Transcript Document
RF Superconductivity and 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 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 Tsp Tc Gas phase metastable for Tc > T > Tsp, spinodal temperature spontaneous separation at Tsp linear stability theory sinusoidal threshold dr ~ e exp(i k·z) lowers energy Type I (Pb) Superconductors and magnetic fields What’s the superheating field? Coherence length: Decay of Y Type II (Nb and Nb3Sn) x Energy gain Energy cost Penetration depth: Decay of H L 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? Metastability threshold and Hsh Why is there a barrier to vortex penetration? Why a superheating field? How to calculate Hsh? Barrier • Field where barrier vanishes • Linear stability analysis determines nucleation mechanism: vortex array x L> x Costly core x enters first; gain from field L later 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!) Theories of superconductivity Validity versus complexity Ginzburg-Landau (GL) • y(r), H(r) order parameters • Spatial dependence OK • Valid only near Tc Ginzburg-Landau valid RF cavity operating conditions 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) n ħwd kF Theories of superconductivity Validity versus complexity Eilenberger Equations • Valid at all temperatures • Assumes D(r), H(r) vary slowly • Green’s function f, g • Vortex core collapse?? Eilenberger equation results MgB2 Nb3Sn Nb at 2K Eliashberg equations • Needs electronic structure • Never done before for Hsh GinzburgLandau Underestimate for Hsh Theories of superconductivity Validity versus complexity Bogoliubov-deGennes equations n kF • 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) 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.