Phase/group refractive index and reflection

[carlos-carlos]

Let's consider a simlified ionosphere. It is a cold plasma without magnetic field and without electron-neutral collisions. The refractive index for radio waves is nf=sqrt(1-(w/wp)^2) (w is the frequency of the radiwave, wp the plasma frequency). It easy to demonstrate that the group refraction index is in this case ng=1/nf.
For vertical incidence the reflection occur at the level where wp=w, i.e where nf->0, and ng ->infinite.
My question is: is this result general?

Does the reflection occur when nf=0 (always)?
Does the reflection occur when ng-> infinite (always)?
Does ng-> infinite when nf->0 (always)?

Regards

Carlos

 

[tech99]

Let's consider a simlified ionosphere. It is a cold plasma without magnetic field and without electron-neutral collisions. The refractive index for radio waves is nf=sqrt(1-(w/wp)^2) (w is the frequency of the radiwave, wp the plasma frequency). It easy to demonstrate that the group refraction index is in this case ng=1/nf.
For vertical incidence the reflection occur at the level where wp=w, i.e where nf->0, and ng ->infinite.
My question is: is this result general?

Does the reflection occur when nf=0 (always)?
Does the reflection occur when ng-> infinite (always)?
Does ng-> infinite when nf->0 (always)?

Regards

Carlos

My understanding is that Refractive Index = SQRT(1-(fc/f)^2)
I had not made the connection that Critical Frequency=Plasma Frequency, but if so, the formulas are different.
We know that at the critical frequency the (group) delay rises steeply and it seems that the wave then stops.
The Wiki article on Plasma Frequency seems to agree with you:-
https://en.wikipedia.org/wiki/Plasma_oscillation

 

[carlos-carlos]

Let's consider a simlified ionosphere. It is a cold plasma without magnetic field and without electron-neutral collisions. The refractive index for radio waves is nf=sqrt(1-(w/wp)^2) (w is the frequency of the radiwave, wp the plasma frequency). It easy to demonstrate that the group refraction index is in this case ng=1/nf.
For vertical incidence the reflection occur at the level where wp=w, i.e where nf->0, and ng ->infinite.
My question is: is this result general?

Does the reflection occur when nf=0 (always)?
Does the reflection occur when ng-> infinite (always)?
Does ng-> infinite when nf->0 (always)?

Regards

Yes. Sorry. The right formula is nf=sqrt(1-(wp/w)^2), wp= plasma frequency, w= frequency of the radiowave. When the wave approaches a region where wp become =w (the electron density is sufficient) nf=0, ng-> infinite, and the reflection occur.

Bt my main question is: is this result general?

Does the reflection occur when nf=0 (always)?
Does the reflection occur when ng-> infinite (always)?
Does ng-> infinite when nf->0 (always)?

RegardsCarlos