Plasma parameter
Encyclopedia
The plasma parameter is a dimensionless number, 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
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
.
An alternative definition of this parameter is given by the average number of electrons in a plasma
contained within a Debye sphere (a sphere of radius the Debye length
).
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
Confusingly, some authors define the plasma parameter as :
.
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
of each species in an ideal plasma is that of an ideal gas
.
Coulomb collision
A Coulomb collision is a binary elastic collision between two charged particles interacting through their own Electric Field. As with any inverse-square law, the resulting trajectories of the colliding particles is a hyperbolic Keplerian orbit...
. In this case, the plasma parameter is given by:
where
- n is the number density of electrons,
- λD is the Debye lengthDebye lengthIn plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
.
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
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. The...
.
An alternative definition of this parameter is given by the average number of electrons in a plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
contained within a Debye sphere (a sphere of radius the Debye length
Debye length
In plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
).
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 asSince 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 bywhere
- ε0 is the permittivity of free space,
- k is Boltzmann's constant,
- qe is the electron charge,
- Teis the electron temperature.
Confusingly, some authors define the plasma parameter as :
.The ideal plasma approximation
One of the criteria which determine whether a collection of charged particles can rigorously be termed an ideal plasma 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
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
of each species in an ideal plasma is that of an ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
.
Plasma properties and Λ
The magnitude of Λ can be summarised below :| Description | Plasma parameter magnitude | |
| Λ<<1 | Λ>>1 | |
| Coupling | Strongly coupled plasma | Weakly coupled plasma |
| Debye sphere | Sparsely populated | Densely populated |
| Electrostatic influence | Almost continuously | Occasional |
| Typical characteristic | Cold and dense | Hot and diffuse |
| Examples | Solid-density laser ablation plasmas Very "cold" "high pressure" arc discharge Inertial fusion experiments White dwarfs / neutron stars atmospheres | Ionospheric physics Magnetic fusion devices Space plasma physics Plasma ball |