# Plasma in solids

One way to create plasma is to focus a very powerful laser pulse to a small beam waist. In gaseous atoms, ionization will occur, yielding a soup of ions and electrons, which we call a plasma.

But you can focus the beam into a transparent solid, like glass, too. Many researchers in the field of high-intensity laser physics say that there is "plasma in the solid". For example, in Durand et al. [Phys. Rev. Lett 110, 115003 (2013)], laser filamentation occurs in fused-silica, which by definition requires plasma (they even calculate plasma absorption). Take a look at side images of the laser filament in their study: My question: is it formally correct to call this a plasma in solids, since we generally think of plasma as an ionized gas? Is it more like material damage, or electron-hold pairs, instead of plasma?

To call a system a plasma, three criteria have to be fulfilled (as I have explained in more detail in another question):

1. $\lambda_D \ll L$, with $\lambda_D$ the Debye length and $L$ the spatial dimension of the plasma,
2. $N_D\gg 1$, with $N_D$ the number of particles in the Debye sphere,
3. $\omega_{pe}\tau_{0e}>1$, with $\omega_{pe}$ the electron plasma frequency and $\tau_{0e}$ the collision time between electrons and neutrals.

Looking into the paper you are referring to, I find the following numbers:

• $n_e\approx 10^{24}\,\mathrm{m}^{-3}$
• $L\approx40\,\mathrm{\mu m}$ (taking the beam diameter as diameter of the plasma column)

Scanning a little bit the literature, I get some additional numbers:

• $T_e\approx 100\,\mathrm{eV}$ [1-3]

With those numbers we can estimate $\lambda_D\approx70\,\mathrm{nm}$ and $N_D\approx1700$, so criterion 1 and 2 are fulfilled.

As for criterion 3, your reference is stating the neutral density to be $n_0\approx10^{28}\,\mathrm{m}^{-3}$. To estimate a value for the collision time, we need to estimate the cross section. I would guess it to be roughly $10^{-15}\mathrm{cm}^2$ $-$ note, I am bit unsure here, so this value might be off by a one or two orders of magnitude. The resulting mean free path evaluates to something on the order of picometers (calculating $\lambda_{\mathrm{}}=1/(\pi r^2 n_0)$) and the corresponding collision time to something on the order of $10^{-18}\mathrm{s}$ (from $\lambda/v_{th}$ with $v_{th}$ the thermal velocity of the electrons). Finally, the product of the electron plasma frequency with the collision time, $\omega_{pe}\tau_{0e}>1$, seems not to be larger than 1 (roughly $10^{-4}$), so this criterion is violated which means that long range interactions are somewhat suppressed in these plasmas.

Please comment and correct if you find anything wrong in the last part.

• Sometimes these "plasmas" in solids are called so because they behave like a plasma optically. I.e., they are reflective. So it would seem that in some cases your third criterion is satisfied. I don't know enough about the topic to say anything more. This reference might help with details. Jun 22, 2018 at 14:56
• @garyp nice reference!
– Alf
Jun 22, 2018 at 18:14
• Very nice response. So you conclude that although this system behaves like a plasma, it technically does not qualify as one based on violation of criterion 3. In that case, do you have any suggestions on what this system would technically be classified as? Jun 24, 2018 at 16:02
• @SeanDaley good question, in my understanding such plasma are often referred to as non-ideal plasmas
– Alf
Jun 24, 2018 at 19:20
• Although I tend to think of a solid as a grouping of atoms/molecules that are spatially rigid on relevant length and time scales, one could argue that some stellar cores may satisfy such a criteria. That is, the density and pressure are sufficiently high to keep even an ionized, kinetic gas from behaving like a typical plasma. Dec 3, 2019 at 20:16