Classical Electrodynamics · Problem 12.21

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · two-fluid-model-superconductor

Problem

A two-fluid model for the electrodynamics of superconductors posits two types of electron, normal and superconducting, with number densities, charges, masses, and collisional damping constants, njn_j, eje_j, mjm_j, and γj\gamma_j, respectively (j=j = N, S). The electrical conductivity consists of the sum of two terms of the Drude form (7.58) with f0N→njf_0 N \to n_j, e→eje \to e_j, m→mjm \to m_j, γ0→γj\gamma_0 \to \gamma_j. The normal (superconducting) electrons are distinguished by γN≠0\gamma_N \neq 0 (γS=0\gamma_S = 0). (a) Show that the conductivity of the superconductor at very low frequencies is largely imaginary (inductive) with a small resistive component from the normal electrons. (b) Show that use of Ohm's law with the conductivity of part a in the Maxwell equations results in the static London equation for the electric field in the limit ω→0\omega \to 0, with the penetration depth (12.100), provided the carriers are identified with the superconducting component of the electric fluid.

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