I need to derive some equations that theoretically describe my experiment. The problem is, no one has done this before using the setup I am using. Ane believe me, it is hard to derive something when you don't have anyone else to help you. However there is this classic paper from Rosenbluth and Liu whivh describe a similar technique, for a slightly different case though (they use lasers accelerate electrons, while I am using another bunch of electrons). I need to go back there and see what they are doing, because th emodern techniques do not work for my case. It is not an easy paper to understand, but I have to try. Yesterday Erdem (labmate) helped me decifer an equation there which I didn't know how they derived it, and as it turned out it was fairly simple to do so (just assume time harmonic regime for the laser and then integrate Newton's second law).
The heart of their work is this: we have a cold plasma (i.e. electrons that have no thermal velocity, they just stand still). Then you put a laser in there. The electric field of the laser will push the electrons off axis, giving them some velocity. Then, you put a second laser in. The magnetic field of the second laser will couple with this velocity the electrons have acquired and there will be a force on them (v x B). This force will push the electrons forward and accelerate them.
Now I just have to work out the equations. Let me see...
