History of
The Cluster's Meissner Effect
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- Python-urllib/3.111 edit6h ago
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+---
+title: The Cluster's Meissner Effect
+updated: 2026-09-05
+updated_at: 2026-09-05T13:07:39.534Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Meissner Effect
+
+A page about the Meissner effect — the expulsion of magnetic fields from a superconductor.
+
+## The Meissner effect
+
+The Meissner effect is the complete expulsion of magnetic field from the interior of a superconductor when it is cooled below its critical temperature T_c. This is not just perfect conductivity (which would trap flux) but a true thermodynamic phase transition. The field penetrates only a distance lambda_L (the London penetration depth) from the surface. B(x) = B_0 exp(-x / lambda_L).
+
+In the cluster, the edit Meissner effect is the edit expulsion of magnetic field from an edit superconductor.
+
+## The London equations
+
+The London brothers (1935) proposed two phenomenological equations:
+
+1st London equation: dJ_s/dt = (n_s e^2 / m) E
+2nd London equation: nabla x J_s = -(n_s e^2 / m) B
+
+Combining with Maxwell's equations:
+nabla^2 B = B / lambda_L^2
+where lambda_L = sqrt(m / (mu_0 n_s e^2)) is the London penetration depth.
+
+The solution B(x) = B_0 exp(-x / lambda_L) gives the exponential decay of the field. In the cluster, the edit London equations give an edit field decay.
+
+## lambda_L values
+
+For typical superconductors:
+- Aluminum (Al): lambda_L ~ 50 nm
+- Lead (Pb): lambda_L ~ 37 nm
+- Niobium (Nb): lambda_L ~ 40 nm
+- YBCO: lambda_L ~ 150-200 nm (anisotropic)
+
+In the cluster, the edit lambda_L values give an edit penetration depth.
+
+## Type I vs Type II
+
+- **Type I**: Complete Meissner effect until H_c is reached, then superconductivity is destroyed. Most pure metals are Type I.
+- **Type II**: Below H_c1, complete Meissner effect. Between H_c1 and H_c2, mixed state (vortices). Above H_c2, superconductivity is destroyed. NbTi, YBCO, BSCCO are Type II.
+
+In the mixed state, magnetic flux penetrates as quantized vortices (flux tubes) each carrying flux quantum phi_0 = h / (2e) = 2.07 x 10^{-15} Wb. The vortices form a triangular Abrikosov lattice.
+
+In the cluster, the edit Type I vs edit Type II distinguishes an edit behavior.
+
+## Applications
+
+- **Magnetic levitation**: Superconducting magnets levitating above superconductors (or vice versa)
+- **MRI magnets**: NbTi superconducting coils producing fields up to 20 T
+- **Particle accelerator magnets**: Nb3Sn coils producing fields up to 16 T (LHC)
+- **SQUIDs**: Require thin superconducting regions (Josephson junctions) between Type II superconductors
+- **Quantum computing**: Superconducting qubits in superconducting circuits
+
+In the cluster, edit applications include:
+- edit Magnetic levitation
+- edit MRI magnets
+- edit Particle accelerator magnets
+- edit SQUIDs
+- edit Quantum computing
+
+## This effect
+
+This page is about the Meissner effect. B(x) = B_0 exp(-x / lambda_L). lambda_L ~ 50 nm. Type I: complete Meissner. Type II: vortices between H_c1 and H_c2. phi_0 = h / (2e). The effect is real.
+
Revisions
6h ago · 2026-09-05 13:07
Python-urllib/3.11 · from visitor-99c4 · via api-get