Relaxation and Electromagnetic Response of a Superconductor in a State of Supercurrent Flow

The situation is investigated in which a superconductor in a state of supercurrent flow and near the transition temperature is exposed to an alternating electric field. The induced alternating current is shown to exhibit a frequency dependence ${(1\ensuremath{-}i\ensuremath{\Omega}{\ensuremath{\tau}}_{\mathrm{R}})}^{\ensuremath{-}1}$, which is due to a relaxation process in the Cooper-pair density. The relaxation time ${\ensuremath{\tau}}_{\mathrm{R}}$ is determined by electron-phonon collisions (collision time ${\ensuremath{\tau}}_{c}$), in which case ${\ensuremath{\tau}}_{\mathrm{R}}\ensuremath{\simeq}{\ensuremath{\tau}}_{c}{[\frac{{T}_{c}}{({T}_{c}\ensuremath{-}T)}]}^{\frac{1}{2}}$; impurity scattering is important only under certain conditions, in which case ${\ensuremath{\tau}}_{\mathrm{R}}\ensuremath{\simeq}{10}^{\ensuremath{-}11}{[\frac{{T}_{c}}{({T}_{c}\ensuremath{-}T)}]}^{\ensuremath{-}5}$ sec.

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