Re: How can the light colour of a plasma be predicted?

Hi Mark

Thank you for your very interesting questions. First of all, your observations are correct: a hydrogen plasma can often be purple (or purplish red), yet the light of the Sun is white. What causes this? I'm afraid the answer to this question is not easy at all, and I can only scratch the surface in this post. First, I'll discuss what a plasma is, and how it can emit light. Then, I will go into more detail about the specifics of your question.

A plasma is in essence a gas in which some of the atoms are molecules are split into ions and free electrons. This fraction is so large that it significantly alters the properties of the gas. This has a pretty big impact. First of all, a plasma is electrically conductive. Secondly, it is chemically active. Molecules form and get destroyed, and they can ionize or recombine with their electron. One more process that is important is the excitation of atoms. In this process, one of the electrons from an atom is moved into a higher orbit. This can be a stepstone towards ionization, or it can lead to the electron falling back, emitting light.

In a plasma like this, there are four main sources of radiation:

1. Line radiation. This emerges from atoms that are excited. Line radiation is monochromatic, just like a laser. What color the light coming from a line is depends (almost solely) on the atom. The rest of the plasma properties (pressure, temperature, energy density, composition) determine which line is strongest.
2. So-called Brehmsstrahlung. This is the light the free electrons emit when they move close to charged particles, like the ions. This radiation is broad-band (emits many colors at the same time) and depends on electron density and temperature, chiefly.
3. Two-particle recombination. In this process, an electron and ion combine, emitting a photon. This produces light that is somewhat similar to the light emitted by Brehmsstrahlung, i.e. broad-band radiation.
4. Molecular radiation. Molecular radiation is emitted by molecules. Practically speaking, it broad-banded, although not as broad-banded as Brehmsstrahlung and the light emitted by two-particle recombination.

Making this even more complicated, these processes might be in partial equilibrium. This means, for instance, that an atomic transition (an electron being excited) absorbs light, rather than emitting it. In the limit, this will result in the emission of blackbody radiation. In this case, the radiative emission is solely determined by the temperature, and the Stefan-Boltzmann law.

As you might have guessed, actually figuring out what sort of radiation a plasma will emit is devilishly difficult. There is a vast amount of interconnected processes. The fact that many plasmas have some sort of transport in them makes matters even worse. The method of choice for solving this problem is by numerical analysis. It is not uncommon for an entire PhD-project to be spent on the analysis of but a single plasma. Radiative transport is particularly hard, as it is non-local: light generated in one part of the plasma can have an almost immediate impact in another part.

Fortunately, some rules of thumb do exist on how what sort of light a plasma will emit. In your specific case, you are talking about a rocket exhaust, I assume from an ion-engine like system. This is a recombining plasma, that is rather sparse. The mains source of light will be from line radiation. This line radiation will be monochromatic, and depend on the plasma composition. For most ion engines, a heavy noble gas is used. The heaviest stable noble gas is Xenon, and this emits a bluish white light. On the other hand, there is nothing stopping you from imagining it is any sort of gas that is being emitted, and this could result in nearly any type of light being emitted. You can look up colors of plasma quite easily on the Internet. Note that denser plasmas tend to be more whitish in general, and sparser plasmas more colorful.

I hope this answers your question.

Regards,

Bart Broks

Sources: I did my PhD in computational plasma physics, so I am fairly familiar with this problem.