How Does Inverse Bremsstralung Affect Photon Absorption?

There are lots of diagrams showing bremsstralung as a deflection of an electron by a nucleus but none of inverse bremsstralung.
Does the inverse process I.e. photon absorption only depend on the direction of the deflection by the nucleus? If not ,what determines wether
the electron will absorb or emit a photon. If you say the electron has to be moving faster after in the inverse process,exactly how does this occur.

I don't believe you question is well formed. Note that the emission or absorption of a single photon by a charged particle is just a single term in one choice of a perturbative expansion of a total physical interaction. Take a classic (not classical [edit]) electron-electron elastic scattering in the center of mass picture.

Here comes Electron A in from the left and Electron B in from the right. Then later there goes A at some angle and B at the opposite angle. Total kinetic energy unchanged, total momentum still 0. But the momentum of each electron changed due to the electromagnetic field and therefore there has been an exchange of photons. How many and which way? That's indeterminate and complementary to the observed behavior presupposed here. There was some superposition of 0, 1, 2,... photons exchanged subject only to the constraint that the later observed deflection yielded the given momentum exchange on the electrons.

Now when you consider such a collision classically you also know that the mutual acceleration of the two charged electrons will induce a classical electromagnetic wave. To account quantum mechanically for this you must treat the formerly elastic collision of two bodies as a many body inelastic collision. This correction, a "collision" of the two electrons plus the quantum e-m field is the Bremsstrahlung radiation. There will be a net emission of a superposition of 0 or 1 or 2 or .... photons of various frequencies.

How much on average is calculated via field theory using perturbative expansions in which the picture drawn of one electron emitting a photon is just a single term in the sum-over-histories calculation.

As to "inverse Brem.." in the presence of a thermal background photon gas there is always the probability that two scattering electrons come out with more energy then they had prior to scattering but that probability is very low. Entropy increase dictates that the net effect is a thermalization of the energy equipartitioning between electron motion and the thermal photonic environment.

maybe a better starting question is under what stellar conditions would we expect inverse bremsstralung to be a significant factor? Has this been worked out In terms of electron density, intensity of radiation field ect?

After a quick search, I now realize what you mean by "inverse bremsstralung". As I mentioned, the thermodynamics dictates that the charged particle will slow via bremsstralung radiation. However the reverse is also true if light of low entropy e.g. a laser beam interacts with charged particles.

https://www.researchgate.net/post/What_is_the_inverse_bremsstrahlung

In the stellar situation I don't think its meaningful to speak of phenomena in terms of this, rather you have a thermalized composite gas of charged fermions and photon gas. I suppose calling the mode of interaction between the plasma and photon gas respectively brem' and inverse brem' radiation may be conceptually useful; this in contrast to e.g. absorption-reemission processes in atoms and other resonant interactions.

Isn't "inverse bremsstrahlung" simply slang for absorption of a photon by charged particles?

Yes, it absorption. There is a nice chapter in “Interpreting astronomical spectra” by D. Emerson on micro processes contributing to spectra, so it is relevant. I did find a good mathematical discussion of free free absorption which is the same as inverse bremsstralung. This led me to Kramers Opacity law, which gave me the answer. However I have yet to fully understand how an electron whose trajectory is bent near an ion can absorb a photon.

Getterdog said:

I have yet to fully understand how an electron whose trajectory is bent near an ion can absorb a photon.

Classically, such an electron can add energy to an electromagnetic wave, or absorb energy from it, depending on the phase of the wave. Quantum mechanically, you would call it stimulated emission vs. absorption. At frequencies ## h \nu \ll kT ## both processes occur with almost equal probability, and by a factor ## 1 - \exp(- h\nu/kT) ## the effective (observable) absorption coefficient is smaller than what you would compute from the number of microscopic absorption processes alone.