# 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. – garyp Jun 22 '18 at 14:56
• @garyp nice reference! – Alf Jun 22 '18 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? – Sean Daley Jun 24 '18 at 16:02
• @SeanDaley good question, in my understanding such plasma are often referred to as non-ideal plasmas – Alf Jun 24 '18 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. – honeste_vivere Dec 3 '19 at 20:16