thermal_bremsstrahlung

plasmapy.formulary.radiation.thermal_bremsstrahlung(frequencies: Unit('Hz'), n_e: Unit('1 / m3'), T_e: Unit('K'), n_i: Unit('1 / m3') = None, ion: = 'p+', kmax: Unit('m') = None) [source]

Calculate the bremsstrahlung emission spectrum for a Maxwellian plasma in the Rayleigh-Jeans limit $$ℏ ω ≪ k_B T_e$$.

$\frac{dP}{dω} = \frac{8 \sqrt{2}}{3\sqrt{π}} \bigg ( \frac{e^2}{4 π ε_0} \bigg )^3 \bigg ( m_e c^2 \bigg )^{-\frac{3}{2}} \bigg ( 1 - \frac{ω_{pe}^2}{ω^2} \bigg )^\frac{1}{2} \frac{Z_i^2 n_i n_e}{\sqrt(k_B T_e)} E_1(y)$

where $$E_1$$ is the exponential integral

$E_1 (y) = - \int_{-y}^∞ \frac{e^{-t}}{t}dt$

and $$y$$ is the dimensionless argument

$y = \frac{1}{2} \frac{ω^2 m_e}{k_{max}^2 k_B T_e}$

where $$k_{max}$$ is a maximum wavenumber approximated here as $$k_{max} = 1/λ_B$$ where $$λ_B$$ is the electron de Broglie wavelength.

Parameters:
Returns:

spectrum – Computed bremsstrahlung spectrum over the frequencies provided.

Return type:

Quantity

Notes

For details, see Bekefi [1966].