Plasma parameters

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged and neutral particles of various species (electrons and ions) that responds collectively to electromagnetic forces. Such particle systems can be studied statistically, i.e., their behaviour can be described based on a limited number of global parameters instead of tracking each particle separately.

Fundamental
The fundamental plasma parameters in a steady state are Using these parameters and physical constants, other plasma parameters can be derived.
 * the number density $$n_s$$ of each particle species $$s$$ present in the plasma,
 * the temperature $$T_s$$ of each species,
 * the mass $$m_s$$ of each species,
 * the charge $$q_s$$ of each species,
 * and the magnetic flux density $$B$$.

Other
All quantities are in Gaussian (cgs) units except energy and temperature which are in electronvolts. For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, $$\mu = m_i/m_p$$ and the ion charge in units of the elementary charge $$e$$, $$Z = q_i/e$$ (in the case of a fully ionized atom, $$Z$$ equals to the respective atomic number). The other physical quantities used are the Boltzmann constant ($$k$$), speed of light ($$c$$), and the Coulomb logarithm ($$\ln\Lambda$$).

Dimensionless

 * number of particles in a Debye sphere $$\left(\frac{4\pi}{3}\right)n\lambda_D^3 \approx 1.72 \times 10^9\,\left(\frac{T^3}{n}\right)^\frac{1}{2}$$
 * Alfvén speed to speed of light ratio $$\frac{v_A}{c} \approx 7.28\,\frac{B}{\left(\mu n_i\right)^\frac{1}{2}}$$
 * electron plasma frequency to gyrofrequency ratio $$\frac{\omega_{pe}}{\omega_{ce}} \approx 3.21 \times 10^{-3}\,\frac{{n_e}^\frac{1}{2}}{B}$$
 * ion plasma frequency to gyrofrequency ratio $$\frac{\omega_{pi}}{\omega_{ci}} \approx 0.137\,\frac{\left(\mu n_i\right)^\frac{1}{2}}{B}$$
 * thermal pressure to magnetic pressure ratio, or beta, β $$\beta = \frac{8\pi nkT}{B^2} \approx 4.03 \times 10^{-11}\,\frac{nT}{B^2}$$
 * magnetic field energy to ion rest energy ratio $$\frac{B^2}{8\pi n_i m_i c^2} \approx 26.5\,\frac{B^2}{\mu n_i}$$

Collisionality
In the study of tokamaks, collisionality is a dimensionless parameter which expresses the ratio of the electron-ion collision frequency to the banana orbit frequency.

The plasma collisionality $$\nu^*$$ is defined as $$ \nu^* = \nu_\mathrm{ei}\,\sqrt{\frac{m_\mathrm{e}}{k_\mathrm{B} T_\mathrm{e}}}\,\frac{1}{\epsilon^\frac{3}{2}} \, qR, $$ where $$\nu_\mathrm{ei}$$ denotes the electron-ion collision frequency, $$R$$ is the major radius of the plasma, $$\epsilon$$ is the inverse aspect-ratio, and $$q$$ is the safety factor. The plasma parameters $$m_\mathrm{i}$$ and $$T_\mathrm{i}$$ denote, respectively, the mass and temperature of the ions, and $$k_\mathrm{B}$$ is the Boltzmann constant.

Electron temperature
Temperature is a statistical quantity whose formal definition is $$T = \left(\frac{\partial U}{\partial S}\right)_{V,N},$$ or the change in internal energy with respect to entropy, holding volume and particle number constant. A practical definition comes from the fact that the atoms, molecules, or whatever particles in a system have an average kinetic energy. The average means to average over the kinetic energy of all the particles in a system.

If the velocities of a group of electrons, e.g., in a plasma, follow a Maxwell–Boltzmann distribution, then the electron temperature is defined as the temperature of that distribution. For other distributions, not assumed to be in equilibrium or have a temperature, two-thirds of the average energy is often referred to as the temperature, since for a Maxwell–Boltzmann distribution with three degrees of freedom, $\langle E \rangle = \frac 3 2 \, k_\text{B} T$.

The SI unit of temperature is the kelvin (K), but using the above relation the electron temperature is often expressed in terms of the energy unit electronvolt (eV). Each kelvin (1 K) corresponds to $8.617 eV$; this factor is the ratio of the Boltzmann constant to the elementary charge. Each eV is equivalent to 11,605 kelvins, which can be calculated by the relation $$\langle E \rangle = k_\text{B} T$$.

The electron temperature of a plasma can be several orders of magnitude higher than the temperature of the neutral species or of the ions. This is a result of two facts. Firstly, many plasma sources heat the electrons more strongly than the ions. Secondly, atoms and ions are much heavier than electrons, and energy transfer in a two-body collision is much more efficient if the masses are similar. Therefore, equilibration of the temperature happens very slowly, and is not achieved during the time range of the observation.