Are longitudinal magnetic waves possible?

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SUMMARY

The discussion centers on the feasibility of longitudinal magnetic waves, specifically within the context of plasma physics and Maxwell's equations. Participants highlight the lack of definitive mathematical proof for the existence of such waves, while referencing the behavior of electromagnetic waves in plasma. Key points include the distinction between near-field and far-field radiation and the implications of frequency and energy coupling methods in plasma. The conversation emphasizes the need for further exploration of longitudinal components in magnetic fields and their decay patterns.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with Lorentz force and its implications
  • Knowledge of electromagnetic waves in plasma
  • Basic principles of near-field and far-field radiation
NEXT STEPS
  • Research "Maxwell's equations and longitudinal waves" for theoretical foundations
  • Explore "Plasma Physics Longitudinal EM" for practical applications
  • Study "near-field vs far-field radiation" to understand wave behavior
  • Investigate methods for "coupling energy to plasma" in experimental setups
USEFUL FOR

Physicists, electrical engineers, and students in advanced electromagnetism or plasma physics who are exploring the theoretical and practical aspects of electromagnetic wave propagation.

Samuel Williams
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Homework Statement



Are longitudinal magnetic waves possible? Give reasons for your answer.

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.
 
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Does the question constrain you to the far-field radiation only?
 
berkeman said:
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.
 
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.
 
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
 

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