# Differences between thermal and non-thermal plasmas

I have a doubt about plasmas which may as well be trivial or very stupid, but I couldn't get a clear and straightforward answer anywhere I looked, and I can't get the grasp of it since I wasn't given an adequate theoretical introduction to plasma physics before doing a preliminary laboratory about them.

As far as I know, the difference between cold (or non-thermal) and hot (thermal) plasmas is in the ionic temperature: cold plasmas have $T_i\ll T_e$, and in particular $T_i \approx T_r$ (where with $T_r$ I indicate room temperature, $25\ mEv$), while $T_e$ (the electronic temperature) stands reasonably high (in our case, an hydrogen plasma, it lies between $2$ and $5\ eV$).

The fact is I'm not sure what causes that difference. I mean, artificial plasmas generated by electromagnetic resonances can be both cold (laboratory plasmas) and hot (fusion ones).

Question number one: can plasmas generated by heat, like stars, only be thermal, or can they be non-thermal too?

Let's then pick an example of a resonance plasma: electrons are given enough energy to break free from atomic bonds. So, I would think that ion temperature stays low because nuclei are almost not given any energy at all by the radiation, maybe because the radiation frequency is similar to the one of the electrons revolving around the nuclei. Is that correct?

I don't think it is because the fact $m_i \gg m_e$ causes the positive ions to move at much lower speed, since temperature depends on kinetic energy, and not on speed alone. So we should take account of the fact nucleons are more massive than electrons when talking about temperature (after all, energy is conserved; since we give a certain energy to all particles, not depending on which species they belong to, with a radiation, and since we talk about temperature we mean thermal energy, ion and electron temperature should then be the same).

Question number two: then, what causes the two temperatures to be that different in laboratory plasmas? What's the difference with fusion ones, why have they $T_i\approx T_e$?

• AFAIK, thermal means the particles follow a Maxwell-Boltzmann distribution while non-thermal means they don't (e.g., a power-law velocity distribution). – Kyle Kanos Jan 27 '16 at 11:00
• @KyleKanos - One of my profs in grad school would always point out that a power-law could be constructed by summing a large number of Maxwellians... So he would laugh and say there is no such thing as a non-thermal distribution (in a somewhat facetious manner). – honeste_vivere Jan 27 '16 at 14:03
• @honeste_vivere: In physics a "thermal" state requires there to be (at least approximately) one temperature, not the superposition of an infinite number of temperatures, so your example doesn't really do anything. – CuriousOne Jan 27 '16 at 15:56
• @honeste_vivere: The interactions only regulate the thermalization timescale, not the definition of thermal state. Yes, plasmas are complicated, but their complications don't change the fundamental definitions of thermodynamics, even though they may make thermodynamics useless for most technically important plasmas. – CuriousOne Jan 27 '16 at 16:35
• @honeste_vivere: Yes, exactly. I do agree, by the way, that most plasmas are very hard to deal with and will, for the most part, not be in thermal equilibrium unless they are in a real bulk (like inside the sun). The boundary layers (like at the edge to vacuum) are almost inevitably in a non-equilibrium state because of the formation of charge layers. – CuriousOne Jan 27 '16 at 16:46

# Background

Generally speaking, in plasma physics one uses the terms cold and hot to refer to the ratio of the thermal, $V_{T,j}$, to bulk flow speeds, $V_{o,j}$. Meaning, a cold(hot) plasma has $V_{T,j} \ll V_{o,j}$($V_{T,j} \gg V_{o,j}$). A quick reference of the possible thermal speeds can be found in this answer. For more information on cold vs. hot, see this answer.

For a proton-electron plasma, if $T_{e} \approx T_{p}$, then due to $m_{e} \ll m_{p}$ one can see that $V_{T,e} \gg V_{T,p}$.

To think about temperature in a plasma you need to be careful about the type of plasma. In a plasma that is not controlled by Coulomb collisions, the temperature is not as clearly defined as one might recall from fluid dynamics. One can still calculate the various velocity moments of the distribution function, but temperature becomes more of a measure of the average kinetic energy of a species in its bulk flow rest frame than the standard thermodynamic quantity.

