The electrons that Diamond uses begin their journey at the Electron Gun. When metals get very hot they start to lose electrons through a process called thermionic emissio. Normally the electrons simply fall back so that no net current flows away from the metal surface.
When an electric field (a positively charged surface) is brought close to the surface that is emitting electrons, the electrons are attracted away and no longer return to the filament. The stronger the electric field (the more positive the anode is made) the faster the electrons are accelerated away.
The kinetic energy acquired by the electrons is equal to the electric work done by the field in ripping them away from near the surface of the filament.
So we can say:
Kinetic energy = electrical work done
½ mc2 = eV
where m is the electron mass
v is its velocity as it leaves the gun
e is the charge of the electron
V is the Voltage on the anode
Electrons are so light that very quickly they reach speeds close to the speed of light. Trying to accelerate electrons much further starts to bring in relativistic effects: the velocity doesn't increase much more but the electron mass starts to increase instead! Sounds quite complicated, but that's relativity for you!