I have a very specific question which is troubling me. I use a heated disk cathode as an electron emitter. I know that the energy distribution of the electrons emitting from the cathode is
$g(E)=\frac{E}{(kT)^2}e^{-E/kT}$.
The cathode is positioned in the magnetic field so that the cathode normal is parallel to the magnetic field, let's say z-direction. Electrons are thus moving forward in the z-direction and circulate in xy plane. I have a retaining field analyser which is measuring the energy distribution of electrons only in z-direction. I would like to calculate an analytical expression for such distribution but I have some problems so I'm asking for some tips.
