but wrong • Ginsburg-Landau theory Hsh~ 0.745 Hc • Eilenberger equations Hsh = 0.84 Hc • Eliashberg equations (hard!) Barrier L> x Costly core x enters first; gain from field L later

  5. Ginzburg-Landau (GL) • y(r), H(r) order parameters • Spatial dependence OK • Valid only near Tc • Bardeen Cooper Schrieffer (BCS) theory • Pairing k, -k within vibration energy • Excellent for traditional superconductors • Hc1(T), Hc2(T) done • Hsh(T) hard (spatial dependence) kF n ħwd Ginzburg-Landau valid RF cavity operating conditions Theories of superconductivity Validity versus complexity

  6. MgB2 Nb3Sn Nb at 2K Ginzburg-Landau Underestimate for Hsh • Eilenberger Equations • Valid at all temperatures • Assumes D(r), H(r) vary slowly • Green’s function f, g • Vortex core collapse?? Theories of superconductivity Eilenberger equation results Validity versus complexity • Eliashberg equations • Needs electronic structure • Never done before for Hsh

  7. 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 Theories of superconductivity Validity versus complexity 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.

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