Exploring 'Cold' Electrons & Plasma Oscillations

[ShayanJ]

In some texts about plasmas, the plasma oscillations are discussed at the extreme of no Thermal motion. One example is the one in wikipedia:

'Cold' electrons

If the thermal motion of the electrons is ignored, it is possible to show that the charge density oscillates at the plasma frequency
$\omega_{pe} = \sqrt{\frac{n_e e^{2}}{m^*\varepsilon_0}}, \left[rad/s\right] (SI \ units), \\ \omega_{pe} = \sqrt{\frac{4 \pi n_e e^{2}}{m^*}}, (cgs \ units),$
where $n_e$ is the number density of electrons, e is the electric charge, m* is the effective mass of the electron, and $\varepsilon_0$ is the permittivity of free space. Note that the above formula is derived under the approximation that the ion mass is infinite. This is generally a good approximation, as the electrons are so much lighter than ions. (One must modify this expression in the case of electron-positron plasmas, often encountered in astrophysics). Since the frequency is independent of the wavelength, these oscillations have an infinite phase velocity and zero group velocity.

Note that, if$m^*$is electron mass $(m^*=m_e)$, plasma frequency $\omega_{pe}$ depends only on physical constants and concentration of electrons $n_e$. The numeric expression for plasma ordinary frequency
$f_{pe}=\omega_{pe}/2\pi$
is
$f_{pe} \approx 8980 \sqrt{n_e} Hz$
with number density $n_e$ in $cm^{–3}$.

But I can't accept that approximation.Because it is assuming that we have a kind of motion called thermal motion and other kinds which arise from other things.But that's wrong and its the motion of particles that causes a feeling of temperature and when there is motion there is a non-zero temperature.
Can anyone explain?
Thanks

 

[DrClaude]

But I can't accept that approximation.Because it is assuming that we have a kind of motion called thermal motion and other kinds which arise from other things.But that's wrong and its the motion of particles that causes a feeling of temperature and when there is motion there is a non-zero temperature.
Can anyone explain?
Thanks

I'm not an expert in plasmas, but I think that what you have to consider is the difference between "absolute" speed and a speed distribution. What temperature gives you is a distribution of velocities. Take for example a container full of gas and fly it in a jet airplane at mach 2: you wouldn't consider that the temperature of the gas has changed because of this, even though the gas molecules are going much faster than they normally do at room temperature.

My guess is that this is the approximation made here: the distribution of velocity of the electrons due to temperature can be neglected, and you can consider the motion to be only due to the plasma oscillation, i.e., as the motion of the electrons in the collective Coulomb field of the ions and electrons.

 

[Khashishi]

The cold plasma approximation of course is not appropriate in all situations. But it can be useful for solving for plasma waves which propagate much faster than the thermal velocity. It doesn't matter if the plasma is pretty hot. It's still looks cold relative to a sufficiently fast plasma disturbance. The cold plasma equations give solutions for relatively fast waves in the plasma, which are approximately correct for a warm plasma.