So in previous post I defined what plasma is and today I will define some additional criteria that are required for plasma formation.  These criteria are necessary to distinguish between an ionized gas and plasma itself.  Before we do this we need to define the quantity known as Debye length which is the measure of the shielding present in plasma.  This type of shielding is called Debye shielding. What happens inside the plasma is that we have a lot of positively charged particles (ions) and negatively charged particles (electrons) floating around.  If we insert a positively charged sphere into the plasma all of the electrons would rush to it and neutralize the charge.  So we would end up with our positive sphere and a bunch of electrons right around it and the number of electrons would be equal to the charge required to neutralize the positive charge.

In this type of configuration electrons that are closes to the positively charged sphere are held at the highest potential and the one further are at lower potenttial.  Because of this the further the electron is from the sphere the easier it is to knock it out and reduce the amount of shielding.  Most of these electrons are knocked out due to the thermal interactions, thus the edge of the shield is at the location where the potential energei is equal to thermal energy KT of the particles.  Thus from here we can define the Debye length, which is the thickness of the shield, as shown below.

(1)

Equation (1) can further be simplified in equations (2) and (3), thus we don’t need to keep track of the constants. Final units are given in square brackets [].

(2)

(3)

Now that we have defined the Debye length we can use it to look at the criteria necesary in order to call an ionized gas a plasma. On of the additional plasma parameters is , which is the number of particles present inside the Debye shield.  Equation for this quantity is given in equation (4).

(4)

From here we can gather the three criteria that plasma must satisfy are outlined below:

So from here we can gather the first criteria that the plasma length defined as L must be much greater than the Debye length.  Second criteria states that the number of particles inside the Debye shield must be much greater than one, this one seems like a pretty obvious one.  Third criteria, which will be covered in more detail later, states that the product of (frequency of typical plasma oscillations) and (mean time between colissions with neutral atoms) is greater than one.  All these three criteria will ensure that the gas behaves like plasma rather than the neutral gas.