It can be shown that the potential, V, around an infinitesimal perturbation of charge q at a distance r is given by
with
where:
• k is Boltzmann’s constant,
• T the electron temperature,
• n the plasma density, and
• e the electron charge.
is called the Debye
length. It is a characteristic length scale of the shielding of the electric field
by the plasma around a small perturbation. In a non-perturbed plasma the space
charge vanishes over volumes greater than the Debye length. Around a large
electric perturbation the electric field is shielded as well but over a length
scale which can be several order of magnitude greater than . The region around such a perturbation where the plasma is
not neutral is called the sheath.
Normal range of values of the Debye length in a various plasma region are given in Table C-1.