# Questions

Question number one: can plasmas generated by heat, like stars, only be thermal, or can they be non-thermal too?

Generally speaking, for a plasma to be considered "thermal" in the context of which you speak, the gas would need to be dominated/controlled by Coulomb collisions. The result would be a Maxwellian-like velocity distribution (i.e., gaussian).

The lower atmosphere (i.e., low chromosphere and photosphere) of the sun is thought to be a collisional plasma, thus much of the plasma is thermalized. However, once the plasma reaches the upper atmosphere (i.e., corona), Coulomb collisions start to lose relevance to other faster mechanisms like wave-particle interactions. This is all ignoring the complications introduced by transient phenomena like solar flares and coronal mass ejections.

The solar wind is generally considered to be weakly collisional at best, but for most scenarios it is usually assumed to be collisionless. The velocity distributions of both the ions and electrons are typically composed of several components.

Ions
For the ions, they are often composed of the following components:

1. the core/beam of the bulk flow, which is a cold bi-Maxwellian;
2. a secondary proton beam streaming along the quasi-static magnetic field; and
3. an alpha-particle beam.

Electrons
For the electrons, they are often composed of the following components:

1. a core distribution which has $V_{T,ec} \gg V_{o,ic}$ ($c$ stands for core) but generally follows the ion core in bulk flow and can often be modeled as a bi-Maxwellian;
2. a hotter halo is not Maxwellian-like, it is better modeled by a kappa distribution (which is similar to having power-law tails extend off of the core);
3. a strahl component, which is an anisotropic (in temperature) beam streaming along the quasi-static magnetic field.

So both the ions and electrons have multiple components, many of which are not modeled as thermalized distributions (i.e., non-Maxwellian profiles). Thus, stars are fully capable of generating what many people would call nonthermal plasmas.

Question number two: then, what causes the two temperatures to be that different in laboratory plasmas? What's the difference with fusion ones, why have they $T_{i} \approx T_{e}$?

This depends upon how the plasmas were made and what the relevant parameters (e.g., plasma beta, ratio of cyclotron-to-plasma frequency, etc.). It may also depend upon the type of ions used, since the mass ratio between ions and electrons is relevant for energy exchange processes between the two species.

The reasons relate to how the plasma is heated once formed. One way of doing this in fusion research is to use the instabilities that naturally occur within all plasmas. An instability is a mechanism by which free energy can be transferred to/from the electromagnetic fields from/to the particles. Generally, the free energy exists in the particles as a non-Maxwellian feature (e.g., a secondary beam or temperature anisotropy) and the instability then radiates an electromagnetic wave. During the process of the radiation, the energy used to produce the wave is taken out of the particle distributions in an attempt to remove the free energy. Once the wave exists, it can then further interact with the plasma (interesting side note: the wave interacts most strongly and efficiently with the types of particle distributions that radiated them in the first place).

Some of these instabilities are very good at transferring energy between the ions and electrons (e.g., lower-hybrid drift, ion-acoustic, whistler-types, etc.). These types of instabilities can lead to situations where $T_{i} \approx T_{e}$ (However, as I stated above, if the plasma is not controlled by collisions, then the temperature is really defined by component.). There is something to note though. The waves radiated by instabilities will interact with particles over a specific range of energies and phases, not the entire distribution. Thus, they often lead to further non-Maxwellian features rather than relaxing the distribution to an isotropic Maxwellian.

So to answer your question, I am inclined to think the temperature equilibriation in fusion plasmas results from the instabilities generated (and sometimes used) to heat the plasma. The plasmas in any lab device are generally created for a specific purpose, so the experimenters generally want specific parameters for various levels of control. Unfortunately, there are dozens of reasons why $T_{i} \approx T_{e}$ and why $T_{i} \neq T_{e}$ in plasmas. Without knowing further specifics, I cannot further elaborate.