The plasma parameter is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
, denoted by capital Lambda, Λ. The plasma parameter is usually interpreted to be the argument of the Coulomb logarithm, which is the ratio of the maximum impact parameter to the classical distance of closest approach in
Coulomb scattering. In this case, the plasma parameter is given by:
where
* ''n'' is the
number density
The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
of electrons,
* λ
D is the
Debye length
In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
.
This expression is typically valid for a plasma in which ion thermal velocities are much less than electron thermal velocities. A detailed discussion of the Coulomb logarithm is available in the ''NRL Plasma Formulary'', pages 34–35.
Note that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general: see
plasma parameters
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 charg ...
.
An alternative definition of this parameter is given by the average number of electrons in a
plasma
Plasma or plasm may refer to:
Science
* Plasma (physics), one of the four fundamental states of matter
* Plasma (mineral), a green translucent silica mineral
* Quark–gluon plasma, a state of matter in quantum chromodynamics
Biology
* Blood pla ...
contained within a
Debye sphere
In plasma (physics), plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a Solution (chemistry), solution and how far its electrostatic effect persists. Wi ...
(a sphere of radius the
Debye length
In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
). This definition of the plasma parameter is more frequently (and appropriately) called the Debye number, and is denoted
. In this context, the plasma parameter is defined as
Since these two definitions differ only by a factor of three, they are frequently used interchangeably.
Often the factor of
is dropped. When the Debye length is given by
, the plasma parameter is given by
where
* ε
0 is the
permittivity of free space
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...
,
* ''k'' is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
,
* ''q''
e is the electron charge,
* ''T''
e is the electron temperature.
Confusingly, some authors define the plasma parameter as:
Coupling parameter
A closely related parameter is the plasma coupling
, defined as a ratio of the Coulomb energy to the thermal one:
The Coulomb energy (per particle) is
where for the typical inter-particle distance
usually is taken the
Wigner-Seitz radius. Therefore,
Clearly, up to a numeric factor of the order of unity,
In general, for multicomponent plasmas one defines the coupling parameter for each species ''s'' separately:
Here, ''s'' stands for either electrons or (a type of) ions.
The ideal plasma approximation
One of the criteria which determine whether a collection of charged particles can rigorously be termed an
is that Λ ≫ 1. When this is the case, collective electrostatic interactions dominate over binary collisions, and the plasma particles can be treated as if they only interact with a smooth background field, rather than through pairwise interactions (collisions). The
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
of each species in an ideal plasma is that of an
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
.
Plasma properties and Λ
Depending on the magnitude of Λ, plasma properties can be characterized as following:
[Se]
The plasma parameter
lecture notes from Richard Fitzpatrick
References
{{reflist
External links
NRL Plasma Formulary 2007 ed.
Plasma physics