Energy conservation and particle acceleration

[Axe199]

As i am a physics amateur and most of what i learned is through videos, i sometimes get confused about energy conservation, my question concerns particle acceleration in CRT for example, we create a potential difference ( which requires energy) between the anode and the cathode, then the electrons are ejected at the cathode and accelerates towards the anode. Now naturally ( according to my narrow knowledge) the kinetic energy gained by the electrons is equal to the energy used in the charge separation to create the potential difference, because the electrons hit the anode they decrease the charge separation, but in the case of a CRT, some of them miss the anode to hit the screen or whatever, so where does this energy come from? the part i don't understand is how it gained energy and it didnt hit the anode to decrease the potential to compensate for the energy it gained.

 

[Orodruin]

You do not need to hit anything to change potential energy. It is sufficient to travel along a path which is not perpendicular to the electric field.

 

[Axe199]

You do not need to hit anything to change potential energy. It is sufficient to travel along a path which is not perpendicular to the electric field.

Can you explain more please