# Are longitudinal magnetic waves possible?

## Homework Equations

Working with Maxwell's equations, Lorentz force, electrostatic and electromagnetic waves in plasma.

## The Attempt at a Solution

No idea whatsoever. I believe it is possible based on articles read on the matter, but have no idea how to prove it mathematically (or disprove if not possible). Any help would be greatly appreciated.

berkeman
Mentor
Does the question constrain you to the far-field radiation only?

Does the question constrain you to the far-field radiation only?
Not that I am aware of, which is why I believe it to be possible. The question is as given with no further details or information.

berkeman
Mentor
So analyze the near-field pattern of an antenna, and show the longitudinal component of the B-field and how it decays with distance from the antenna...?

I haven't really thought about that to be honest, since the section of work is with regards to plasma and magnetized plasma.

berkeman
Mentor
Well, depending on the frequencies used to heat the plasma, and the methods used to couple that energy to the plasma, is any of the EM in the near field? If it's microwave radiation that is coupled in via waveguides, you are probably in the far field by the time the EM gets to the plasma...

There is no frequency given, so I'm "assuming" we can take any value and essentially work under any ideal conditions that would provide such waves. I have been googling for a while which is why I decided to post here. There are a few good ones, but they seem to refer mainly to electromagnetic waves propagating with no sure solution given. I have been reading this mainly

https://physics.stackexchange.com/questions/22170/why-no-longitudinal-electromagnetic-waves/22177

but again, I can't see how to prove it. Thanks for the assistance so far btw