BrandonBerchtold said:
I specifically split my questions into different threads because that seemed more useful to other readers than to post numerous different questions under one unrelated heading. I'd be happy to post further questions in this thread if that is preferred?
I also specifically omitted any unnecessary context as I wanted to be as concise as possi le with what I was asking. I can try to add more context to future questions.
Also out of curiosity, what additional context are you looking for in this question? I am designing a c++ program to simulate an accelerator based deuterium-deuterium fusion reactor design (I can elaborate on the design if you'd like) I came across in some readings. The questions I am asking are mainly to get an idea of how to implement these various components (magnetic lens, parallel plate accelerator, current transformer, etc.) into my program. I want to incorporate a current transformer to accelerate ionized deuterium into the device but I am unsure how to derive the equations that govern the acceleration. How could I determine the acceleration of the particles and the total energy they acquire from the transformer. I would likely be using a numerical integration technique as opposed to a closed form equation to determine the acceleration force in my simulation. Would the acceleration be governed by Biot Savart Law?
(Also if you want me to contain my questions to a single post and add more context, please just ask instead of posting passive aggressive comments. I'm not posting on here to be annoying, I'm here because I want to learn.)
I have a feeling that you are missing A LOT of the physics involved here.
First of all, what you showed in your figure is not a "transformer". You will not induced any current in the coil simply by having a steady flow of charge. This is basic intro General Physics E&M, i.e. Lenz's Law. It was why you were told that it doesn't work with a direct-current source, which is essentially what you have.
What you may have read about "current transformer" may be a misunderstanding (I have used many current transformers in my former line of work in accelerator science). An Integrated Current Transformer (ICT) is a common device used in accelerators to measure the amount of charge per bunch inside the vacuum beam pipe. This might be what you may have come across.
HOWEVER, the "transformer" here is inside the device itself. It does not include the beam, the way you have it written. AND, it measures PULSED or bunched charges, not continuous stream.
Finally, ICT devices impose little to no effect on the charge bunches that passed through it. It shouldn't, because it is a diagnostic device and it should disrupt the charge beam as little as possible. Thus, your intention of using such a "transformer" to accelerate the beam itself is puzzling. In fact, if anything, such a device will suck energy out of a beam (example: wakefields), since the beam transferred some of its energy to generate current in the coils.
Not only that, what is being generated by the coils are axial magnetic fields. No increase in kinetic energy of charge particles can be achieved with magnetic fields (Lorentz force).
So there is a lot of issues with basic physics here that makes your scheme not only difficult to understand, but puzzling.
Zz.
