Kinetic inductance

Kinetic inductance is the manifestation of the inertial mass of mobile charge carriers in alternating electric fields as an equivalent series inductance. Kinetic inductance is observed in high carrier mobility conductors (e.g. superconductors), and at high frequencies.

Explanation

A change in electromotive force (emf) will be opposed by the inertia of the charge carriers since, like all objects with mass, they prefer to be travelling at constant velocity and it therefore takes a finite time to accelerate the particle. This is similar to how a change in emf is opposed by the finite rate of change of magnetic flux in an inductor. The resulting phase lag in voltage is identical for both energy storage mechanisms, making them indistinguishable in a normal circuit.

Kinetic inductance arises naturally in the Drude model of electrical conduction when the relaxation time (collision time) $au$ is taken to be non-zero. This model defines a complex conductivity in a time-varying electric field of frequency $omega$ given by $\{sigma(omega)\; =\; sigma\_\{1\}\; -\; isigma\_\{2$ - the imaginary part arising due to kinetic inductance. This complex conductivity can be expanded into its real and imaginary components:

$sigma\; =\; frac\{ne^2\; au\}\{m(1+iomega\; au)\}\; =\; frac\{ne^2\; au\}\{m(1+omega^2\; au^2)\}-ifrac\{ne^2omega\; au^2\}\{m(1+omega^2\; au^2)\}$

where $m$ is the mass of the charge carrier (i.e.; effective electron mass in metallic conductors) and $n$ is the carrier number density. In normal metals the collision time is normally $approx\; 10^\{-14\}$ s, so for frequencies < 100 GHz the term $\{omega^2\; au^2\}$ is very small and can be ignored. Kinetic inductance is therefore only really noticeable at optical frequencies and in superconductors when $\{\; au\; ightarrow\; infty\}$.

Applications

Kinetic inductance in superconductors is exploited to make efficient microwave delay lines as it increases the inductance per unit length of superconducting transmission lines. Kinetic inductance can also be used for sensitive photon detection, as the change in the superconducting carrier (Cooper pair) density brought about by an incident photon produces a measurable change in kinetic inductance.

See also

* Drude model
* Electrical conduction
* Electron mobility
* Inductance
* Superconductivity