# Can radioactive decay particles be modeled as plasma?

Since plasma is simply ionized gas (ie. charged particles), with the exception of neutron ejection (no charge) and gamma radiation (photons), can the natural decays of an isotope be modeled as plasma?

Is there some lower density limit for plasma models to be valid? Would something like the daughter particles of alpha decay, a single He+2 charge and a single daughter-2 charge be effectively plasma? (or more technically, 2 different plasmas)

Let's assume this radioactive decay is happening in a vacuum like outer space for example. Within the walls of a vacuum chamber are these decayed charged particles plasma? And more importantly, if there are many (ie. lots of radiation from the fuel source), will the particles collectively behave like plasma?

To call a certain system a plasma there are usually three criteria that need to be fulfilled:

1. $\lambda_D\ll L$, with $\lambda_D$ the Debye length and $L$ the spatial dimension of the plasma,
2. $N_D\gg1$, with $N_D$ the number of particles in the Debye's sphere,
3. $\omega_{pe}\tau_{0e}>1$, with $\omega_{pe}$ the electron plasma frequency and $\tau_{0e}$ the collision time between electrons and neutrals.

I'll try to explain:

1. A plasma consists of charged particles (and neutrals). If you put a small test charge into a plasma, its electric field is quickly shielded by particles of the opposite charge. The Debye length is the length after which the electric field of the test charge has decreased to $1/e$ of its original value. The result is that a plasma is in general quasi-neutral. Hence, if this criterion is not fulfilled, the plasma is no longer quasi-neutral.
2. As just explained a test charge is screened by particles in the plasma. The parameter $N_D$ is a measure for the number of those particles (the screening particles are said to be inside the Debye sphere which has a radius of $\lambda_D$). Since the main interacting force in a plasma are Coulomb interactions, we have a lot of collective motions going on. If this criterion in not fulfilled, there are too few particles to exhibit a pronounced collective behaviour in the plasma and this feature is lost.
3. If, somehow, an electric field is applied to a plasma, the electrons will react to it, trying to cancel this field. They will start to oscillate and the frequency is the plasma frequency. This oscillation is the result of the Coulomb interaction and, as already said in the previous point, is the main interaction in a plasma. Long range interactions dominate. Unless you have a lot of collisions between neutral and electrons going on, such that the system will be more of gas-kinetic type (and no longer plasma-like).

Having said that, it is clear that there is no strict boundary and transition to the plasma state. Trying to answer your question, if you have only the two particles, they would certainly not be called a plasma. If you have a bunch of them, that might be the case (i.e. we have to calculate the parameters mentioned above - they depend on number density and energy of the particles).

• Surely your first condition is $\lambda_D\ll L$? – A.V.S. Apr 24 '18 at 17:55
• I'm so glad I asked, Thanks! I'll have to run the number to see at what point a contained alpha decaying isotope would behave like plasma. Container size, EM field, and decay rate are all going to play a factor. – RocketTwitch Apr 25 '18 at 0:08
• @Twitchykid I'm glad that I could help, feel free to accept the answer, if you like :-) – Alf Apr 25 '18 at 19:32
• @Alf Wanted to see if anyone else felt like answering but it's been over 24 hours so accepted :) – RocketTwitch Apr 26 '18 at 0:06