The effect of a radio wave on an electron

[tech99]

This is my simple thinking on the topic. If I consider the ionosphere as a conductor, then neglecting Earth's magnetic field, the electrons will have the same motion, though smaller, as those in the transmitting antenna. The latter does not have a DC component. The EM wave can have asymmetrical half-cycles, that is permissible, but due to the absence of any DC component, they will have the same area (field x time), so that overall the electron must end up at the same position and with the same velocity after the passage of one complete wave.

 

[sophiecentaur]

If the wave is pulsed, then Fourier tells us it is a continuous carrier modulated by the pulse waveform.

You are assuming simple amplitude modulation but many signals are not modulated symmetrically with amplitude (old steam TV, for instance). You can go for any shape you like if your transmitting equipment will support it.
Edit: I see you just made more or less the same comment.

 

[A.T.]

If I consider the ionosphere as a conductor,

What exactly does this mean? Which of the below proportionalities are you assuming?

In the ionosphere, the acceleration of the electron is proportional to E(t).
In a resistor, the drift-velocity of the electrons is proportional to E(t).

they will have the same area (field x time), so that overall the electron must end up at the same position and with the same velocity after the passage of one complete wave.

If the field is proportional to the acceleration of the electron, and not to its velocity, then why would it end up at the same position, if it was initially at rest? Only the velocity changes (integral of acceleration) have to cancel over the passage of one complete wave.

 

[Roberto Pavani]

Just a small note: the TV signal mentioned is DC-coupled at baseband, the asymmetry exists only because there's a ground reference. Once radiated, it's effectively AC-coupled: no DC component can propagate through an EM wave, so the energy over a full cycle is always balanced.

As for treating the ionosphere as a conductor, that changes the scenario entirely. At that point you need to model it as a conductor with losses, or as a plasma and things get considerably more complicated, both for RF propagation in plasmas and for resonance effects in the ionospheric cavity.

I think the original problem considers a single electron precisely to avoid all of this.

 

[sophiecentaur]

the asymmetry exists only because there's a ground reference. Once radiated, it's effectively AC-coupled:

Sorry; AM TV is not an example - except that is is not pure DSB AM; the higher frequencies are not DSB so the envelope is not exactly symmetrical. Nevertheless, it is not hard to produce a signal on which the (say) positive excursions of the carrier are not the same amplitude as the negative excursions. But, of course, the mean level will still be zero. If you can do it at AC coupled audio, you can do it at RF.

I think the original problem considers a single electron precisely to avoid all of this.

Agreed but iit concludes / implies that electrons will all go in the same direction and that's the flaw in the suggestion of failure of constant momentum. The 'ideal' model is incomplete.

Good chat tho'.

 

[sophiecentaur]

There is a change of velocity for different ion densities which accounts for refraction on the way through (mf and LF propagation through the ionosphere) and often total internal reflection. That took comms engineers by surprise in the early days. Good and bad news, there.

But, having thought about this for a while (after several decades) there's no problem in the whole concept; change in momentum of photons and electrons gives dispersion

 

[sophiecentaur]

@tech99 As I wrote in posting #5,
In the ionosphere, the acceleration of the electron is proportional to E(t).
In a resistor, the drift-velocity of the electrons is proportional to E(t).

In a metal, the terminal velocity is relevant. In the upper atmosphere there is no loss mechanism on a moving particle due to the very low density of the plasma

 

[tech99]

In a metal, the terminal velocity is relevant. In the upper atmosphere there is no loss mechanism on a moving particle due to the very low density of the plasma

Yes agree. Disregarding Earth's magnetic field, I think the electron in the ionosphere will have simple harmonic motion which is greater as the frequency becomes lower.

 

[Roberto Pavani]

Not an expert in RF plasma propagation, but the ionosphere reflects most HF (3–30 MHz), and the electron gyrofrequency f_H ≈ 1.4 MHz (for B ≈ 50 μT) dominates the electron dynamics below that frequency. "Simple harmonic motion" seems an oversimplification.

See ITU-R P.531-16 for the role of f_H in the ionospheric refractive index.
https://www.itu.int/rec/R-REC-P.531-16-202509-I/en

 

[tech99]

Yes I agree with that but the initial question seems to be about just the effect of an EM wave on an electron in a plasma and does not include Earth's magnetic field.

 

[Sagittarius A-Star]

Yes agree. Disregarding Earth's magnetic field, I think the electron in the ionosphere will have simple harmonic motion which is greater as the frequency becomes lower.

plus a drift in $x$-direction

$x(t) = \dfrac{a_0}{\omega}t-\dfrac{a_0}{\omega^2}\sin\omega t$