# What defines a cold plasma?

Been looking for this very simple answer for a while now, and google returns a face cream with the words cold plasma in it. Very frustrated.

Just wondering, what constitutes a cold plasma in the sense of the energies of the electrons and the energy of photons. Are we looking at non-relativistic photons and the electron velocities being quite slow? i.e.,

$$\beta<<\frac{h\nu}{mc^2}<<1$$

Or are we looking at mildly fast electrons,

$$\frac{h\nu}{mc^2}<<\beta<<1$$

• What's the context? – DilithiumMatrix Nov 17 '15 at 22:49
• Sadly, I haven't been given a specific context. Just the fact that I am dealing with a cold plasma. It relates to compton scattering. – GCien Nov 17 '15 at 22:52
• For most scientists working in the field of plasma physics "cold" plasma would probably mean temperatures 10 eV or less (<100000K). Such plasma temperatures are relevant to plasma processing, etching etc. On the other hand "hot" plasma would be usually understood as something relevant to fusion and astrophysics, with temperatures on the order of 1000 eV and more. – Maxim Umansky Nov 18 '15 at 5:09
• The context is going to determine the answer. There are numerous different definitions (technical and practical) for a 'cold' plasma --- but it varies depending on if you're looking at terrestrial fusion experiments, space weather, stellar coronae, black-hole accretion disks... – DilithiumMatrix Nov 18 '15 at 16:43

This "answer" is just an excert from Cold Plasma

The second type of plasma, named cold or non-equilibrium plasma, is characterised by the electron temperature higher than the ion tempera- ture; it is produced under vacuum conditions using low power rf or microwave or dc sources. The interactions of the plasma particles on the materials produce the modification of the surfaces in order to add different functional properties with respect to the bulk material.

Also I am sure you have checked out Plasma on Wikipedia, where it does make the point that "cold" is relative to your frame of reference, so if you manage to boost to the proper frame of reference, you end up with a "cold" plasma.

Sorry if you have gone through these already, or it's obvious stuff to you already , but the comments box is too small for this post. Maybe google "cold plasma physics velocity" to narrow down your search, and follow on from there, unless you actually want to buy face cream:)

# Zeroth Order Approximation

In the simplest approximation, cold implies that $T_{e} = T_{i} = 0$, where $T_{s}$ is the average temperature of species $s$. There is an entire branch of plasma theory based upon this assumption. It is another way of saying that you assume the plasma is initially at rest with no thermal fluctuations. It also implies the plasma has no pressure, thus no pressure waves can exist if $T_{e} = T_{i} = 0$.

I wrote an answer describing potential wave modes in such a system at: https://physics.stackexchange.com/a/138460/59023.

# Finite Temperature Approximation

In a slightly less extreme approximation, one can argue the plasma is cold when the plasma beta, $\beta$, is very small. That is: $$\beta = \frac{2 \mu_{o} \ n_{o} \ k_{B} \left( T_{e} + T_{i} \right) }{B_{o}^{2}} \ll 1$$ where $n_{o}$ is the charged particle number density, $B_{o}$ is the quasi-static magnetic field, $\mu_{o}$ is the permeability of free space, and $k_{B}$ is the Boltzmann constant. I wrote an answer describing how to define the particle temperatures at: https://physics.stackexchange.com/a/218643/59023.

The answer to your question really depends upon the application or circumstances in which you are interested. For instance, we have found through observations that the whistler mode wave, or the R mode when $\Omega_{ci} < \omega < \Omega_{ce}$ (where $\Omega_{cs}$ is the cyclotron frequency of species $s$), is well characterized by cold plasma dispersion relation in the high density limit (i.e., $\omega^{2} \ll \omega_{pe}^{2}$ and $\Omega_{ce}^{2} \ll \omega_{pe}^{2}$, where $\omega_{ps}$ is the plasma frequency of species $s$) even though we know the plasma is not cold.