Fundamental Parameters

Consider an idealized plasma consisting of an equal number of electrons, with mass $m_e$ and charge $-e$ (here, $e$ denotes the magnitude of the electron charge), and ions, with mass $m_i$ and charge $+e$ . Without necessarily assuming that the system has attained thermal equilibrium, we shall employ the symbol

$$T_s \equiv \frac{1}{3} \,m_s\, \langle \,v_s^{\,2}\rangle$$ (1.1)

to denote a kinetic temperature measured in units of energy. Here, $v$ is a particle speed, and the angular brackets denote an ensemble average (Reif 1965). The kinetic temperature of species $s$ is a measure of the mean kinetic energy of particles of that species. (Here, $s$ represents either $e$ for electrons, or $i$ for ions.) In plasma physics, kinetic temperature is invariably measured in electron-volts (1 joule is equivalent to $6.24\times 10^{18}$ eV).

Quasi-neutrality demands that

$$n_i \simeq n_e \equiv n,$$ (1.2)

where $n_s$ is the particle number density (that is, the number of particles per cubic meter) of species $s$ .

Assuming that both ions and electrons are characterized by the same temperature, $T$ (which is, by no means, always the case in plasmas), we can estimate typical particle speeds in terms of the so-called thermal speed,

$$v_{t\,s} \equiv \left(\frac{2\,T}{m_s}\right)^{1/2}.$$ (1.3)

Incidentally, the ion thermal speed is usually far smaller than the electron thermal speed. In fact,

$$v_{t\,i} \sim \left(\frac{m_e}{m_i}\right)^{1/2}v_{t\,e}.$$ (1.4)

Of course, $n$ and $T$ are generally functions of position in a plasma.