*Bremsstrahlung* (German for "braking radiation") is a type of
electromagnetic radiation emitted by high-temperature
plasmas -- where atoms are ionized -- when free
electrons interact with the electric field surrounding
atomic nuclei. Bremsstrahlung is also known as
*free-free emission* because the electrons merely pass by the atomic
nuclei, and are not locked into the electron orbitals.

Whenever a free electron encounters a positively charged ion, it will
undergo an acceleration. As the electron moves past, the
dipole of the electron and ion changes with time, which
results in the emission of energy in the form of photons. The
frequency of the emitted photons will depend upon how fast the
electrons are moving, the charge on the ions, and the density of electrons
and ions in the plasma.

A common physical situation is the case of thermal bremsstrahlung, where the
electron velocities follow a
Maxwell-Boltzmann distribution.
In astronomy, we observe thermal bremsstrahlung from many sources containing
hot, optically thin plasmas like supernova remnants,
accretion disks,
and the hot gas within Abell clusters. Thermal bremsstrahlung is also
emitted in hot laboratory plasmas, and in the fireballs of nuclear
explosions.

The emission coefficient for thermal bremsstrahlung is given by

ε_{ν} = 6.8 × 10^{-38} Z^{2} n_{e} n_{i}
T^{-1/2} e^{-hν/kT} g (erg s^{-1} cm^{-3} Hz^{-1})

where ε is the emitted energy per unit volume per unit frequency
(ν), *Z* is the charge on the ions (for protons, it's just +1),*n*_{e,i} are the electron and ion densities, *T* is the
temperature, *h* is Planck's constant, *k* is Boltzmann's constant, and *g* is the Gaunt
factor, a quantum mechanical correction to the classical
scattering
equations used here. The Gaunt factor has a small dependence on the
photon frequency ν -- of order ν^{-1/2} -- which means that when
you put everything together, you find that the emission from a given volume
of plasma has a nearly flat spectrum (i.e. only a weak dependence on
the frequency). This distinguishes it from the
sharply-peaked blackbody radiation spectrum, and the synchrotron radiation
spectrum. So, when you measure the spectrum of a given source, you can use
the shape of the spectrum to determine whether you are observing black body
radiation, bremsstrahlung, synchrotron radiation, or perhaps something else
(a hot, Comptonized spectrum perhaps, or discrete
emission lines). This in turn can tell you about the physical
properties of what you're observing -- is it a thin gas or a dense gas, what is its temperature, what is it made of,
et cetera.

Note: bremsstrahlung is fundamentally different from
synchrotron radiation,
also sometimes seen in high-energy plasmas. Bremsstrahlung comes entirely
from the interactions of particles within a plasma, while synchrotron
radiation comes from the interaction of charges (mostly electrons) with
magnetic fields.

Source: mostly Radiative Processes in Astrophysics by Rybicki and Lightman.
A discussion of Gaunt factors can
be found in some quantum books -- R and L cite Novikov and Thorne's article in
*Black Holes*, Gordon and Breach (1973).