chemical_potential_interp

plasmapy.physics.quantum.chemical_potential_interp(n_e, T)

Fitting formula for interpolating chemical potential between classical and quantum regimes.

See [1], [2] for more information.

Parameters:

• n_e (Quantity) – Electron number density.
• T (Quantity) – Temperature in units of temperature or energy.

Returns:

beta_mu – The dimensionless chemical potential, which is a ratio of chemical potential energy to thermal kinetic energy.

Return type:

Quantity

Raises:

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

Warning

~astropy.units.UnitsWarning

If units are not provided, SI units are assumed.

Notes

The ideal chemical potential is given by [1]:

\[\frac{\mu}{k_B T_e} = - \frac{3}{2} \ln \Theta + \ln \frac{4}{3 \sqrt{\pi}} + \frac{A \Theta^{-b - 1} + B \Theta^{-(b + 1) / 2}}{1 + A \Theta^{-b}}\]

where

\[\Theta = \frac{k_B T_e}{E_F}\]

is the degeneracy parameter, comparing the thermal energy to the Fermi energy, and the coefficients for the fitting formula are A=0.25945, B=0.0072, b=0.858.

References

[1]	(1, 2) Ichimaru, Statistical Plasma Physics Addison-Wesley, Reading, MA, 1991.

[2]	Gregori, G., et al. “Theoretical model of x-ray scattering as a dense matter probe.” Physical Review E 67.2 (2003): 026412.

Example

>>> from astropy import units as u
>>> chemical_potential_interp(n_e=1e23*u.cm**-3, T=11000*u.K)
<Quantity 8.17649673>