Electrostatic waves in a plasma

In summary, the derivation for pure electrostatic solutions in 1-D situations agrees well with experiments, but in more general situations, the 1-D assumption fails. However, in kinetic theory, it is possible to construct exact solutions to the nonlinear kinetic model for 1-D electrostatic waves. These waves are only electrostatic in a frame of reference moving with the wave and are a good model for places like the Earth's magnetosphere.
  • #1
Getterdog
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TL;DR 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
 
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  • #2
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
 
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  • #3
Getterdog said:
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.
 

1. What is a plasma?

A plasma is a state of matter that occurs when a gas is heated to extremely high temperatures or exposed to strong electromagnetic fields. In this state, the gas becomes ionized, meaning that the atoms lose or gain electrons, resulting in a mixture of positively and negatively charged particles.

2. How are electrostatic waves generated in a plasma?

Electrostatic waves in a plasma are generated by the collective motion of charged particles in response to an applied electric field. This can occur naturally in space plasmas, or can be artificially induced in laboratory plasmas.

3. What are the properties of electrostatic waves in a plasma?

Electrostatic waves in a plasma have several important properties, including their frequency, wavelength, and phase velocity. They can also exhibit a variety of different modes, such as ion-acoustic waves, Langmuir waves, and electron plasma waves.

4. How do electrostatic waves affect the behavior of a plasma?

Electrostatic waves play a crucial role in the dynamics of plasmas, influencing processes such as energy transport, particle acceleration, and wave-particle interactions. They can also be used to diagnose the properties of a plasma and control its behavior.

5. What are some applications of electrostatic waves in a plasma?

Electrostatic waves in a plasma have a wide range of applications, including in plasma-based technologies such as fusion energy, plasma processing, and space propulsion. They are also important in understanding natural phenomena such as auroras, solar flares, and cosmic rays.

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