PS508A: We have seen how complicated a mixture a plasma can be: Fundamentals of Industrial Plasmas Assignment, DCU, Ireland

Particle Transport and Loss

We have seen how complicated a mixture a plasma can be, so to simplify
matters let us consider the simplest possible plasma made only of electrons,
one type of ion and one type of neutral. The transport of charged particles
is dealt with in this section. For low pressure plasmas this deals with the
basic question of how particles move to the walls. We also look at what
happens right next to any solid walls in contact with the plasma.

8.1 Diffusion

Particles in a gas undergo a random walk process as they move about. Collisions change the direction of motion while the particles move in straight
lines between collisions. Because we are dealing with enormous numbers of
particles, we can take it that the changes in direction are completely random, and this means that there is no preferred direction for the particles to
move in. If we start by labeling a group of particles in a region A and then
follow them, we will find them spreading out in all directions as they move
about and collide with other particles and each other.

Now consider two separated (equal volume) regions A and B. If we label all
the particles in these regions and follow them, we will find that after a time
some of the particles from A find their way to B and vice versa. However,
if A initially contained more particles than B then we would find that more
particles from A have ended up in B than the other way round.

The random walk process thus tends to equalise the density in the gas,
smoothing out any peaks and filling in any hollows, and this applies equally
well whether we are considering neutral molecules or charged particles. The
diffusion of particles can be expressed by Fick’s law which relates the resulting flux Γ to the density gradient which causes it,

Γ = −D∇n