Presentation on theme: "Two Major Open Physics Issues in RF Superconductivity H. Padamsee & J"— Presentation transcript:
1Two Major Open Physics Issues in RF Superconductivity H. Padamsee & J Two Major Open Physics Issues in RF Superconductivity H. Padamsee & J. SethnaWhat is the RF critical magnetic field? Is itHc1, Hc, Hsh?How does it depend on temperature?How does it depend on Ginzburg-Landau parameter(k = l/x)?High-Field Q-slope (next session)Why does the RF surface resistance of niobium increase sharply at high RF magnetic field?
2Quick Review of DC Critical Magnetic fields Internal magnetic fieldNormal StateMeissnerStateExternal fieldHc
3Type I and Type II SCGinzburg and Landau treated the surface energy associated with a normal/SC phase boundary.Qualitatively, the free energy per unit volume increases by µ0 Ha2 l/2 over the penetration depth (L due to the diamagnetism; work is done to exclude the magnetic fluxand falls by µ0 Hc2 x0 /2 over the coherence length due to the increase of the super-electron density.If the coherence length is smaller than the penetration depth, there is a negative surface energy and it is energetically favorable at equilibrium to have normal/superconducting boundaries… Type II.If x0 > L, there is a positive surface energy and the formation of normal/SC regions is not favorable, Type I
4Magnetization vs External Field Hc1, Hc2, Hc Boundary between Type I and Type II defined by G-L parameter k = l/xG-L theory relates Hc1, Hc2 and Hc to k, over a restricted range of k.Hsh is the maximum permissible value of the applied field, which satisfies GL equations. Metastability allows Hsh > Hc1 (or Hc) = Hc2/√2Hc
5Measuring Hc1 and Hc of Nb, 4 Measuring Hc1 and Hc of Nb, 4.2 K from Magnetization Curves Gives questionable results for Hc1 and Hc due to flux pinning, which depends on state of sampleDESY
6Hc1 and Hc are also difficult to measure because of hysteresis (flux pinning)… Rarely (if ever) do you get a reversible curve
7Attempted Magnetization Measurements on NON-Reversible Nb (Saito)
9Superheating FieldHsh is defined as the maximum permissible value of the applied field, which satisfies GL equations.Matricon and Saint-James solved GL equations numerically for the one-dimensional case where half of the space is occupied by a superconductor.
10Hsh in RF Fields In RF, fields change rapidly, within nanoseconds. If the time it takes to nucleate fluxoids is long compared to the rf period ( s)There is a tendency for the meta-stable superconducting state to persist up to Hsh > Hc1.T. Yogi Measured Hsh > Hc1 for Alloys Sn-In and In-Bi over a range of kappa values to show no discontinuity across Type I and Type II
12T. Hays Measured the RF Critical Field for Superconductors: Nb and Nb3Sn Using High Pulse Power We plan to repeat these measurements with large grain and single crystal cavities (if funded)
13Heuristic Arguments to determine Hsh In the process of phase transition, a boundary must be nucleated.In a Type I superconductor, the positive surface energy suggests that, in dc fields, the Meissner state can persist metastably beyond the thermodynamic critical field, up to the superheating field, Hsh.At this field, the surface energy per unit area vanishes:For Type II superconductors, it is also possible for the Meissner state to persist meta-stably above Hc1,How far above Hc1 ? is the open question
14Saito extended the energy balance argument to other dimensional forms of nucleation such as a line nucleation (vortex nucleation).The diamagnetic energy is given byand the condensation energy isBalancing the two contributions, the superheating field isIs line nucleation the proper model for the RF critical field, i.e. the superheating field?
15Issues with this Energy Balance Approach for H > Hc1 As an energy-balance argument, the vortex nucleation model gives an upper bound on the equilibrium critical field for vortex penetration, which is related to Hc1.Nothing in the energy balance argument discusses meta-stability, which is the key aspect for HshThe line nucleation model is useful in the context of nucleation on in-homogeneities on the scale of the coherence length, but not as a fundamental limit for uniform, flat, pure superconductors.
16Temperature Dependence Saito determines k (T) = Hc2 (T) /√2Hc (T) and Hc(T) from DC magnetic field dataThis is questionable for two reasonsSuperheating is a prediction from the Abrikosov, G-L theory, which is a perturbation theory. Therefore it is valid for T ~ Tc or D ~ 0Non-local effects important at lower temperatures have been shown to introduce large qualitative changes in vortex behavior.Hysteresis (pinning) in magnetization gives unreliable answers for Hc1 and HcFinal problem, Saito introduces Hsh-rf = √2 Hsh-dc ??This is incorrect for phase transition field
18ProblemIf Hrf (0) = 1800 Oe,According to Saito, Hsh (dc) at zero temperature = 1270 Oewhich is << Hc1 (known to be 1740 – 1900 Oe) !!
19Experimentally Peak RF Magnetic Fields Are Rising Experimentally Peak RF Magnetic Fields Are Rising ! Cavities material and surfaces are getting better !
20How to correctly calculate Hsh? Field where barrier vanishesLinear stability analysis will also determine vortex arrayAt large k and T~Tc, 1-D analysis gives Hsh = Hc (as discussed)At lower T, we need the Eilenberger equations(Non-local, Green’s functions, …)
21Fundamental limits to Hsh in Niobium What can theory tell us? James P. Sethna, Gianluigi CatelaniWhy a superheating field?How to calculate Hsh?Field where barrier vanishesLinear stability analysisdetermines nucleationmechanism: vortex arrayAt large k and T~Tc, 1-D analysisHsh = Hcx“Line nucleation” wrongYogi, Saito Hsh~Hc /k discouragingVia “energy balance”, no barrier calculationDoes not work for large k,Hsh < Hc1 = Hc ln(k)/(√2 k)Correct balance theory gives Hc1 not HshBarrierL> xCostly core x enters first;gain from field L later
22James P. Sethna, Gianluigi Catelani Which Theory?James P. Sethna, Gianluigi CatelaniIf we trusted Ginsburg-Landau far below Tc, things looks good:Niobium:Hsh ~ 2400 Oe → 63 MV/mNb3Sn:Hsh ~ 4000 Oe → 110 MV/mBut Ginsburg-Landau is only valid near Tc ;RF cavities at 2K << Tc for NbAt lower T, we need theEilenberger equations(Non-local, Green’s functions, …)Known corrections from G-L:small effects on Hc1, Hc2huge effect on vortex core(collapse from x to 1/kF)Unknown so far:Effect on HshWork proposed & in progress…
23Eilenberger/Gorkov for Hsh in Nb James P. Sethna, Gianluigi CatelaniEquations of motion for the (anomalous) Green’s functions f(w,n,x) and g(w,n,x)Self-consistent equation for gap DMaxwell equation for H from currentConstraint on the Green’s functionMatsubara frequencies w and Fermi wavevector direction nSolve 1D ODE for uniform, superconducting stateFind 2D instability threshold Hsh (functional eigenvalue crosses zero)