quantum_theta

plasmapy.formulary.quantum.quantum_theta(T: Unit('K'), n_e: Unit('1 / m3'))[source]

Compare Fermi energy to thermal kinetic energy to check if quantum effects are important.

The quantum theta (\(θ\)) of a plasma is defined by

\[θ = \frac{E_T}{E_F}\]

where \(E_T\) is the thermal energy of the plasma and \(E_F\) is the Fermi energy of the plasma.

Parameters:

T (Quantity) – The temperature of the plasma.
n_e (Quantity) – The electron number density of the plasma.

Examples

>>> import astropy.units as u
>>> quantum_theta(1*u.eV, 1e20*u.m**-3)
<Quantity 127290.619...>
>>> quantum_theta(1*u.eV, 1e16*u.m**-3)
<Quantity 59083071...>
>>> quantum_theta(1*u.eV, 1e26*u.m**-3)
<Quantity 12.72906...>
>>> quantum_theta(1*u.K, 1e26*u.m**-3)
<Quantity 0.00109...>

Returns:: theta
Return type:: Quantity

Notes

The thermal energy of the plasma (\(E_T\)) is defined by

\[E_T = k_B T\]

where \(k_B\) is the Boltzmann constant and \(T\) is the temperature of the plasma.