Why is it that only thermal energy is available in a particle propagating throughout a space-charge layer in a plasma (not kinetic)? In this PDF on page 5 the author explains that a particle moving through a space-charge (electron density in a plasma) gains only thermal energy. Should there not also be kinetic energy?
 A: 
In this PDF on page 5 the author explains that a particle moving through a space-charge (electron density in a plasma) gains only thermal energy.

After a little more digging, I think I found to what you refer (which is actually on page 3).
The plasma oscillations to which the author refers are known as Langmuir waves.  In freshman physics, you probably learned that the magnitude electric field between a parallel plate capacitor goes as:
$$
E \approx \frac{\sigma}{\varepsilon}
$$
where $\sigma$ is the charge density per unit area and $\varepsilon$ is the electrical permittivity between the plates.  If the two parallel plates are infinite, then the above approximation becomes an equation as discussed at https://physics.stackexchange.com/a/65194/59023.

Should there not also be kinetic energy?

In a plasma, however, there are two things missing that are involved in parallel plate capacitors:


*

*external battery doing work on the system; and

*mechanical forces holding two charged sheets apart.


So then one can go back to freshman physics and think about two finite charge sheets.  For now, assume something holds them apart.  If the sheets of charge are finite in size, then the following must be true assuming no external fields or power source are present:
$$
\oint_{C} \mathbf{E} \cdot d\mathbf{l} = 0
$$
Meaning, there is no net electric potential across the sheets.  Therefore, particles cannot gain a net kinetic energy since the field is conservative and there are no external batteries/power sources doing work on the system.
Now if we let go of the two sheets of charge, they will oscillate and produce the standard plasma oscillations that are always observed (e.g., seen as the upper hybrid line or plasma line, as shown at http://www-lep.gsfc.nasa.gov/waves/index.html).  There is, however, nothing to prevent Coulomb collisions from occurring during the oscillation, which can result in a net change in the average kinetic energy of the particles in their bulk flow rest frame, i.e., heating and/or cooling.
