Debye_number

plasmapy.formulary.parameters.Debye_number(T_e: Unit("K"), n_e: Unit("1 / m3")) -> Unit(dimensionless)

Return the number of electrons within a sphere with a radius of the Debye length.

Aliases: nD_

Parameters:

• T_e (Quantity) – Electron temperature
• n_e (Quantity) – Electron number density

Raises:

• TypeError – If either argument is not a Quantity
• astropy.units.UnitConversionError – If either argument is in incorrect units
• ValueError – If either argument contains invalid values

Warns:

~astropy.units.UnitsWarning – If units are not provided, SI units are assumed

Returns:

N_D – Number of electrons within a sphere with a radius of the Debye length

Return type:

Quantity

Notes

The Debye number is the number of electrons contained within a sphere with a radius of a Debye length and is given by

\[N_D = \frac{4\pi}{3}n_e\lambda_D^3\]

The Debye number is also known as the plasma parameter.

Collective behavior requires a Debye number significantly larger than one.

See also

Debye_length()

Example

>>> from astropy import units as u
>>> Debye_number(5e6*u.K, 5e9*u.cm**-3)
<Quantity 2.17658...e+08>