Uploaded by karlberggren on 17.01.2011

Transcript:

Kinetic Inductance Explained

I'm gonna talk today about Kinetic Inductance. So kinetic inductance is different from what

you normally think of when you think of inductance because it's due to the kinetic energy of

the charge carriers rather than due to magnetic fields or magnetic inductance. So, if you

for instance think about any inductor, we can actually draw a kinetic inductor the same

way we would draw a magnetic inductor. It has a current, and the voltage across the

inductor varies with the rate of change of the current and the constant of the proportionality

as the inductance. If we think about the energy stored in the inductor, we can write that

as one-half L-I squared. And I should mention in this videos that I'm gonna assume that

you've got some circuits and physics background at least up to the sophomore level, so if

you need a refresher on some of these things you can leave some comments at the bottom

and we'll point out some resources that may help you.

So if we think about the magnetic field that's generated by current flowing through a wire,

what you'd realize is that that magnetic field stores energy. But there's another type of

energy that is stored from the current through the wire which we normally don't have to worry

about because in normal metals and at low frequencies, it's dissipated quickly into

the metal just through collisions and so it doesn't play a role in the circuits. But that's

kinetic energy, and the kinetic energy you can calculate from your classical mechanics,

it's just one-half times the total mass times the velocity squared. Now, we're kind of making

a simplification here to assume that everything, all these charge carriers in here, are moving

with the same velocity. But let's assume that, let's assume they have some charge E and they

have some number density which we'll call N, okay, so there's a simple relation that

relates the current to the average velocity and that's just the current as a cross-sectional

area times the number density times the charge times the average velocity, the charge carriers,

and you can re-arrange that if you like to do Algebra, and that's V equals I over A-N-E

and then you can substitute this into our kinetic energy relation which I'll do for

you. One-half times the mass which is just the mass of an electron times the number density

times the volume which is A times the length of the wire. L is the length of the wire,

so that's the total mass times the velocity which is I over A-N-E, this is squared. And

if you do the algebra carefully, make sure you don't lose any factors of, or do anything

like that, or you'd end up with one-half L-N over A-N-E squared, I squared. And then, if

you notice the analogy, this is a close analogy to the expression we used at the start for

magnetic field inductance, one-half L-I squared, and that's indeed the point because this term

here is effectively an inductance. So we call it L of K, and that's the kinetic inductance.

So, just a couple of things to note about it, so the kinetic inductance is a lot like

resistance in that it can be written as a geometric factor, the length of the wire divided

by the area, times a material definite factor which is the mass charged carrier divided

by their density times E squared, and that, so we can write that as L over A times something that we'll

call the inductivity which we'll write as a cursive L, and that's the inductivity.

So, that's all for today. This kinetic inductance plays an important role in thin superconducting

films, it dominates over the magnetic inductance in many cases. It also plays an important

role in high frequency fields interacting with metals, so it's the dominant form of

inductance in a plasmon for example, and so this area is something worth knowing about

that's not normally discussed.

I'm gonna talk today about Kinetic Inductance. So kinetic inductance is different from what

you normally think of when you think of inductance because it's due to the kinetic energy of

the charge carriers rather than due to magnetic fields or magnetic inductance. So, if you

for instance think about any inductor, we can actually draw a kinetic inductor the same

way we would draw a magnetic inductor. It has a current, and the voltage across the

inductor varies with the rate of change of the current and the constant of the proportionality

as the inductance. If we think about the energy stored in the inductor, we can write that

as one-half L-I squared. And I should mention in this videos that I'm gonna assume that

you've got some circuits and physics background at least up to the sophomore level, so if

you need a refresher on some of these things you can leave some comments at the bottom

and we'll point out some resources that may help you.

So if we think about the magnetic field that's generated by current flowing through a wire,

what you'd realize is that that magnetic field stores energy. But there's another type of

energy that is stored from the current through the wire which we normally don't have to worry

about because in normal metals and at low frequencies, it's dissipated quickly into

the metal just through collisions and so it doesn't play a role in the circuits. But that's

kinetic energy, and the kinetic energy you can calculate from your classical mechanics,

it's just one-half times the total mass times the velocity squared. Now, we're kind of making

a simplification here to assume that everything, all these charge carriers in here, are moving

with the same velocity. But let's assume that, let's assume they have some charge E and they

have some number density which we'll call N, okay, so there's a simple relation that

relates the current to the average velocity and that's just the current as a cross-sectional

area times the number density times the charge times the average velocity, the charge carriers,

and you can re-arrange that if you like to do Algebra, and that's V equals I over A-N-E

and then you can substitute this into our kinetic energy relation which I'll do for

you. One-half times the mass which is just the mass of an electron times the number density

times the volume which is A times the length of the wire. L is the length of the wire,

so that's the total mass times the velocity which is I over A-N-E, this is squared. And

if you do the algebra carefully, make sure you don't lose any factors of, or do anything

like that, or you'd end up with one-half L-N over A-N-E squared, I squared. And then, if

you notice the analogy, this is a close analogy to the expression we used at the start for

magnetic field inductance, one-half L-I squared, and that's indeed the point because this term

here is effectively an inductance. So we call it L of K, and that's the kinetic inductance.

So, just a couple of things to note about it, so the kinetic inductance is a lot like

resistance in that it can be written as a geometric factor, the length of the wire divided

by the area, times a material definite factor which is the mass charged carrier divided

by their density times E squared, and that, so we can write that as L over A times something that we'll

call the inductivity which we'll write as a cursive L, and that's the inductivity.

So, that's all for today. This kinetic inductance plays an important role in thin superconducting

films, it dominates over the magnetic inductance in many cases. It also plays an important

role in high frequency fields interacting with metals, so it's the dominant form of

inductance in a plasmon for example, and so this area is something worth knowing about

that's not normally discussed.