# Is there a phase transition between a gas and plasma?

Does a phase transition occur as a gas is heated to create a plasma? If so, is this a first or second order phase transition?

Also, does the presence of a phase transition depend on the pressure or composition? It seems to me that in the dilute limit (i.e. low pressures), no phase transition should occur because the fraction of atoms that are ionized will follow a Boltzmann distribution, which is a smooth function of temperature. However, the presence of phase transitions in Debye-Hückel theory seems to suggest that a gas-plasma transition could occur at higher pressures.

• Yea - this is an adequate explanation of what a phase transition is: en.wikipedia.org/wiki/Phase_transition. From gas to plasma you have ionization; from plasma to gas you have recombination. – astromax Nov 6 '13 at 19:48
• What would be the order parameter? – codeAndStuff Nov 6 '13 at 19:58
• @astromax: really? If you created a plasma in a calorimeter would you see discontinuities? I suspect there would be no obvious transition. – John Rennie Nov 6 '13 at 20:00
• @JohnRennie, if you could define an order parameter that becomes finite once the constituents start to dissociate then you could identify the critical point. However, whether you could call it a phase transition as in the phenomenological theory may be another question because I am unfamiliar with plasmas in general. You may be stuck calling it a crossover... – codeAndStuff Nov 6 '13 at 20:04
• @MaxGraves I would imagine that the density of the fluid could be an order parameter, as in a liquid-gas transition. The fraction of molecules that are ionized might work as well. – Max Radin Nov 6 '13 at 20:14

The short rough answer is no. The transition between gaseous state and plasma is continuous and gradual. Phase transition typically happens at constant temperature for given pressure, which doesn't happen for plasma. Have a look here.

Some references classify the transition from gaseous state to plasma as a special type of phase transition called second order phase transition.The difference between the second order and first order (standard well known phase transition) is that second order is gradual while first order is sudden. Have a look here.

So if you are referring to standard definition of phase transition, the answer is no.

Hopefully that helped

• Why the downvote? I know nothing about plasmas - if there is a flaw in this answer, I'd like to know what it is. Downvoting without leaving an explanation means no-one learns anything. – WetSavannaAnimal Nov 6 '13 at 23:41
• Thanks for your answer. I wasn't the one who downvoted, but I would say that the "standard" definition of a phase transition includes second order transitions. – Max Radin Nov 7 '13 at 16:45
• As long as the difference between liquid turning into gas and gas turning into plasma is clear, that is great!! It doesn’t really make a big difference to say yes or no as long as the concept is clear – Gotaquestion Nov 7 '13 at 16:48
• @MaxRadin Your question became vague after you edited it. I am doing my PhD in plasma and people in plasma field talk about phase transitions either for plasma crystallization or dense plasma like quark-gloun plasma. No body really argues about phase transition when creating plasma. I feel your question is about creating plasma and its pressure dependence rather than classifying its creation into phase transition or not, am I right? – Gotaquestion Nov 7 '13 at 18:02

The plasma properties already become palpable at a low degree of ionization. On the other hand the degree of ionization never reaches 100% in a macroscopic plasma (where thermal collisions occur): there will always be some electrons and ions recombining somewhere (equilibrium). So it seems like the 'perfect' plasma state is only asymptotic as $T\rightarrow\infty$. For practical purposes, a plasma with a high degree of ionization is considered fully ionized.

The obvious order parameter is something like the fraction of atoms or molecules ionized, say "x'. Simple stat mech says that at any finite temperature that will be in the range (0,1). The question is whether, for some density of particles, there's a discontinuity as a function of T in either x (first order) or dx/dT (second order). There's a reason some such discontinuity could happen. As more ions form, the Debye screening cloud lowers the free-energy of ion formation. That cooperative phenomenon, like many others, e.g. spin-spin interactions in magnets,can in principle lead to runaway feedback to a new phase. It's a quantitative question. A very quick first calculation indicates that unless the density of ions becomes larger than ~(kT/e^2)^3 (in cgs units), there won't be a phase transition. (Here k is Boltzmann's constant, T is temperature, and e is the ion charge.) Since x doesn't get large until T is pretty high, (Boltzmann factor), and since you don't have a gas to start with unless the overall concentration is pretty low, I think you typically don't get a phase transition. Somebody with more detailed knowledge should check that. Of course, the quantitative comparisons are completely different for say quark-gluon matter, etc.

• Hi mike, and welcome to Physics Stackexchange! This isn't a bad answer, but you may want to break up long posts into more than one paragraph for readability. Also, you can typeset math with Latex-style MathJax on this site. (If you're not familiar with the notation, here is a very complete reference.) – user10851 Feb 12 '15 at 23:56