# Qualitative difference between bremsstrahlung and thermal bremsstrahlung

Hopefully this is an easy question. I hear the terms bremsstrahlung and thermal bremsstrahlung being used. However, I, incorrectly, thought that they were used interchangeably.

So, what is te qualitative difference between bremsstrahlung and thermal bremsstrahlung?

The difference is in population sizes. With (just) bremsstrahlung, you're talking about a single electron passing near an atom. This results in the typical expression of the radiated power, $$P_{br}\sim \gamma^4\left(\dot{\boldsymbol\beta}^2+\frac{\boldsymbol\beta\cdot\dot{\boldsymbol\beta}}{1-\beta^2}\right)$$ with $\gamma$ the Lorentz factor and $\boldsymbol\beta=\mathbf v/c$. This leads to $P\propto a^2$ (with $a=\dot\beta$), so the emission depends on the deceleration of the electron as it passes the atom.
With thermal bremsstrahlung, you're talking about a (large) population of electrons that follow the Maxwell-Boltzmann distribution (a thermal population since the electron distribution depends on $T$) and are undergoing the bremsstrahlung process. This leads to the power of $$P_{ff}\sim T^{1/2}$$ so the emission here depends on the temperature of the gas cloud.