Stopping power vs linear energy transfer (LET)

Question

I wonder about the difference between stopping power and linear energy transfer. I would like to refer to http://radonc.wikidot.com/stopping-power-v-linear-energy-transfer-let where it is quite exactly given:

Stopping Power is closely related to LET except that LET does not include radiative losses of energy (which is lost to the medium and so not absorbed!)

but I don't get it. What exactly are radiative losses (and why are they not absorbed by medium?)? Furthermore, both quantities are given as $ dE/dx $ respectively $ dE/dl $ while both, $ dx $ and $ dl $, represent a distance. So, mathematically spoken, there is no difference, or?

Answer 1

"STOPPING POWER refers to the inelastic energy losses by an electron moving through a medium ... which represents the kinetic energy loss by the electron per unit path length"

...

"LINEAR ENERGY TRANSFER of charged particles in a medium is the quotient dE/dl, where dE is the average energy locally imparted to the medium"

So the linear energy transfer is the amount of energy (per length) the medium receives from the particle, while the stopping power is the amount of energy (per length) the particle loses. The difference between these two is the amount of energy (per length) that is lost to the rest of the environment. These are called radiative losses.

Radiative losses occur when the electron is accelerated-- when this happens, it releases some energy into the electromagnetic field in the form of a wave. It would happen even in the absence of a medium if the electron were accelerated in some other fashion (say, if it's going around a ring in a particle accelerator). The energy lost (per time) from a uniformly accelerating charge to the electromagnetic field is given by the Larmor formula, $$P = \frac{q^2 a^2}{6 \pi \epsilon_0 c^3}$$