# Electrostatic waves in a plasma

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## Summary:

Electrostatic waves in plasma with no B produced?
I’m having A bit of confusion regarding this. In a plasma by turning on an electric field ,wouldn’t this cause an oscillation of the electrons about the ions,effectively a oscillating dipole thus inducing a magnetic field, by amperes law? My text (plasma physics by F.Chen )has curlE =0 I’m not seeing how no magnetic field is created in electrostatic waves. Thanks for any help. Jack

jasonRF
Gold Member
Hi Jack,

The derivation you are referring to is almost certainly special in 2 ways: it is in 1-D, and it is a linearization of some plasma model (probably a fluid theory?). I think that the 1-D nature is probably the main reason why we can find the pure electrostatic solutions. In more general situations (and for some other kinds of waves) the 1-D assumption fails, but still the predictions of an electrostatic approximation can agree very well with experiments.

I'm not sure if there an equivalent fluid-theory calculation, but at least in kinetic theory (which Chen has a basic chapter on) it is possible to construct exact solutions to the nonlinear kinetic model for 1-D electrostatic waves of almost any profile you want.
Bernstein–Greene–Kruskal modes - Wikipedia
Of course they are electrostatic in only one frame of reference, and in this case it is the frame moving with the wave. EDIT: this is for a collisionless model, which is a very good model for places like the Earth’s magnetosphere.

jason

Last edited:
tech99
Gold Member
Summary:: Electrostatic waves in plasma with no B produced?

I’m having A bit of confusion regarding this. In a plasma by turning on an electric field ,wouldn’t this cause an oscillation of the electrons about the ions,effectively a oscillating dipole thus inducing a magnetic field, by amperes law? My text (plasma physics by F.Chen )has curlE =0 I’m not seeing how no magnetic field is created in electrostatic waves. Thanks for any help. Jack
If we have two charges vibrating "end to end", they each have a magnetic field surrounding them, but this does not seem to link the two charges together. I don't think they are linked by the magnetic fields but just by an electric field. This is also the experience using metal rods mounted end-to-end at radio frequencies, where we find electric coupling.