Boltzmann distribution of electrons at thermal equilibrium in a plasma

Question

In Chen's Introduction to Plasma Physics and Controlled Fusion, it says the following during the discussion of Debye shielding:

However the last equation tells me that the electron density $n_e$ will be larger in places of higher potential, in apparent contradiction with the statement that at places where the potential energy is large, fewer particles are present. Where is my interpretation wrong?

Answer 1

Your are confusing electric potential and potential energy.

The charge of the electron is negative.

Therefore the potential energy of the electron is negative where the electric potential is large, (and positive where it is very negative). As expected, where the electric potential is large, the potential energy of electrons is very negative and the density is large.