Electrostatic waves in a plasma

[Getterdog]

TL;DR

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]

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

 

[tech99]

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.