# quantum_theta¶

plasmapy.formulary.dimensionless.quantum_theta(T: Unit(‘K’), n_e: Unit(‘1 / m3’))

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

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.