# Thomas_Fermi_length¶

plasmapy.formulary.Thomas_Fermi_length(n_e: Unit("1 / m3")) -> Unit("m")

Calculate the exponential scale length for charge screening for cold and dense plasmas.

Parameters: n_e (Quantity) – Electron number density. lambda_TF – The Thomas-Fermi screening length in meters. Quantity TypeError – If argument is not a Quantity. UnitConversionError – If argument is in incorrect units. ValueError – If argument contains invalid values. ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed.

Notes

The Thomas-Fermi screening length is the exponential scale length for charge screening and is given by

$\lambda_TF = \sqrt{\frac{2 \epsilon_0 E_F}{3 n_e e^2}}$

for an electron degenerate gas.

This quantity is often used in place of the Debye length for analysis of cold, dense plasmas (e.g. warm dense matter, condensed matter).

The electrical potential will drop by a factor of 1/e every Thomas-Fermi screening length.

Plasmas will generally be quasineutral on length scales significantly larger than the Thomas-Fermi screening length.

Example

>>> from astropy import units as u
>>> Thomas_Fermi_length(1e23 * u.cm**-3)
<Quantity 5.37991409e-11 m>