Heat generated by particles passing through material

[Fr34k]

Lets say you have a stream/beam of electrons, you know the current (I), time (t) and all the dimensional characteristics of the beam.
You can now calculate the amount of electrons that pass some material in the amount of time.
[itex]N=\frac{I t}{e_0}[/itex], where e₀ is elementary charge.
Now each electron deposits some amount of energy in the material,calculated with Bethe-Bloch (dE/dx) multiply that by the distance traveled in the material and you get all the energy an electron loses by passing through the material.
Now I have the problem of simulating that heat generation (q) term.
[itex]q=\frac{N E_0}{V t}[/itex], all the energy deposited in a volume in the amount of time that electrons were passing. If you put all this together, you get something like:
[itex]q=\frac{I dE/dx}{e_0 S}[/itex], where S is the area of the beam.
Now what I can't figure out is, why this is not time dependent? It should have been. Where are the flaws in my understanding?
Thanks for suggestions/comments.

 

[Aaron Bex]

It sounds like you have a good understanding of the physics behind calculating the energy deposited in a material. It is possible that the flaw in your understanding may be related to the time-dependence of the energy lost by the electrons. Since the energy lost by an electron depends on both the number of electrons and the distance they travel, it would make sense that the energy loss would be time-dependent. Perhaps you can take a look at the Bethe-Bloch equation to see how the energy loss might be affected by time.