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.
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 (
LK
\tau
{\sigma(\omega)=\sigma1-i\sigma2
\sigma=
ne2\tau | |
m(1+i\omega\tau) |
=
ne2\tau | \left( | |
m |
1 | -i | |
1+\omega2\tau2 |
\omega\tau | |
1+\omega2\tau2 |
\right)
where
m
n
≈ 10-14
{\omega\tau}
\sigma0=ne2\tau/m
{\tau → infty}
For a superconducting wire of cross-sectional area
A
l
I
1 | |
2 |
(2me
2)(n | ||
v | lA)= | |
s |
1 | |
2 |
2 | |
L | |
KI |
where
me
2me
v
ns
l
A
I
I=2evnsA
e
L | \right)\left( | ||||
|
l | |
A |
\right)
The same procedure can be used to calculate the kinetic inductance of a normal (i.e. non-superconducting) wire, except with
2me
me
2e
e
ns
n
L | \right)\left( | ||||
|
l | |
A |
\right)
The kinetic inductance increases as the carrier density decreases. Physically, this is because a smaller number of carriers must have a proportionally greater velocity than a larger number of carriers in order to produce the same current, whereas their energy increases according to the square of velocity. The resistivity also increases as the carrier density
n
\omega\tau
Kinetic inductance is the principle of operation of the highly sensitive photodetectors known as kinetic inductance detectors (KIDs). The change in the Cooper pair density brought about by the absorption of a single photon in a strip of superconducting material produces a measurable change in its kinetic inductance.
Kinetic inductance is also used in a design parameter for superconducting flux qubits:
\beta