# I Modified Cycloid motion of charged particle

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1. Mar 29, 2017

### peasqueeze

I need a charged particle trajectory in crossed E and B that is a cycloid in the x-y plane. This part is simple enough, but I want the trajectory to be parabolic in the x-z plane. The images will help explain what I need.

The left image shows the shape I want to achieve, and the right image shows my current attempt. The fields producing the image on the right are...
$$\vec{B} = B_{0}\hat{z}$$
$$\vec{E}=\gamma E_{y}\hat{x}+E_{y}\hat{y}+E_{z}\hat{z} ; E_{z}<<1$$

So- how can I modify the above electric and magnetic fields to produce this 'parabolic cycloid'
Note: I know the image on the right doesn't look like a cycloid exactly, but, for my model, I needed really tight loops. So don't get hung up on that detail.

2. Apr 3, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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