8.7. Bremsstrahlung

class cherab.core.model.plasma.bremsstrahlung.Bremsstrahlung

Emitter that calculates bremsstrahlung emission from a plasma object.

The bremmstrahlung formula implemented is equation 5.3.40 from I. H. Hutchinson, ‘Principles of Plasma Diagnostics’, second edition, Cambridge University Press, 2002, ISBN: 9780511613630, https://doi.org/10.1017/CBO9780511613630

Note that in eq. 5.3.40, the emissivity \(j(\nu)\) is given in (W/m^3/sr/Hz) with respect to frequency, \(\nu\). Here, the emissivity \(\epsilon_{\mathrm{ff}}(\lambda)\) is given in (W/m^3/nm/sr) with respect to wavelength, \(\lambda = \frac{10^{9} c}{\nu}\), and taking into account that \(d\nu=-\frac{10^{9} c}{\lambda^2}d\lambda\).

\[\epsilon_{\mathrm{ff}}(\lambda) = \left( \frac{e^2}{4 \pi \varepsilon_0} \right)^3 \frac{32 \pi^2}{3 \sqrt{3} m_\mathrm{e}^2 c^3} \sqrt{\frac{2 m_\mathrm{e}^3}{\pi e T_\mathrm{e}}} \frac{10^{9} c}{4 \pi \lambda^2} n_\mathrm{e} \sum_i \left( n_\mathrm{i} g_\mathrm{ff} (Z_\mathrm{i}, T_\mathrm{e}, \lambda) Z_\mathrm{i}^2 \right) \mathrm{e}^{-\frac{10^9 hc}{e T_\mathrm{e} \lambda}}\,,\]

where \(T_\mathrm{e}\) is in eV and \(\lambda\) is in nm.

\(g_\mathrm{ff} (Z_\mathrm{i}, T_\mathrm{e}, \lambda)\) is the free-free Gaunt factor.

Variables:

  • plasma (Plasma) – The plasma to which this emission model is attached. Default is None.

  • atomic_data (AtomicData) – The atomic data provider for this model. Default is None.

  • gaunt_factor (FreeFreeGauntFactor) – Free-free Gaunt factor as a function of Z, Te and wavelength. If not provided, the atomic_data is used.

  • integrator (Integrator1D) – Integrator1D instance to integrate Bremsstrahlung radiation over the spectral bin. Default is GaussianQuadrature.

emission(point, direction, spectrum)

Calculate the emission for a point in the plasma in a specified direction.

Models implementing this method must add their spectral response to the supplied spectrum object. The spectrum units are spectral radiance per meter (W/m^3/str/nm).

If a model has a directional response, the model should pass through its own reference axis e.g. Thomsen scattering laser direction.

Parameters:

  • point – Point in plasma space.

  • direction – Direction in plasma space.

  • spectrum – Spectrum to which emission should be added.

Returns:

Updated Spectrum object.