Simulation Of Vortex Pinning in Two-Band Superconductors Chad Sockwell Florida State University kcs12j@my.fsu.edu February 5, 2016 Chad Sockwell (FSU) Modeling SC February 5, 2016 1 / 13
About Me Chad Sockwell Undergrad in Physics and S.C. at FSU (Honors Thesis) Modeling Superconductivity With Max Gunzburger and Janet Peterson Currently Master’s student in S.C. Applying to DOE Fellowship Possible PhD in Physics or SC Chad Sockwell (FSU) Modeling SC February 5, 2016 2 / 13
Outline Background and Motivation Simulation of Superconductivity Challenges and Future Work Chad Sockwell (FSU) Modeling SC February 5, 2016 3 / 13
Background What is a Superconductor Some are penetrated only by (SC)? tubes of flux (Vortices) Zero Electrical Resistance No Waste Heat Normal metals are penetrated by Mag. Fields Some SC are not (Meissner Effect) Figure : 3D SC with Vortices Chad Sockwell (FSU) Modeling SC February 5, 2016 4 / 13
Why Vortex Dynamics are Important Moving Vortices (Flux flow) creates Resistance f ˆ x = J ˆ y × B ˆ z E ˆ y = B ˆ z × u ˆ x Vortices (B) + Current (J)= Flux flow Flux Flow induces Electric Field (E) and Voltage (V) Resistance Now Exists ( V I =R) Chad Sockwell (FSU) Modeling SC February 5, 2016 5 / 13
Vortex Pinning Comes to the Rescue Immobilizing the Vortices Is Crucial Non Superconducting Metal= Normal Metal= Pinning Sites (Outlined in Black) Vortices ”Stick” To Impurities Limited Increase In J c Chad Sockwell (FSU) Modeling SC February 5, 2016 6 / 13
Applications of Large Scale Simulations Large Scale Simulations Could Improve Technology: Efficient Current Carriers MRI Powerful Magnets (by Efficient Mag Lev magnetization) Chad Sockwell (FSU) Modeling SC February 5, 2016 7 / 13
Modeling Vortex Pinning with Normal Inclusions TD-Ginzburg-Landau model ( Coupled System of NL PDES) ψ ∈ C , Like complex phase field order parameter A ∈ R 2 magnetic vector potential Γ( ∂ψ ∂ t − i κ σ Jy ) + ( | ψ | 2 − τ ) ψ + ( i κ ∇ − A ) 2 ψ = 0 in Ω σ∂ A ∂ t − J + ∇ × ∇ × A + i 2 κ ( ψ ∗ ∇ ψ − ψ ∇ ψ ∗ ) + | ψ | 2 A = ∇ × H in Ω ∇ × A × n = ( H − J ˆ z ( x − L / 2)) × n on ∂ Ω A · n = 0 on ∂ Ω ∇ ψ · n = 0 on ∂ Ω ψ ( t = 0) = ψ 0 ; A ( t = 0) = A 0 ; ∇ · A ( t = 0) = 0 in Ω Chad Sockwell (FSU) Modeling SC February 5, 2016 8 / 13
Model To Simulation Simulation of Magnesium Diboride (Two Band Model) Need Material Parameters: κ , σ , Γ Various Inputs: Field ( H ), Applied Current ( J ), Temperature ( τ ) Change Material Parameters in Normal Metals (Impurities) Γ( ∂ψ ∂ t − i κ σ Jy ) + ( | ψ | 2 − τ ) ψ + ( i κ ∇ − A ) 2 ψ = 0 in Ω σ∂ A ∂ t − J + ∇ × ∇ × A + i 2 κ ( ψ ∗ ∇ ψ − ψ ∇ ψ ∗ ) + | ψ | 2 A = ∇ × H in Ω Chad Sockwell (FSU) Modeling SC February 5, 2016 9 / 13
Numerical Methods FEM → Triangular Piecewise Parabolic Elements & Gauss Quadrature Newton’s Method, Full Jacobian Sparse Storage (CRS) Adaptive Backward Euler Parallel Solver (SUPERLU) (9/10 NL Time Cost) These methods were ”Good Enough for Now” Chad Sockwell (FSU) Modeling SC February 5, 2016 10 / 13
Passing a Resistance Free Current Metal - Superconductor Interface ψ → 0 in Vortices and Metals Flux Flow produces Resistive (or Normal) Current Impurities Outline In Black Normal Current → Resistance Did Pinning Prevent Flux Flow? Chad Sockwell (FSU) Modeling SC February 5, 2016 11 / 13
Computational Challenges For Practical Simulation Large Spatial and Time Scale Large Storage Costs → Distributed memory Long Solve Times → Parallel Iterative Solvers & Preconditioners Trilinos Distributed Environment & Solver’s ML & Hypre AMG Preconditioners? Jacobian Free Newton-Kylov Methods? 3D-Modeling to Infinity BEM for the Exterior? Finding Maximum Current Optimization, Continuation? Chad Sockwell (FSU) Modeling SC February 5, 2016 12 / 13
Need Lots of Vortices Chad Sockwell (FSU) Modeling SC February 5, 2016 13 / 13
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