Basic definitions and parameters
In this chapter we learn in what conditions a new state of matter - plasma - appears.
What is plasma
Plasma is usually said to be a gas of charged particles. Taken as it is, this definition
is not especially useful and, in many cases, proves to be wrong. Yet, two basic
necessary (but not sufficient) properties of the plasma are: a) presence of freely
moving charged particles, and b) large number of these particles. Plasma does not
have to consists of charged particles only, neutrals may be present as well, and their
relative number would affect the features of the system. For the time being, we,
however, shall concentrate on the charged component only.
Large number of charged particles means that we expect that statistical behavior
of the system is essential to warrant assigning it a new name. How large should it
be ? Typical concentrations of ideal gases at normal conditions are n ∼ 1019 cm−3 .
Typical concentrations of protons in the near Earth space are n ∼ 1 − 10cm−3 .
Thus, ionizing only a tiny fraction of the air we should get a charged particle gas,
which is more dense than what we have in space (which is by every lab standard a
perfect vacuum). Yet we say that the whole space in the solar system is filled with
a plasma. So how come that so low density still justifies using a new name, which
apparently implies new features ?
A part of the answer is the properties of the interaction. Neutrals as well as
charged particles interact by means of electromagnetic interactions. However, the
forces between neutrals are short-range force, so that in most cases we can consider
two neutral atoms not affecting one another until they collide. On the other hand,
each charged particle produces a long-range field (like Coulomb field), which can
affect many particles at a distance. In order to get a slightly deeper insight into the
significance of the long-range fields, let us consider a gas of immobile (for simplicity) electrons, uniformly distributed inside an infinite cone, and try to answer the
question: which electrons affect more the one which is in the cone vertex ? Roughly
speaking, the Coulomb force acting on the chosen electron from another one which
is at a distance r, is inversely proportional to the distance squared, fr ∼ 1/r2 .
Since the number of electrons which are at this distance, Nr ∝ r2 , the total force,
Nr fr ∼ r0 , is distance independent, which means that that electrons which are
very far away are of equal importance as the electrons which are very close. In other