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Lecture Note 1
1.1 Plasma
99% of the matter in the universe is in the plasma state.
Solid -> liquid -> Gas -> Plasma (The fourth state of matter)
Recall: Concept of Temperature
A gas in thermal equilibrium has particles of all velocities, and the most probable
distribution of these velocities is known as the Maxwellian distribution.
The average kinetic energy Eav equals 1/2kT per degree of freedom. k is Boltzmann’s
constant.
Since T and Eav are so closed related, it is customary in plasma physics to give
temperatures in units of energy. To avoid confusion on the number of dimensions
involved, it is not Eav , but the energy corresponding to kT that is used to denote the
temperature. For kT = 1 eV = 1.6 x 10-19 J, we have
19
23
1.6 10 11,600
1.38 10
T
?
?
×
= =
×
Thus the conversion factor is
1eV = 11,600 K
A plasma is a gas in which an important fraction of the atoms in ionized, so that the
electrons and ions are separately free.
When does this ionization occur? When the temperature is hot enough.
Saha Equation:
Which tells us the amount of ionization to be expected in a gas in thermal equilibrium:
3/ 2
i 2.4 1021 exp( / )
i
n i
n T U kT
n n
? × ?
Here ni and nn are, respectively, the number density (number per m3) of ionized atoms
and of neutral atoms, T is the gas temperature in K, k is Boltzmann’s constant, and Ui is
the ionization energy of the gas—that is, the number of ergs required to remove the
outmost electron from an atom. For ordinary air at room temperature, T ~ 300 K, and Ui
= 14.5 eV (for nitrogen). The fractional ionization /( ) / i i n i n n n + n ? n n is ridiculously low:
i 10 122
n
n
n
? ?
As the temperature is raised, the degree of ionization remains low until Ui is only a few
times kT. Then / i n n n rises abruptly, and the gas is in plasma state.
Any ionized gas cannot be called a plasma, of course; there is always some small degree
of ionization in any gas. A useful definition is as follows:
A plasma is a quasineutral gas of charged and neutral particles which exhibits collective
behavior.
Collective behavior:
For ordinary air, the molecule is neutral, there is no net electromagnetic force on it, and
the force of gravity is negligible. The molecule moves undisturbed until is makes
collision with another molecule, and these collisions control the particle’s motion. The
situation is totally different in a plasma, which has charged particles. As these charges
move around, they can generate local concentrations of positive or negative charge,
which give rise to electric fields. Motion of charges also generates currents, and hence
magnetic fields. These fields affect the motion of other charged particles far away.
It is the long-ranged Coulomb force that gives the plasma a large repertoire of possible
motions and enriches the field of study known as plasma physics. By “collective
behavior” we mean motions that depend not only on local conditions but on the state of
the plasma in remote regions as well.
Quasi Neutral:
If a gas of electrons and ions (singly charged) has unequal numbers, there will be a net
charge density, ? .
? = ne (?e) + ni (+e) = e(ni ? ne )
This will give rise to an electric field via.
0 0 / / ( ) i e ?? E = ? ? = e ? n ? n
Example: Slab
0
0
/
/
dE
dx
E x
? ?
? ?
=
? =
This results in a force on the charges tending to expel whichever species is in excess.
That is, if i e n > n , the E field causes i n to decrease, e n to increase tending to reduce the
charge.
This restoring force is enormous!
Example
Consider Te = 1 eV, ne = 1019 m-3 (a modest plasma; c.f. density of atmosphere
nmolecules~3 x 1025 m-3
Suppose there is a small difference in ion & electron densities ( ) i e ?n = n ? n
So ? = ?n? e
Then the force per unit volume at distance x is
2 2