2) Plasma oscillations
Imagine having a homogeneous distribution of positive and
negative charges (electrons and protons or nuclei), with charges +e and -e and masses
M and m respectively. M is at least 2000 times larger than m, so we can safely
say that the protons stay fixed in a homogeneous distribution, while the
electron gas is free to move.
Suppose we have a rectangular box of plasma with equal density of
negative (electrons) and positive (ions) charges. We take all the electrons and
move them to the right. The situation now is the following
The positive (left) and the negative (right) regions will attract
each other. This will lead to the electrons moving to the left. If one thinks
of a harmonic oscillator (although we have not proven that this is one!), one
expects the electrons to continue moving to the left, because of their inertia,
until the above figure is reversed
This will reverse the situation, with the electrons moving to the
right, and so on!
Now that we know what we expect, we can use simple math to
actually derive it. Ready to be young plasma physicists?
Let us assume that the charge density of the plasma is “n”, and
the dislocation distance is “x”. The electric field (remember the parallel
plate capacitor) is
.
The force is proportional to the distance, so this IS a harmonic
oscillator (our intuition was right)!
By using 
, which describes
an oscillation with frequency 
. This is called
Plasma Frequency.
Wasn’t hard, right?
An important
note: Obviously real
plasmas are not rectangular boxes that we can manipulate so easily! In that
case, what we will have will be an area of increased electron density. They
will repel each other, leading to their separation. Due to their inertia they
will leave behind an area of small electron density (net positive charge), so
they will be then pulled back together.
Do you know any
waves that exhibit such a behavior, producing regions of high and low density?
Sound Waves!!!
Sound waves are
longitudinal waves, unlike the transverse electromagnetic waves in vacuum!
WHAT? We have
the laws of electromagnetism leading to waves different than the good-old
vacuum plane-waves!
We see that plasmas increase the
complexity of wave phenomena.
Are you
intrigued? Do you want to know what other types of waves can occur in plasmas?
If yes, the next
session is for you!