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 very high frequencies.
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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 traveling at constant velocity and therefore it 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 (
where
For a superconducting wire, the kinetic inductance can be calculated by equating the total kinetic energy of the Cooper pairs with an equivalent inductive energy:
where
The same procedure can be used to calculate the kinetic inductance of a normal (i.e. non-superconducting) wire, except with
The kinetic inductance increases as the carrier density decreases. Physically, this is because a smaller number of carriers must have a greater velocity than a larger number of carriers in order to achieve the same current. In a normal metal wire, the resistivity also increases as the carrier density
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 be used to make sensitive photon detectors, known as kinetic inductance detectors (KIDs), as the change in the Cooper pair density brought about by the absorption of a photon in a strip of superconducting material produces a measurable change in kinetic inductance.
Kinetic inductance is also used in a design parameter for superconducting flux qubits: