vsnever
commented
1 year ago Hi, @skuba31. I totally agree. This factor, 0.95 • 10-19, should be replaced with an actual expression for accuracy and clarity, and included as a constant just like the EXP_FACTOR. The reference to Beurskens is no longer appropriate because we have already replaced their fit for the Gaunt factor with the much more general precalculated tables from Carson expanded by de Avillez & Breitschwerdt. The reference to Hutchinson is more appropriate. Can you make a PR?
skuba31
Currently, the reference for the bremsstrahlung formula is the Beurskens ITER LIDAR article, which uses an unexplained constant and is not in SI units. Looking into references I was able to find an article by Kadota, where the formula is also presented. However, without derivation or explanation and it is written in some form of CGS unit system as the vacuum permittivity is not present. This is the oldest English written reference. It is pointing to Kontinuierliche Spektren (in German), where I hit the limits of my language skills. My colleague recommended me Hutchinson's Principles of Plasma Diagnostics where the formula is derived and the constants are in SI units. Some information about the gaunt factor is also present. The downside is that it is written with respect to frequency. But this can be solved by substitution factor.
$$ P{\mathrm{ff}} \approx \int{f\mathrm{min}}^{f\mathrm{max}} j\mathrm{ff} (f) \mathrm{d}f = \int{\lambda\mathrm{max}}^{\lambda\mathrm{min}} - \frac{c}{\lambda^2} j\mathrm{ff}\left(\frac{c}{\lambda}\right) \mathrm{d}\lambda = \int{\lambda\mathrm{min}}^{\lambda\mathrm{max}} \frac{c}{\lambda^2} j\mathrm{ff}\left(\frac{c}{\lambda}\right) \mathrm{d}\lambda $$
I did simple test and the bremsstrahlung based on Hutchinson was 1.008937... times greater than that computed using current formula. This seems to be caused by the limited accuracy of the constant in Beurskens article $0.95\cdot10^{−19}$.
As the difference is less than a percent, I would propose to at least include Hutchinson as a reference to the documentation for better clarity and optionally implement the equation with pre_factor based on fundamental constants or change it to be based on Hutchinson's book.