edit: sorry image links are down
In Cycles you have a “panoramic” button in the camera settings tab, alongside ortographic and perspective - which you are probably set to now. Play with the settings in fisheye or set it to equirectangular to capture a sphere. You won’t see a graphic difference in the viewport camera icon, but if you go into camera view (Numpad 0) you should be able to see what you are capturing. I think you should be able to control your end format by cropping the result vertically.
I am unsure whether this is what you are trying to do but you may probably want to remove the cyllindrical plane and just render a particle field on a black background. And if you are rendering from a video file you may even forget the plane and particle field completely and just composite the video frames.