# Plasma parameters

It has been suggested that Electron temperature be merged into this article. (Discuss) Proposed since September 2018. |

**Plasma parameters** define various characteristics of a plasma, an electrically conductive collection of charged particles that responds *collectively* to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains.^{[1]} The behaviour of such particle systems can be studied statistically.^{[2]}

## Contents

## Fundamental plasma parametersEdit

All quantities are in Gaussian (cgs) units except energy and temperature expressed in eV and ion mass expressed in units of the proton mass ; is charge state; is Boltzmann's constant; is wavenumber; is the Coulomb logarithm.

### FrequenciesEdit

**electron gyrofrequency**, the angular frequency of the circular motion of an electron in the plane perpendicular to the magnetic field:

**ion gyrofrequency**, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field:

**electron plasma frequency**, the frequency with which electrons oscillate (plasma oscillation):

**ion plasma frequency**:

**electron trapping rate**:

**ion trapping rate**:

**electron collision rate in completely ionized plasmas**:

**ion collision rate in completely ionized plasmas**:

### LengthsEdit

**electron thermal de Broglie wavelength**, approximate average de Broglie wavelength of electrons in a plasma:

**classical distance of closest approach**, the closest that two particles with the elementary charge come to each other if they approach head-on and each has a velocity typical of the temperature, ignoring quantum-mechanical effects:

**electron gyroradius**, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:

**ion gyroradius**, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field:

**plasma skin depth**(also called the electron inertial length), the depth in a plasma to which electromagnetic radiation can penetrate:

**Debye length**, the scale over which electric fields are screened out by a redistribution of the electrons:

**ion inertial length**, the scale at which ions decouple from electrons and the magnetic field becomes frozen into the electron fluid rather than the bulk plasma:

**mean free path**, the average distance between two subsequent collisions of the electron (ion) with plasma components:

- ,
- where is an average velocity of the electron (ion) and is the electron or ion
**collision rate**.

### VelocitiesEdit

**electron thermal velocity**, typical velocity of an electron in a Maxwell–Boltzmann distribution:

**ion thermal velocity**, typical velocity of an ion in a Maxwell–Boltzmann distribution:

**ion speed of sound**, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons:

- ,
- where is the adiabatic index

**Alfvén velocity**, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field:

### DimensionlessEdit

- number of particles in a Debye sphere

- Alfvén velocity/speed of light

- electron plasma/gyrofrequency ratio

- ion plasma/gyrofrequency ratio

- thermal/magnetic pressure ratio ("beta")

- magnetic/ion rest energy ratio

## CollisionalityEdit

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 is defined as^{[3]}^{[4]}

where denotes the electron-ion collision frequency, is the major radius of the plasma, is the inverse aspect-ratio, and is the safety factor. The plasma parameters and denote, respectively, the mass and temperature of the ions, and is the Boltzmann constant.